Practical Applied - 
 
 ELECTRICITY 
 
 A BOOK IN PLAIN ENGLISH 
 FOR THE PRACTICAL MAN. 
 THEORY, PRACTICAL AP- 
 PLICATIONS AND EXAMPLES 
 
 BY 
 DAVID PENN MORETON, B.S., E.E. 
 
 ASSOCIATE PROFESSOR OF ELECTRICAL ENGINEERING AT ARMOUR 
 INSTITUTE OF TECHNOLOGY, ASSOCIATE MEMBER OF THE AMERI- 
 CAN INSTITUTE OF ELECTRICAL ENGINEERS, MEMBER 
 OF THE SOCIETY FOR THE PROMOTION OF 
 ENGINEERING EDUCATION, ETC. 
 
 ILLUSTRATED 
 
 The Reilly & Britton Co. 
 Chicago 
 
COPYRIGHT, 1911, 1913, 1916 
 
 By DAVID PENN MORETON 
 
 CHICAGO 
 
PREFACE TO THE THIRD EDITION 
 
 In bringing out the third edition of Practical Applied 
 Electricity, the body of the book, with the exception of a 
 few minor changes, remains the same as in the second 
 edition. Several pages of material, giving a summary of the 
 more common direct- and alternating-current relations, have 
 been added at the back of the book. 
 
 This book is intended primarily for those persons who are 
 desirous of obtaining a practical knowledge of the subject of 
 Electricity, but are unable to take a complete course in Elec- 
 trical Engineering. It is the opinion of the author that such 
 persons should have a thorough understanding of the funda- 
 mental principles of the subject, in order that they may easily 
 understand the applications in practice. Numerous examples 
 are solved throughout the book, which serve to illustrate the 
 practical application of certain laws and principles and give 
 the reader an opportunity to more readily grasp their true 
 significance. 
 
 The text is based, to a certain extent, upon a series of lec- 
 .tures given in the evening classes in the Department of Elec- 
 trical Engineering at Armour Institute of Technology. The 
 arrangement is not the one usually followed, and to some it 
 may not appear to be logical; but it is one the author has 
 found very satisfactory. 
 
 Although the book was not originally intended to be used 
 as a text-book, it is, however, especially adapted for use in the 
 practical courses given in the various High and Manual Train- 
 ing Schools, and at the same time gives a substantial ground- 
 work for the more advanced college and university courses. 
 
 The author wishes to express his thanks to the various man- 
 ufacturing companies who have been very kind in supplying 
 material and cuts, and to Professor E. H. Freeman, head of 
 the Department of Electrical Engineering of Armour Insti- 
 tute of Technology, for a number of valuable suggestions. 
 
 DAVID PENN MORETON 
 ARMOUR INSTITUTE OF TECHNOLOGY 
 
 389482 
 
DEDICATED 
 
 TO MY 
 
 FATHER AND MOTHER 
 CHARLES BROWN MORETON 
 
 AND 
 
 SALLIE PENN jMORETON 
 
 IN 
 
 APPRECIATION OF THEIR UNTIRING 
 EFFORTS WHILE I WAS RE- 
 CEIVING MY EARLY 
 EDUCATION 
 
CONTENTS 
 
 I ELECTRICAL CIRCUIT AND ELECTRICAL 
 UNITS 
 
 II CALCULATION OF RESISTANCE 
 
 III SERIES AND DIVIDED CIRCUITS, MEASURE- 
 
 MENT OF RESISTANCE 
 
 IV PRIMARY BATTERIES .... 
 V MAGNETISM ...... 
 
 VI ELECTROMAGNETISM .... 
 
 VII ELECTROMAGNETIC INDUCTION, FUNDA- 
 MENTAL THEORY OF THE DYNAMO 
 
 VIII ELECTRICAL INSTRUMENTS AND EFFECTS 
 OF A CURRENT .... 
 
 IX DIRECT- CURRENT GENERATOR 
 X DIRECT- CURRENT MOTORS 
 
 XI ARMATURES FOR DIRECT-CURRENT DYNA- 
 MOS ...... 
 
 XII STORAGE BATTERIES, THEIR APPLICA- 
 TIONS AND MANAGEMENT 
 
 XIII DISTRIBUTION AND OPERATION 
 
 XIV DISEASES OF DIRECT-CURRENT DYNA- 
 
 MOS 
 
 XV ELECTRIC LIGHTING .... 
 
 XVI ELECTRIC WIRING .... 
 
 XVII ALTERNATING-CURRENT CIRCUIT . 
 
 XVIII ALTERNATING-CURRENT MACHINERY 
 
 XIX RESUSCITATION ..... 
 
 XX LOGARITHMS AND REFERENCE TABLES 
 
 34 
 
 58 
 77 
 86 
 
 102 
 
 121 
 166 
 193 
 
 219 
 
 237 
 257 
 
 280 
 294 
 316 
 332 
 358 
 386 
 390 
 
PRACTICAL APPLIED ELECTRICITY 
 
 CHAPTER I 
 
 THE ELECTRICAL CIRCUIT AND ELECTRICAL UNITS 
 
 1. Electricity. There are certain phenomena of nature 
 that are taking place about us every day which we call elec- 
 trical, and to that which produces these phenomena we give 
 the name electricity. The exact nature of electricity is not 
 known, yet the laws governing its action, under various con- 
 ditions, are well understood, just as the laws of gravitation 
 are known, although we cannot define the constitution of 
 gravity. Electricity is neither a gas nor a liquid; its be- 
 havior sometimes is similar to that of a fluid so that it is 
 said to flow through a wire. This expression of flowing does 
 not really mean there is an actual movement in the wire, 
 similar to the flow of water in a pipe, when it possesses elec- 
 trical properties,, but is simply a convenient expression for 
 the phenomena involved. According to the modern electron 
 theory of electricity, there is a movement of some kind tak- 
 ing place in the circuit, but the real nature of this move- 
 ment is not as yet very well understood. A great many electrical 
 problems can be easily understood by comparing them to a 
 similar hydraulic problem, where the relation of the various 
 quantities and the results are apparent under given condi- 
 tions, and on account of the similarity of the two, the hy- 
 draulic analogy will often be used to illustrate what actu- 
 ally takes place in the electrical circuit. 
 
 2. Electrical Circuit. The electrical circuit is the path in 
 which the electricity moves. The properties of electrical cir- 
 cuits and the electrical quantities associated with them make 
 an appropriate beginning for the study of the subject of 
 electrical engineering, for electrical energy is in almost all 
 
 1 
 
2 : ' *." T-RACT.^CAE APPLIED ELECTRICITY 
 
 practical applications utilized in circuits. These circuits are 
 of various forms and extent, and are made for many different 
 purposes, but all possess to a greater or less extent the same 
 properties and involve the same electrical quantities. Sup- 
 pose, for example, a door bell that is operated from two 
 
 Battery 
 
 Push Button 
 
 Bell 
 
 Fig. 1 
 
 or three dry cells, as shown in Fig. 1. This combination 
 forms an electrical circuit, typical of all electrical cir- 
 cuits. It contains a source of electrical energy (the bat- 
 tery), an energy transforming device (the bell), and the 
 necessary connecting materials (wire and push button). It 
 is closed upon itself and like the circumference of a circle 
 has neither beginning nor end. (A table of symbols com- 
 monly used in representing the different pieces of electrical 
 apparatus is given in Chapter 20.) 
 
 3. Hydraulic Analogy of the Electrical Circuit. Before con- 
 sidering the relation of the various electrical quantities asso- 
 ciated with the electric circuit it would, no doubt, be best 
 to make a brief study of a simple hydraulic problem, simi- 
 lar to the electrical circuit, and the relation of the various 
 quantities involved. It must be clearly understood that the 
 similarity between the water and the electrical circuits is in 
 regard to action only, and does not in any way imply an 
 identity between electricity and water. A simple hydraulic 
 circuit is shown in Fig. 2, where (P) is a pump that sup- 
 plies water, under a constant pressure, to the pipe (T). The 
 water is conducted through the pipe (T) to the tank (K), 
 the amount of water flowing through the pipe being regu- 
 lated by the valve (V). The pipe (T) is composed of a 
 number of different pieces of pipe, differing in area of 
 
THE ELECTEICAL CIRCUIT 
 
 3 
 
 cross-section, length, and condition of their inner surface, 
 some being rough and some smooth. Pressure gauges (Gj, 
 G 2 , etc.) are placed along the pipes at certain intervals, as 
 shown in the figure, to indicate the pressure in the pipe at 
 different points. Assume, first, that the valve (V) is closed; 
 no water will then be flowing through the pipe and all of 
 the various pressure gauges will indicate the same pressure 
 in the pipe. Assume, as a second condition, that the valve (V) 
 is partly opened; there will be a flow of water in the pipe, 
 and the pressure gauges will indicate a different pressure, 
 their indications decreasing as you pass along the pipe, 
 starting from the end attached to the pump. Opening the 
 
 K- 
 
 
 Fig. 2 
 
 valve still more will increase the flow of water and also 
 the difference in indications of the various gauges. If the 
 gauge (G e ) at the end of the pipe indicates zero pressure, 
 it is apparent that the total pressure supplied by the pump 
 has all been used in forcing the water through the pipe. If, 
 on the other hand, the last gauge indicates a certain pres- 
 sure, then the total pressure supplied by the pump has not all 
 been used and there still remains a certain amount, neg- 
 lecting that pressure required to force the water through 
 the valve (V), that could be used in driving a water wheel, 
 placed in such a position that the water could strike against 
 the buckets on the wheel and cause it to rotate. The differ- 
 
4 PRACTICAL APPLIED ELECTRICITY 
 
 ence in pressure indicated by any two gauges is a meas- 
 ure of the pressure required to cause the water to flow be- 
 tween the two points where the gauges are connected to the 
 pipe. If it were possible to have a pipe that would offer no 
 opposition to the passage of the water through it, there would 
 be no difference in the indications of the various gauges and 
 the water would flow from the end of the pipe under the 
 same pressure as that produced by the pump. Anything that 
 increases the opposition to the flow of the water will increase 
 the value of the pressure required to cause a certain quan- 
 tity to pass through the section of pipe, between the pres- 
 sure gauges, whose indications are being noted. Qr, if the 
 same pressure is maintained over a given section and its 
 opposition to the passage of water is increased, the quantity 
 passing in a given time will be decreased; similarly the 
 quantity will be increased if the opposition is decreased. 
 As an example, suppose a water motor is connected in the 
 pipe (T) and it is perfectly free to turn, there will then be a 
 very small pressure required to cause a certain quantity to 
 flow through the motor in a given time. If, however, the 
 water motor is loaded, it will offer a much greater resist- 
 ance to the passage of water through it; and, if the pres- 
 sure remains constant, the quantity passing in a given time 
 will be decreased. The rate of flow can be maintained 
 constant when the opposition increases by increasing the 
 pressure. The total pressure supplied by the pump will be 
 distributed over the various sections of the pipe in propor- 
 tion td their opposition. The opposition offered by the pipe 
 can be called its resistance and it will depend upon the 
 area, length, nature of the inner surface, and any obstruc- 
 tion that might be in the pipe, such as sand, gravel, or sieves. 
 The quantity of water passing a given point in a pipe in a 
 unit of time, usually one second, is called the current. These 
 three quantities, pressure, current, and resistance, are related 
 to each other in a very simple way, as can be seen from 
 the above problem, and this relation, expressed in the form 
 of an equation is: 
 
 Pressure 
 
 Current = (1) 
 
 Resistance 
 
THE ELECTRICAL CIRCUIT 5 
 
 It must be remembered that this equation does not. hold 
 in its strictest sense for the hydraulic problem, but will 
 serve to illustrate the relation between the electrical quan- 
 tities that are to be discussed in one of the following sections. 
 
 4. Electrical Circuit Compared with Hydraulic Circuit. 
 In the electrical circuit, as indicated in Fig. 3, there is a 
 source of electrical pressure, the battery, that corresponds 
 to the pump in the hydraulic analogy. The wire by means 
 of which the electricity is conducted corresponds in the 
 hydraulic analogy to the pipe through which the water flows, 
 
 D 
 
 1 l^J oH 75-^ 
 
 
 B 
 
 
 I 
 
 Fig. 3 
 
 while the electric motor (M), in Fig. 3, corresponds to the 
 water motor referred to in the example under section (3). If 
 all the electrical pressure is consumed in causing a given 
 quantity of electricity to flow through the wire in a given 
 time, there will be no pressure available to operate the elec- 
 trical motor or any other electrical device, just as there would 
 be no pressure available to operate the water motor in the 
 hydraulic problem when all the pressure was used in caus- 
 ing the water to flow through the pipe. The difference in 
 electrical pressure between any two points on the wire is a 
 measure of the pressure required to cause a given quantity 
 of electricity to pass from one of the points to the other 
 in a given time. This difference in pressure will depend 
 upon the opposition offered by the circuit between the two 
 points and the quantity passing between them in a given 
 time. With an increase in the opposition offered by the cir- 
 cuit there must be an increase in pressure to maintain a 
 constant flow. If, on the other hand, the pressure remains 
 constant and the opposition to the flow increases or decreases, 
 there will be a decrease or increase in the quantity of 
 
6 PKACT1CAL APPLIED ELECTKICITY 
 
 electricity passing a certain point in the circuit in a given 
 time. 
 
 5. Electrical Quantities. There are three electrical quan- 
 tities associated with the electrical circuit that correspond 
 to those given for the hydraulic analogy. These quantities 
 are the current of electricity, the electromotive force which 
 causes the current, and the resistance which hinders the free 
 flow of the electricity. 
 
 6. Current of Electricity. The rate at which the move- 
 ment, or flow, of electricity takes place is the current tor 
 a uniform movement it is the amount of electricity flowing 
 per unit of time usually the second. The unit quantity of 
 electricity is the coulomb, and if the rate of flow is such 
 that one coulomb flows per second, there is said to be a 
 current of one ampere. 
 
 At any instant the current is the same at all parts of a 
 circuit having no branches, and it is the same for all points 
 in each branch, where there are branches. A mistake is 
 often made in thinking that the current is used up that 
 there is practically no current returning to the source of 
 the electrical energy. Such a condition is not true. The 
 current in the return conductor to the battery or dynamo 
 is exactly the same as the current in the conductor carry- 
 ing the electricity from the battery or dynamo. The cur- 
 rent that leaves a motor, lamp, or bell is no different in 
 value from that which enters them. It is the energy of the 
 electricity that is used up, just as it is the energy possessed 
 by the water that is imparted to the water wheel and causes 
 it to rotate without the water itself being consumed. The 
 symbol used in representing the current is the letter (I). 
 
 7. Resistance. Resistance is that property possessed by 
 substances which opposes the free flow of electricity, but 
 does in no way tend to cause a flow in the opposite direction 
 to that in which the electricity actually moves. 
 
 All substances resist the movement of electricity through 
 them, but the resistance offered by some is very much greater 
 than that offered by others, and as a result all materials 
 may be grouped under one of two heads, namely, conductors 
 and insulators. 
 
 Conductors are those substances offering relatively low 
 resistance. 
 
THE ELECTRICAL CIRCUIT 7 
 
 Insulators are those substances offering a high resistance as 
 compared to conductors. 
 
 There is no such thing as a perfect conductor or a perfect 
 insulator, but conductors and insulators are merely relative 
 terms and define the degree to which a substance conducts. 
 Metals have by far the least resistance of any substances 
 and are used in electrical circuits where a minimum resist- 
 ance is desired. The most common insulators in use are 
 porcelain, glass, mica, stoneware, slate, marble, rubber, oils, 
 paraffin, shellac, paper, silk, cotton, etc. 
 
 The unit in which resistance is measured is the ohm, and 
 it is represented by the symbol (R). 
 
 8. Electromotive Force. As every part of the circuit offers 
 resistance to the flow of electricity, there must be some 
 force, or pressure, to overcome this resistance and maintain 
 the current. This is the electromotive force or electricity 
 moving force. Electromotive force, or e.m.f., as it is abbre- 
 viated, can be generated in a number of different ways; 
 perhaps the two most common are the chemical production 
 in a primary cell and the mechanical generation by the proc- 
 ess of electro-magnetic induction in a generator. Electro- 
 motive force does not create electricity, but simply imparts 
 energy to it, as a mechanical force may produce motion in 
 a body and as a result convey energy to the body. An elec- 
 tromotive force may exist without producing a current, just 
 as a mechanical force may exist without producing motion. 
 The unit in which electromotive force is measured is the 
 volt. 
 
 9. Electromotive Force and Potential Difference. The 
 electromotive force in any circuit is the total generated 
 electrical pressure acting in the circuit, while the potential 
 difference is the difference in electrical pressure between 
 any two points in the circuit. The electricity in its passage 
 around the circuit loses some of its energy; hence, between 
 any two points in the circuit there will be a difference in 
 energy or potential possessed by the electricity. In over- 
 coming the resistance of the wire between the points (A) and 
 CB), Fig. 4, the electricity will lose some of its energy and 
 will, therefore, have less potential at (B) than at (A), or, in 
 other words, there is a difference in potential between (A) 
 and (B). This difference in potential in the electrical circuit 
 
8 
 
 PEACTICAL APPLIED ELECTRICITY 
 
 is analogous to the difference in pressure between two points 
 on the pipe in the hydraulic circuit. This potential differ- 
 ence, or p.d., as it is abbreviated, is due to the current through 
 the resistance, for when the current stops, the difference in 
 potential will no longer exist. The potential difference is 
 measured in the same unit as the electromotive force, the 
 volt. The sum of all the potential differences in any elec- 
 trical circuit is numerically equal to the effective e.m.f. act- 
 ing in the circuit. If two points can then be located on a 
 circuit so that all the p.d.'s around the circuit will be be- 
 tween them, the potential difference between the points and 
 the e.m.f. acting in the circuit will be numerically equal. 
 
 Generator 
 
 Fig. 4 
 
 10. Ohm's Law. Current, electromotive force, and resist- 
 ance are always present in an active circuit and there is a 
 simple, but very important, relation connecting them. This 
 relation was first discovered by Dr. G. S. Ohm in 1827 and 
 has, as a result, been called Ohm's Law. Dr. Ohm discovered 
 by experiment that the difference of potential, represented 
 by the symbol (E), between any two points on a conductor, 
 is, all other conditions remaining constant, strictly propor- 
 tional to the current (I), or 
 
 E = Constant X I 
 
 (2) 
 
 By measuring (E) in volts and (I) in amperes, the constant in 
 the above equation is numerically equal to the resistance, be- 
 tween the points, in ohms. The expression can then be re- 
 duced to the form 
 
 Volts = Resistance X Amperes 
 E = RI 
 
 (3) 
 
THE ELECTRICAL CIRCUIT 9 
 
 or, as it is usually written, 
 
 Amperes = Volts -f- Ohms 
 
 E 
 
 I = - (4) 
 
 R 
 
 and as a third form, 
 
 Ohms = Volts -5- Amperes 
 E 
 
 R = (5) 
 
 I 
 
 The above relations hold true for all or any part of a cir- 
 cuit composed of metals and electrolytes, but it does not 
 seem to be true for gases, under certain conditions, nor for 
 insulators. 
 
 Example. The total resistance of a certain circuit is 55 
 ohms. What current will a pressure of 110 volts produce in 
 the circuit? 
 
 Solution. The value of the current is given in terms of 
 the pressure and the resistance in equation (4) and by a 
 direct substitution in this equation we have 
 
 110 
 I = = 2 
 
 55 
 
 Ans. 2 amperes. 
 
 Example. A current of 10 amperes is produced in a circuit 
 whose resistance is 12% ohms. What pressure is required? 
 
 Solution. The electrical pressure is given in terms of the 
 resistance and the current in equation (3) and by a direct 
 substitution in this equation we have 
 
 E = 12V 2 X 10 = 125 
 
 Ans. 125 volts. 
 
 11. Coulomb, Ampere, Ohm, and Volt. The International 
 Electrical Congress that met in Chicago in 1893 officially 
 passed upon the following values for the coulomb, ampere, 
 ohm, and volt, and they are known as the practical units. 
 
 (a) In defining the coulomb advantage is taken of the 
 fact that electricity in passing through a solution of silver 
 nitrate deposits silver on one of the conductors immersed 
 
10 PRACTICAL APPLIED ELECTRICITY 
 
 in the solution and the amount deposited is proportional to 
 the quantity of electricity that passed through the solution. 
 (See chapter on "Instruments.") The coulomb will deposit, 
 under standard conditions, .001 118 of a gram of silver. 
 
 (b) Since the current is the rate of flow of electricity, 
 then the ampere is the unit rate of flow, or one coulomb 
 per second, and its value is, therefore, that current which 
 will deposit silver at the rate of .001118 of a gram per sec- 
 ond. When smaller currents are to be measured, the mi Mi- 
 ampere, or one-thousandth of an ampere, and the micro- 
 ampere, or one-millionth of an ampere, are frequently used. 
 
 (c) The International ohm, as nearly as known, is the 
 resistance of a uniform column of pure mercury 106.3 centi- 
 meters long and 14.4521 grams in mass, at the temperature 
 of melting ice. This makes the cross-section one square 
 millimeter. The microhm is one-millionth of an ohm and 
 the megohm is one million ohms. These units are very fre- 
 quently used in the measurement of very small or very large 
 resistances. 
 
 (d) The volt, the unit of electromotive force or poten- 
 tial difference, is that e.m.f. or p.d. which, when applied to 
 a conductor having a resistance of one ohm, will produce in 
 it a current of one ampere. One volt equals the 100 9l434 part 
 of the e.m.f. of a Clark Standard Cell at 15 degrees centi- 
 grade. A smaller unit, called the millivolt, or one-thousandth 
 of a volt, is often used in measuring small e.m.f.'s and p.d.'s. 
 Another unit, called the kilovolt, has a value of one thousand 
 volts. 
 
 PROBLEMS ON OHM'S LAW 
 
 (1) The difference in potential between the terminals of 
 a generator is 110 volts. If the generator is causing a cur- 
 rent of 12 amperes in the circuit to which it is connected, 
 what is the resistance of the circuit? 
 
 Ans. 9.17 ohms. 
 
 (2) What e.m.f. must a dynamo generate to supply an 
 electroplating current of 20 amperes through a circuit whose 
 total resistance is .2 ohms? Ans. 4 volts. 
 
 (3) An electric-car heater is supplied with a p.d. of 500 
 
THE ELECTRICAL CIRCUIT U 
 
 volts from the trolley. What must its resistance be in or- 
 der that the current may not exceed 8 amperes? 
 
 Ans. 62.5 ohms. 
 
 (4) The difference in potential between the terminals of 
 an incandescent lamp is 110 volts when there is a direct 
 current of .5 ampere through the lamp. What is the re- 
 sistance of the lamp? Ans. 220 ohms. 
 
 (5) The field circuit of a dynamo takes a current of 1.5 
 amperes from a 110-volt circuit. What is the resistance of 
 the field winding? Ans. 73% ohms. 
 
 (6) A certain bell requires a p.d. at its terminals of 8 
 volts to operate it. The bell has a resistance of 50 ohms. 
 What current is required to operate the bell? 
 
 Ans. .16 ampere. 
 
 (7) An e.m.f. of 5 volts is connected to a line and bell 
 having a combined resistance of 12y 2 ohms. What current 
 is there through the bell? Ans. .4 ampere. 
 
 (8) A lamp has a hot resistance of 55 ohms and requires 
 a current of 1 ampere to cause it to light up to full candle- 
 power. What p.d. must exist between the terminals of the 
 lamp when it burns at full candle-power? 
 
 Ans. 55 volts. 
 
 12. Electrical Force. Force is defined as that which 
 tends to produce motion, or a change of motion; thus a force 
 must always be applied to a body to cause it to move, and 
 a force must be again applied to cause the body to come 
 to rest. It must be remembered that a force does not al- 
 ways produce motion, but only tends to produce it, as when 
 you push on a brick wall you apply muscular force, but there 
 is no motion. There are a number of different, kinds of 
 force: Gravitational force, as a result of which all bodies fall 
 from a higher to a lower level: mechanical force, which is 
 produced by the expansion of the steam in the engine cylin- 
 der, and may be used in driving a generator; and electrical 
 force is that force which produces or tends to produce a 
 movement of electricity. It is commonly produced in the pri- 
 mary battery or by an electrical generator. 
 
12 PEACTICAL APPLIED ELECTRICITY 
 
 13. Electrical Work or Energy. When a force overcomes 
 a certain resistance, work is done; or work is the result of 
 a force acting through a certain distance. Force may exist 
 without any work being done. Thus, a generator may be op- 
 erating and generating an electrical force, but it is not 
 sufficient to overcome the resistance between the terminals 
 of the machine, therefore, no current is produced and the 
 generator is not doing any work. If, however, a conductor 
 be connected to the terminals of the generator, a current 
 will be produced and as a result the generator will do work. 
 The electrical work done by the dynamo will show itself 
 as heat and the wire will become heated as a result. En- 
 ergy is the ability to do work. Electrical energy, then, is 
 the capacity or ability to do electrical work. Energy is 
 measured in the same unit as work and it is numerically 
 equal to the work done. Thus the energy possessed by a 
 certain quantity of electricity, with respect to its energy at 
 some other electrical level, is equal to the work done on or 
 by the quantity in moving from the first to the second 
 electrical level. When a quantity moves from a higher to 
 a lower level, it gives up energy or does work; when it is 
 moved from a lower to a higher electrical level, work is 
 performed and the energy of the quantity of electricity is 
 increased. 
 
 14. The Joule. The joule, the unit of electrical work 
 or energy, is the amount of work performed in raising one 
 coulomb of electricity through a difference in electrical 
 pressure of one volt. Work is independent of the time. 
 In other words, it will require the same amount of work 
 to raise a certain weight a given height in one hour as 
 would be required to raise it the same height in one minute. 
 The name for the mechanical unit of work is a compound 
 word in which one of the parts is a force unit and the other 
 part is a distance unit. The unit commonly used is the foot- 
 pound, the pound being the unit of force and the foot the unit 
 of distance. The electrical work performed in an electrical 
 circuit is equal to 
 
 Joules = Volts X Amperes X Time (in seconds) (6) 
 
 Amperes times time is equal to the quantity of electricity 
 moved, so that the right-hand portion of the above equation 
 
THE ELECTKICAL CIECUIT 13 
 
 is the product of a certain quantity and the difference in 
 electrical pressure through which it is moved. 
 
 15. Electrical Power. Power is the rate of doing work, 
 or the rate at which energy is expended. The unit of elec- 
 trical power is a unit of electrical work performed in a unit 
 of time, or a joule per second, and it is called the watt, rep- 
 resented by the symbol (W). 
 
 Electrical Work 
 
 Electrical Power= (7) 
 
 Time 
 
 Substituting the value of the electrical work given in equa- 
 tion (6) in equation (7)-, we have 
 
 Volts X Amperes X Time 
 
 Electrical Power = 
 
 Time 
 
 = Volts X Amperes, or (8) 
 
 W = El (9) 
 
 One watt, therefore, equals one volt multiplied by one am- 
 pere, or any product of volts and amperes whose result is 
 unity. Equation (9) may be written 
 
 W 
 
 I = (10) 
 
 or E 
 
 W 
 
 E= (11) 
 
 I 
 
 Example. A 220-volt generator supplies 20 amperes to a 
 motor. How many watts does the motor consume? 
 Solution. Substituting directly in equation (9) we have 
 
 W = 220 X 20 = 4400 
 
 Ans. 4400 watts. 
 
 Example. An arc lamp requires 880 watts from a 110-volt 
 circuit to operate it. What current does the lamp take? 
 Solution. Substituting in equation (10) we have 
 
14 PRACTICAL APPLIED ELECTRICITY 
 
 880 
 
 I = = 8 
 
 110 
 
 Ans. 8 amperes. 
 
 16. Mechanical Horse-Power. If a body weighing 33000 
 pounds be raised one foot in one minute, there is a rate of 
 working, or expenditure of energy, equivalent to one horse- 
 power (abbreviated h.p.). The horse-power any machine 
 is developing is equal to the foot-pounds of work done per 
 minute divided by 33 000, or the foot-pounds of work done 
 per second divided by 550. 
 
 17. Relation between the Watt and the Foot-Pound. Dr. 
 Joule discovered experimentally that 
 
 One watt = .7375 foot-pound per second (12) 
 or 
 
 One foot-pound per second = 1.356 watts (13) 
 
 18. Electrical Horse-Power. Since the mechanical horse- 
 power is 550 foot-pounds per second, an equivalent rate of 
 doing work would be 
 
 550 
 
 = 746 watts = 1 electrical horse-power (14) 
 
 .7375 
 
 Then to change from mechanical horse-power to the elec- 
 trical units, multiply by 746, or 
 
 Watts = h.p. X 746 (15) 
 
 To determine the horse-power a generator is developing, de- 
 termine its output in watts and divide by 746, or 
 
 E X I watts 
 
 hp.= = (16) 
 
 746 746 
 
 19. Kilowatt. The kilowatt (abbreviated k.w.) is a larger 
 unit of electrical power than the horse-power. It is equal 
 to 1000 watts or about 1% horse-power. 
 
 20. Larger Units of Energy. The joule is a very small 
 unit of electrical energy or work, and as a result larger 
 
THE ELECTK1CAL CIRCUIT 15 
 
 units are usually used in practice. The watt-hour is one 
 watt expended for one hour. The kilowatt-hour is equal to 
 1000 watts expended for one hour. The watt-hour is equiva- 
 lent to 3600 watt-seconds or 60 watt-minutes. 
 
 Watt-hours = watts X hours (17) 
 
 Kilowatt-hours = k.w. X hours (18) 
 
 Horse-power hour = h.p. X hours (19) 
 
 The dials of the integrating wattmeters used by central 
 station companies usually record the energy supplied to the 
 consumer for lighting or power purposes in watt-hours or 
 kilowatt-hours. 
 
 Example. Ten incandescent lamps take a current of 2 1 X> 
 amperes from a 220-volt circuit. What will it cost to operate 
 these lamps . for five hours if the power company charges 
 14 cents per kilowatt-hour? 
 
 Solution. Substituting in equation (9), we can determine 
 the power taken by the lamps in watts: 
 
 Power = 220 X 2% = 550 watts 
 
 Now by substituting in equation (17), we can determine the 
 energy consumed in watt-hours 
 
 Energy = 550 X 5 = 2750 watt-hours 
 
 One kilowatt-hour is equivalent to 1000 watt-hours, hence 2750 
 watt-hours are equal to 2.75 kilowatt-hours. The total cost 
 then would be 
 
 2.75 X 14 = 38% 
 
 38% cents. 
 
 21. Units. Units are of two kinds fundamental and de- 
 rived. The fundamental units are the ones from which all 
 others are derived and in terms of which all physical meas- 
 urements may be made. They are fundamental in the sense 
 that no one is derived from the others. The derived units 
 are all those that are dependent for their definition upon the 
 fundamental ones. 
 
 The three fundamental units in use are those of length, 
 mass, and time. Of these the only unfamiliar one may be 
 
16 
 
 PEACTICAL APPLIED ELECTKICITY 
 
 that of mass, which means the quantity of matter in a 
 body. From these three fundamental units are derived all 
 others in use, such, for example, as those of force, work, 
 and energy already mentioned, and all of the electrical units. 
 
 22. Systems of Units. Unfortunately there are two sys- 
 tems of units in use in this country. One is the ordinary 
 commercial, or English System, and the other the universal 
 scientific, or Metric System. In each of these systems we 
 have the three fundamental units and also a set of derived 
 units. It is quite essential that you know something of 
 the metric system, since all the electrical units are based 
 upon it, and a great many dimensions will be given in units 
 that belong to this system. Table No. I will show the most 
 common units in the two systems. 
 
 The English System is sometimes spoken of as the foot- 
 pound-second (f.p.s.) system, because of the three funda- 
 mental units upon which it is based. Similarly the Metric 
 System is frequently spoken of as the centimeter-gram-sec- 
 ond (c.g.s.) system. 
 
 The relation between the units of the two systems is given 
 in Table A, Chapter 20. 
 
 TABLE NO. I 
 
 RELATION OP UNITS IN ENGLISH AND METRIC SYSTEMS 
 
 
 
 UNITS 
 
 
 SYSTEM 
 
 LENGTH 
 
 MASS 
 
 TIME 
 
 English or 
 (F, P. S.) 
 
 Yard (yd.) 
 Foot (ft.) 
 
 Pound (Ib.) 
 Ounce (oz.) 
 
 Second (sec.) 
 
 Metric or 
 (C. G. S.) 
 
 Meter (m.) 
 Centimeter (cm.) 
 
 Kilogram (kg.) 
 Gram (g.) 
 
 Second (sec.) 
 
 PROBLEMS ON POWER AND ENERGY CALCULATIONS 
 
 (1) If 4000 watts are expended in a circuit, how many 
 horse-power are being developed? 
 
 Ans. 5.36-1- horse-power. 
 
THE ELECTKICAL CIRCUIT 17 
 
 (2) If 20 horse-power of mechanical energy were converted 
 into electrical energy, how many watts would be developed? 
 
 Ans. 14 920 watts. 
 
 (3) One hundred and twenty-five horse-power expended 
 continuously for one hour will produce how many kilowatt- 
 hours? Ans. 93.25 k.w.-hours. 
 
 (4) How many watts are expended in a 110-volt, 16- 
 candle-power lamp that requires a current of .5 ampere? 
 
 Ans. 55 watts. 
 
 (5) How many horse-power will be absorbed by a circuit 
 of series arc lamps taking 9.6 amperes, the line pressure 
 being 2000 volts Ans. 25.73 + horse-power. 
 
 (6) A motor takes a current of 5 amperes from a 110- 
 volt circuit. What will it cost to operate this motor for 10 
 hours, if the central station company charges 12 cents per 
 kilowatt-hour? Ans. 66 cents. 
 
CHAPTER II 
 
 CALCULATION OF RESISTANCE 
 
 23. Resistance. Resistance has been defined as a prop- 
 erty of materials which opposes the free flow of electricity 
 through them. The value of the resistance of any conductor 
 in ohms will, however, depend upon the dimensions, tempera- 
 ture, and the kind of material of which it is composed. 
 
 24. Conductance. The inverse of resistance is known as 
 the conductance of a conductor. That is, if a conductor 
 has a resistance of (R) ohms, its conductance .is equal to 
 (14-R). The unit in which the conductance is measured is 
 the mho, and it is the conductance offered by a column of pure 
 mercury 106.3 cm. long and 14.4521 grams in mass at the 
 temperature of melting ice. This unit is little used in 'prac- 
 tice except in the calculation of the resistance of a divided 
 circuit, which will be taken up later. 
 
 25. Resistance Varies Directly as the Length of a Con- 
 ductor. The resistance of a conductor is directly propor- 
 tional to its length, the temperature and cross-section of the 
 conductor remaining constant. That is, the resistance in- 
 creases at the same rate the length of the conductor in- 
 creases, just as the resistance of a pipe to the flow of wa- 
 ter increases as the length of the pipe is increased, all 
 other conditions remaining constant. Hence, if the length 
 of a conductor is increased to four times its original value, 
 the resistance will be four times as much; or if the length 
 is divided into four equal parts, the resistance of each part 
 will be one-fourth of the total resistance. 
 
 Example. The resistance of a piece of wire fifteen feet 
 long is 5 ohms. What is the resistance of 1000 feet of the 
 same kind of wire? 
 
 18 
 
CALCULATION OF RESISTANCE 19 
 
 Solution. Since the resistance of a conductor is directly 
 proportional to its length, we can determine the resistance 
 of one foot of the wire, knowing the resistance of five feet, 
 by dividing 5 by 15: 
 
 5 -r- 15 = y 3 
 
 The resistance of one foot, then, is % ohm, and the resist- 
 ance of 1000 feet would be 1000 times as much, or 
 1000 X % = 333% 
 
 Ans. 333 y 3 ohms. 
 
 Example. The resistance of a certain conductor thirty 
 feet long is 30 ohms. What is the resistance of three inches 
 of the conductor? 
 
 Solution. The length of the conductor in inches is equal 
 to the number of inches per foot (12) multiplied by the num- 
 ber of feet: 
 
 12 X 30 = 360 
 
 Since the length is 360 inches and the resistance is 30 ohms, 
 the resistance per inch can be obtained by dividing 30 by 
 360: 
 
 30 -r- 360 = i/i 2 
 
 The resistance of one inch is then i 2 ohm and the resist- 
 ance of three inches will be three times one-twelfth: 
 
 3 X Ii2 - 3 /i2 = % 
 
 Ans. ^4 ohm. 
 
 26. Resistance Varies Inversely as the Cross-Section of a 
 Conductor. The resistance of a conductor is inversely pro- 
 portional to the cross-section, the temperature and length 
 of the conductor remaining constant. That is, the resist- 
 ance decreases at the same rate the area of the cross-sec- 
 tion increases, all other quantities remaining constant. 
 Hence, if the area of a conductor is reduced to one-fourth 
 its original value, the resistance will be four times as much, 
 or if its area is increased to four times its previous value 
 the resistance will be decreased to one-fourth its original 
 value. 
 
 Example. A conductor % 00 square inch in area has a 
 resistance of .075 ohm per foot. What is the resistance 
 of a conductor of the same material } 5 of a square inch 
 in area and one foot long? 
 
20 PRACTICAL APPLIED ELECTKICITY 
 
 Solution. Since the resistance varies inversely as the re- 
 lation between the areas, and the relation between the areas 
 in this case is 
 
 %5 -* a /ioo = 4 
 
 the resistance of the conductor of larger cross-section will 
 be % the resistance of the conductor of smaller cross- 
 section. 
 
 % of .075 = .018 75 
 
 Ans. .018 75 ohm. 
 
 27. Area of Circular Conductors. Most all conductors 
 have a circular cross-section; and it is necessary to know 
 how to calculate their areas in terms of their diameters or 
 radii in order to determine the relation between their re- 
 sistances. The area of any circle is obtained by multiplying 
 the radius by itself and this product by a constant called 
 Pi. The value of this constant is 3.1416, and it is the num- 
 ber of times the diameter must be used in order to reach 
 around the circle. It is represented by the Greek symbol (TT). 
 Hence, the area of any circle can be obtained by using the 
 equation 
 
 Area = r2 x TT (20) 
 
 Area = radius X radius X pi 
 
 Since the diameter of a circle is equal to twice the radius, 
 this equation may be rewritten in terms of the diameter, 
 
 Area = (j) 2 X * 
 
 7T 
 
 Area = X d 2 
 
 4 
 Area = .7854 d 3 (21) 
 
 From the above equation it is seen that the area of one 
 circle bears the same relation to the area of another as exists 
 between their respective diameters squared. That is, if two 
 circles have diameters 3 and 5, the relation between their 
 areas will be the relation between (3) 2 and (5) 2 , or 9 and 25. 
 The circle of smaller diameter will have % 5 the area of 
 the circle of larger diameter. 
 
 Example. The resistance of a wire .1 inch in diameter and 
 
CALCULATION OF RESISTANCE 21 
 
 10 feet long is 10 ohms. What is the resistance of a wire 
 of the same material and same length .3 inch in diameter? 
 
 Solution. The ratio of the areas of the two wires will be 
 the ratio between .I 2 and .3 2 which is .01 and .09. The larger 
 wire will have 9 times the area of the smaller wire and since 
 the resistance varies inversely as the area it will have one- 
 ninth the resistance. 
 
 1/9 of 10 = 19/9 = 11/9 
 
 Ans. 1% ohms. 
 
 28. Resistance Changes with Temperature. A change in 
 the temperature of all substances will cause a change in their 
 resistance. In the majority of cases an increase in tempera- 
 ture means an increase in resistance. Carbon is the best 
 example of substances whose resistance decreases with an 
 increase in temperature. The resistance of the carbon fila- 
 ment of an incandescent lamp is about twice as great when 
 the lamp is cold as when it is lighted. The change in resist- 
 ance due to a change in temperature is quite different for 
 different materials, and it is also slightly different for the 
 same materials at different temperatures. Alloys, such as 
 manganin, have a very small chance in resistance due to a 
 change in temperature, and standard resistances are, as a 
 rule, made from such alloys, as it is desired to have their 
 resistance remain as near constant as possible. 
 
 29. Temperature Coefficient. The temperature coefficient 
 of a material is defined as the change in resistance per ohm 
 due to a change in temperature of one degree. The resistance 
 at centigrade or 32 Fahrenheit is usually taken as the 
 standard resistance, which we will call R . Now, let the 
 resistance at some higher temperature (t) be measured and 
 call it R t . Then R Rt is the change in resistance for a 
 
 Rt Ro 
 change in temperature of (t) degrees, and is the 
 
 Ro 
 
 change in resistance per ohm for the given change in tem- 
 perature (t). The change in resistance for each ohm due to 
 a change in temperature of one degree is 
 Rt Ro 
 
 - = a (22) 
 
 Rot 
 
22 PBACTICAL APPLIED ELECTRICITY 
 
 in which (a) is the temperature coefficient. When the re- 
 sistance increases with an increase in temperature, as in 
 the case of metals, then Rt is greater than R and (a) is 
 positive; if Rt decreases with a rise of temperature, as in 
 the case of carbon, then (a) is negative. The above ex- 
 pression for the temperature coefficient can be changed to 
 the form 
 
 R t = R (i 4- at) (23) 
 
 This equation gives the value of the resistance (R t ) at any 
 temperature (t) in terms of the resistance (R ) the tempera- 
 ture coefficient (a), and the change in temperature (t). 
 
 30. Values of Temperature Coefficients. Table No. II gives 
 the value of the temperature coefficient for a number of 
 materials when the temperature change is expressed in centi- 
 grade (a c ) and Fahrenheit (a f ) degrees. 
 
 TABLE NO. II 
 TEMPERATURE COEFFICIENTS 
 
 Material a c a t 
 
 Aluminum 0.004 35 0.002 417 
 
 Carbon 0.0003 0.00017 
 
 Copper 0.004 20 0.002 33 
 
 Iron 0.00453 0.00252 
 
 Lead (pure) 0.004 11 0.002 2 
 
 Mercury 0.00088 0.00049 
 
 Nickel 0.00622 0.00345 
 
 Platinum 0.002 47 0.001 37 
 
 Silver 0.003 77 0.002 1 
 
 Tin 0.004 2 0.002 3 
 
 Zinc (pure) 0.004 0.002 2 
 
 The relation between the two coefficients as given in the 
 table is the same as that between the centigrade and the 
 Fahrenheit degree; that is at = % a c . 
 
 Table B, Chapter 20, gives the relation between the cen- 
 tigrade and Fahrenheit thermometer scales. 
 
 The above values of the temperature coefficients are based 
 upon a change in resistance, due to a change in temperature 
 
CALCULATION OF RESISTANCE 23 
 
 from centigrade or 32 Fahrenheit. If the original tem- 
 perature of the conductor is not centigrade or 32 Fahren- 
 heit, the value of the temperature coefficient will not be the 
 same as that given in Table No. II. There will be a different 
 value obtained for (a) for each different initial temperature. 
 Table No. Ill gives the change in the value of (a) for copper 
 for initial temperatures from to 50 centigrade. 
 
 TABLE NO. Ill 
 
 VALUES OP 
 
 THE TEMPERATURE COEFFICIENT OF COPPER AT 
 
 DIFFERENT INITIAL 
 
 TEMPERATURES 
 
 CENTIGRADE 
 
 Initial 
 
 Temp, coefficient 
 
 Initial 
 
 Temp, coefficient 
 
 temperature 
 deg. Cent. 
 
 per 
 deg. Cent. 
 
 temperature 
 deg. Cent. 
 
 per 
 deg. Cent. 
 
 
 
 .004 200 
 
 26 
 
 .003 786 
 
 1 
 
 .004 182 
 
 27 
 
 .003 772 
 
 2 
 
 .004 165 
 
 28 
 
 .003 758 
 
 3 
 
 .004 148 
 
 29 
 
 .003 744 
 
 4 
 
 .004 131 
 
 30 
 
 .003 730 
 
 5 
 
 .004 114 
 
 31 
 
 .003 716 
 
 6 
 
 .004 097 
 
 32 
 
 .003 702 
 
 7 
 
 .004 080 
 
 33 
 
 .003 689 
 
 8 
 
 .004 063 
 
 34 
 
 .003 675 
 
 9 
 
 .004 047 
 
 35 
 
 .003 662 
 
 10 
 
 .004 031 
 
 36 
 
 .003 648 
 
 11 
 
 .004015 
 
 37 
 
 .003 635 
 
 12 
 
 .003 999 
 
 38 
 
 .003 622 
 
 13 
 
 .003 983 
 
 39 
 
 .003 609 
 
 14 
 
 .003 967 
 
 40 
 
 .003 596 
 
 15 
 
 .003 951 
 
 41 
 
 .003 583 
 
 16 
 
 .003 936 
 
 42 
 
 .003 570 
 
 17 
 
 .003 920 
 
 43 
 
 .003 557 
 
 18 
 
 .003 905 
 
 44 
 
 .003 545 
 
 19 
 
 .003 890 
 
 45 
 
 .003 532 
 
 20 
 
 .003 875 
 
 46 
 
 .003 520 
 
 21 
 
 .003 860 
 
 47 
 
 .003 508 
 
 22 
 
 .003.845 
 
 48 
 
 .003 495 
 
 23 
 
 .003 830 
 
 49 
 
 .003 483 
 
 24 
 
 .003 815 
 
 50 
 
 .003 471 
 
 25 
 
 .003 801 
 
 
 
24 PRACTICAL APPLIED ELECTRICITY 
 
 31. Calculation of Resistance Due to Change in Tempera- 
 ture. When the resistance of a conductor at a given tem- 
 perature is known, which we will assume is centigrade, 
 its resistance at some other temperature may be calculated 
 by the use of the temperature coefficient. If it is desired 
 to calculate the resistance of a conductor at a higher tem- 
 perature than that at which it was measured, proceed as 
 follows: Multiply the temperature coefficient by the change 
 in temperature and the product will be the change in 
 resistance of each ohm for the given change in tempera- 
 ture; multiplying this product by the original resistance in 
 ohms gives the total change in resistance of the conductor. 
 This increase in resistance must now be added to the original 
 value and the result is the resistance at the second 
 temperature. 
 
 The method just given for calculating the resistance with 
 a change in temperature can be expressed by the following 
 equation : 
 
 (24) 
 
 or, it is usually written 
 
 R t = Ro (1 + at) (25) 
 
 In the above equation (R t ) is the resistance at the second 
 temperature, (R ) the resistance at the first temperature, 
 (0 centigrade), (a) the temperature coefficient, and (t) the 
 number of degrees above or below freezing (0 centigrade or 
 32 Fahrenheit). 
 
 The value of (a) to use in the equation will depend upon 
 whether the change in temperature (t) is to be measured 
 on the centigrade or on the Fahrenheit scale. 
 
 By an inspection of equation (25) it is apparent that if the 
 resistance of a conductor at a higher temperature is known, 
 the resistance at a lower temperature can be calculated from 
 the equation 
 
 Rt 
 
 R = - (26) 
 
 1 + at 
 
 When the resistance of a conductor at two different tem- 
 peratures is known, the change in temperature can be calcu- 
 lated from the equation 
 
CALCULATION OF RESISTANCE 25 
 
 Rt Ro 
 
 /97V 
 
 \"* ) 
 
 R a 
 
 Practical use is made of this equation in what is known 
 as the resistance thermometer, where the change in resist- 
 ance of a coil of wire is measured and the change in tem- 
 perature calculated. (R ) is then the resistance of the coil 
 at a known temperature (T ), and (R t ) is the resistance of 
 the coil at some other temperature (T^. (TJ is then 
 equal to 
 
 T! = To + t (28) 
 
 If there is an increase in resistance, (t) is positive and if 
 there is a decrease, (t) is negative. Hence (T x ) will be 
 greater or less than (T ) depending upon the sign of (t). 
 
 Example. The resistance of a certain copper conductor 
 is 15 ohms at centigrade. What is its resistance at 50 
 centigrade? 
 
 Solution. The temperature coefficient for copper, when the 
 temperature is measured on the centigrade scale, is, from 
 Table No. II, found to be .0042. Substituting the values for 
 (R ), (a), and (t) in equation (25), we have 
 
 Rt = 15 (1 + .0042 X 50) =18.15 
 
 Ans. 18.15 ohms. 
 
 Example. The resistance of a silver wire is 25 ohms at 
 45 Fahrenheit. What resistance will it have at 32 Fah- 
 renheit? 
 
 Solution. The temperature coefficient for silver is found 
 from Table No. II to be .0021. Substituting the values for (a), 
 (t), which is (45 32 = 13), and (R t ) in equation (26), we have 
 
 25 25 
 
 Ro = - - = 24.33 
 
 1 + 13 X .0021 1.0273 
 
 Ans. 24.33 ohms. 
 
 Example. A certain platinum coil that is used 'as a re- 
 sistance thermometer has a resistance of 100 ohms at 
 centigrade. What is the temperature of the coil when its 
 resistance is 115 ohms? 
 
 Solution. The temperature coefficient for platinum is found 
 
26 PBACTICAL APPLIED ELECTRICITY 
 
 from Table No. Ill to be .00247. Substituting the values of the 
 resistance and (a) in equation (27), we have 
 
 115 100 15 
 
 t = - - = 60.73 
 
 100 X .002 47 .247 
 
 Since the original temperature (T ) of the coil or the one 
 at which (R ) was determined was centigrade, the final 
 temperature (TO can be determined by substituting the values 
 of (T ) and (t) in equation (28), which gives 
 
 T x = + 60.73 = 60.73 
 
 Ans. 60.73 degrees centigrade 
 
 All of the above calculations are based on an initial tem- 
 perature of centigrade or 32 Fahrenheit. It is often the 
 case that the resistance of a conductor is known at some 
 temperature other than freezing, and it is desired to know 
 its resistance at some other temperature. Thus, the resist- 
 ance of a certain coil of wire may be known at 20 centi- 
 grade and it is desired to know its resistance at 60 centi- 
 grade. In this case the resistance of the coil at centi- 
 grade should be determined first, by the use of equation 
 (26), and the value of (R ), thus determined, together with 
 the value of (a) and (t) substituted in equation (25), which 
 will give the value of the resistance at the second tempera- 
 ture. The above operations can be combined, which will 
 give the equation 
 
 (29) 
 
 In the above equation (t,) is the final temperature and (t) 
 is the initial temperature, above or below freezing; (R t ) 
 the original resistance; (Rt+ti) the final resistance; and (a) 
 the temperature coefficient. If the temperatures are meas- 
 ured on the Fahrenheit scale, the values of (t) and (t,) 
 should be measured above or below 32 depending upon 
 whether the temperature be above or below freezing. 
 
 Example. A coil of platinum wire has a resistance of 100 
 
CALCULATION OF RESISTANCE 27 
 
 ohms at 45 Fahrenheit. What will the resistance of this 
 coil be at 75 Fahrenheit? 
 
 Solution. This problem can be solved by using equation 
 (29). The value of (R t ) to substitute in the equation is 
 100; the value of (t) is (45 32), or 13; the value of (tj is 
 (75 32), or 43; and the value of (a) is .00137. Substitut- 
 ing the above values in the equation gives the value of 
 (Rt+ti), which is the value of the resistance of the coil at 
 (ti) degrees above freezing, or in this case 75 Fahrenheit: 
 
 100 (1 + .00137 X 43) 
 
 R t+tl = - - = 104.03 + 
 
 (1 + .001 37 X 13) 
 
 Ans. 104.03-f ohms. 
 
 The error introduced, if the calculation be made without 
 reducing the resistance to zero, is not very large, depending 
 upon the initial temperature, and in the majority of ordinary 
 cases equation (25) can be used. When this equation is used 
 (R ) represents the initial resistance, which should be writ- 
 ten (Rt); (Rt) represents the final resistance, which should 
 be written (Rt+tJ ; and (t) represents the change in tempera- 
 ture, which is equal to (t x t). Equation (25) may then be 
 rewritten as follows: 
 
 R t+tl = Rt [1 + a a t) ] (30) 
 
 Using this equation in calculating the resistance in the last 
 problem gives 
 
 R t+tl = 100 [1 + .001 37 (75 43) ] 
 = 100 (1 + .0411) 
 = 104.11 
 
 Ans. 104.11 ohms. 
 
 Equation (29) must then be used when an accurate determi- 
 nation of the resistance is desired. Equation (29) can be 
 rewritten so that the value of (tj can be calculated when 
 the proper substitution is made: 
 
 [Rt +tl Cl + at)] R t 
 
 tx = (31) 
 
 aR t 
 
 32. Relation of Resistance to Physical Dimensions. From 
 
 section (26) we know the resistance varies directly as the 
 length, and from section (27) inversely as the area of the 
 
8 PRACTICAL APPLIED ELECTRICITY 
 
 cross-section. These two relations may be combined with a 
 constant, giving the following equation: 
 
 I 
 R = K (32) 
 
 A 
 The above equation expresses three facts: 
 
 (a) The resistance (R) varies directly as the length (I) of 
 the conductor. 
 
 (b) The resistance varies inversely as the cross-sectional 
 area (A) of the conductor. 
 
 (c) The resistance depends upon the material of which 
 the conductor is composed. The quality of any material as 
 a conductor is expressed by the letter (K), which has a 
 definite value for every substance. 
 
 33. Meaning of K. The physical meaning of (K) in equa- 
 tion (32) may be readily determined by making (Z) and 
 (A) equal to unity. Then length (I) may be measured in any 
 unit of length and the area (A) may be measured in any 
 unit of area. (K), then, is the resistance of a conductor 
 of unit length and unit cross-section, and there will be as 
 many values of (K) as there are units in which we may 
 measure (?) and (A). There are two values of (K) that are 
 in common use and these only will be considered. They are 
 the specific resistance and the mil-foot resistance. 
 
 34. Specific Resistance. If the length of a conductor is 
 one centimeter and its cross-section one square centimeter, 
 then, by equation (32), we have R = K; that is, (K) is the 
 resistance of a cubic centimeter of the material considered. 
 If the length of the conductor is one inch and the area one 
 square inch, then (K) is equal to the resistance of a cubic 
 inch of the material. The resistance of a cubic centimeter 
 or cubic inch of any material is called the specific resist- 
 ance of the material, and it is usually expressed in microhms 
 at centigrade. (A microhm is the one-millionth part of 
 one ohm. 
 
 35. Circular Mil. In the majority of cases electrical con- 
 ductors have a circular cross-section and when we calculate 
 the cross-sectional area from the diameter, the awkward fac- 
 tor .7854, or (7r-^-4), appears. To avoid this factor a more con- 
 venient practical unit of area has been adopted the circular 
 mil (c.m.). The circular mil is the area of a circle whose 
 
CALCULATION OF EESISTANCE 39 
 
 diameter is one mil or .001 of an inch. The square mil, 
 on the other hand, is the area of a square whose side is one 
 mil. The advantage in the use of the circular mil is that 
 when the diameter of the conductor is given in mils, its cir- 
 cular-mil area may be determined by squaring the diameter. 
 Conversely, the diameter may be determined, when the cir- 
 cular-mil area is given, by taking the square root of the 
 area. This gives the diameter in mils and from it the diame- 
 ter in inches may be obtained by dividing by one thousand. 
 
 36. Mil-Foot Resistance. The mil-foot resistance of a ma- 
 terial is defined as being the resistance of a volume of the 
 material one foot in length and having a uniform cross-sec- 
 tion of one circular mil. Then if (I) is equal to one foot 
 and (A) is equal to one circular mil, in equation (32) (K) 
 will be equal to (R). The mil-foot resistance is really a 
 particular value for the specific resistance, ' as it is the re- 
 sistance of a certain volume. 
 
 Values of Specific and Mil-Foot Resistance. The values 
 of the specific resistances of some of the common materials 
 are given in Table No. IV. 
 
 TABLE NO. IV 
 
 SPECIFIC. RESISTANCE, PER CENT RELATIVE RESISTANCE AND 
 CONDUCTANCE, OF DIFFERENT MATERIALS 
 
 Material 
 
 Measurements at Centigrade 
 
 Relative 
 Resist- 
 ance % 
 
 Relative 
 Conduc- 
 tivity % 
 
 Microhms 
 per cubic 
 cm. 
 
 Microhms 
 per cubic 
 inch 
 
 Mil- 
 foot 
 res. 
 
 Copper (Matthies- 
 sen's Standard) 
 Copper, annealed,. 
 Silver 
 
 1.594 
 1.56 
 1.47 
 5.75 
 9.07 
 20.4 
 
 8.98 
 94.3 
 
 2.2 
 2. 6 
 
 .6276 
 .614 
 .579 
 2.26 
 3.57 
 8.04 
 
 3.53 
 37.1 
 
 .865 
 1.01 
 
 9.54 
 9.35 
 8.82 
 34.5 
 54.5 
 123. 
 
 53.9 
 566. 
 
 13.2 
 15.4 
 
 100.0 
 97.5 
 92.5 
 362. 
 570. 
 1280. 
 
 565. 
 5930. 
 
 138. 
 161. 
 
 100.0 
 102.6 
 108.2 
 27.6 
 17.6 
 7.82 
 
 17.17 
 1.69 
 
 72.5 
 62.1 
 
 Zinc (pure) 
 Iron (very pure).. 
 Lead (pure) 
 Platinum ( a n - 
 nealed) 
 
 Mercury 
 
 Gold (practically 
 pure) 
 
 A.1 u m i n u m (99% 
 pure) 
 
 
30 PKACTICAL APPLIED ELECTK1CITY 
 
 The above values are based upon Matthiessen's determina- 
 tion of what he thought to be the specific resistance of pure 
 copper. The copper he used, however, contained considerable 
 impurities and as a result the copper obtainable at the pres- 
 ent time has a specific resistance less than that determined 
 by Matthiessen in 1860. 
 
 37. Relative Conductivity. The conductivity of a mate- 
 rial is equal to the reciprocal of its specific resistance. The 
 relative conductivity of any material would be the percent- 
 age relation between the conductivity of the material and 
 the conductivity of copper, which is taken as the standard: 
 
 Conductivity of material 
 
 % relative conductivity = x 100, or 
 
 Conductivity of copper 
 
 Specific resistance of copper 
 = X 100 (33) 
 
 Specific resistance of material 
 
 The value of the per cent relative conductivity of a number 
 of different materials is given in Table No. IV. 
 
 38. Relative Resistance. The relative resistance of a ma- 
 terial in per cent is the relation between its specific resist- 
 ance and the specific resistance of the standard, multiplied 
 by 100: 
 
 % relative Specific resistance of material 
 
 resistance = X 100 (34) 
 
 Specific resistance of standard 
 
 The value of the per cent relative resistance of a number 
 of different materials is given in Table No. IV. 
 
 39. Relation between Square and Circular-Mil Measure. 
 In the calculation of the resistance of electrical conductors 
 it is often necessary to change from the square to the circu- 
 lar mil or vice versa. The relation of the area represented 
 by one circular mil as compared to the area represented 
 by one square mil can be easily shown by reference to Fig. 5. 
 The small square in the figure represents an area corre- 
 sponding to 100 square mils (these areas are greatly exag- 
 gerated in the figure). A circle drawn inside the square as 
 
CALCULATION OF KES1STANCE 
 
 31 
 
 shown will have an actual area less than the square. The 
 area of the square in square mils is equal to the product 
 of the two sides measured in mils, or it is the value of the 
 side in mils squared. The circle has an area in square mils 
 equal to the diameter squared times .7854, or the area of 
 the circle is .7854 of the area of the square. Now the area 
 of the circle in circular mils (by definition of the circular 
 mil, Sec. 35) is equal to the diameter in mils squared (d)2. 
 
 The number of square mils en- 
 
 closed by the circle will then be 
 
 equal to .7854 of the number of 
 circular mils enclosed by the circle, 
 or the actual area corresponding to 
 a circular mil is less than the area 
 corresponding to one square mil. 
 This results in there always being 
 a, greater number of circular mils 
 in any area than there are square 
 mils. To change from circular to 
 square mils, multiply the area in 
 circular mils by .7854 and the result 
 is the area in square mils. Or, to 
 
 change from square to circular mils, divide the area in square 
 mils by .7854 and the quotient thus obtained will be the area 
 in circular mils. 
 
 Example. The diameter of a circular copper conductor 
 is 102.0 mils. Determine the area of the above conductor in 
 both circular and square mils. 
 
 Solution. The area of any circular conductor in circular 
 mils is equal to the diameter of the conductor in mils, 
 squared, or 
 
 Circular-mil area = d2 = (102.0)2 = 10 404 
 
 Ans. 10 404 circular mils. 
 
 (2) The area of a circle in square measure is equal to 
 .7854 times the diameter of the circular squared, or 
 
 Square mil area = .7854 X d- = .7854 X (102.0) 2 = 8171.3 
 
 Ans. 8171.3 square mils. 
 
 40. Calculation of Resistance from Dimensions and Spe- 
 cific Resistance. The resistance of any conductor may be 
 
 Fig. 5 
 
32 PRACTICAL APPLIED ELECTRICITY 
 
 calculated by the use of equation (32) if the dimensions of 
 the conductor and the value of (K) are known. The value 
 of the constant (K) used in the equation will, of course, 
 depend upon the units used in expressing the length and 
 area of the conductor. When the length (Z) of the conductor 
 is expressed in feet and the area (A) in circular mils, the 
 constant (K) corresponds to the mil-foot resistance of the 
 material. The value of this constant for different materials 
 can be obtained from Table No. II. The mil-foot resistance of 
 commercial copper at 25 centigrade is approximately 10.8. 
 
 41. Wire Gauges. For many purposes it is desirable to 
 designate the size of a wire by gauge numbers rather than 
 by a statement of their cross-section. A number of wire 
 gauges have been originated by different manufacturers of 
 wire, such as the B. & S. gauge, commonly called the Amer- 
 ican gauge, Brown and Sharpe Manufacturing Company, 
 which is the one generally used in this country. In the meas- 
 urement of iron and steel wire the "Birmingham wire gauge" 
 (B. W. G.), or Stub gauge is usually used. There are a num- 
 ber of other gauges such as the Roebling, Edison, and 
 New British standard, but these are not used very much. 
 The diameters in mils of the different size wires is given 
 in Table D, Chapter 20. 
 
 The B. & S. gauge is by far the most common wire gauge 
 in use in this country and for that reason it will be used 
 almost entirely in wiring calculations. Tables E and F, 
 Chapter 20, give the properties of copper wire. 
 
 42. How to Remember the Wire Table. The wire table 
 has a few simple relations, such that if a few constants are 
 carried in the memory, the whole table can be constructed 
 mentally with approximate accuracy. The chief relations, 
 without proof, may be enumerated below and verified from 
 the table. 
 
 The following approximate relations should be remembered: 
 No. 10 B. & S. gauge wire is 100 mils in diameter, approxi- 
 mately; has an area of 10000 c.m.; has a resistance of one 
 ohm per thousand feet; and weighs 31.43 pounds per thou- 
 sand feet, at 20C. (68F.). No. 5 wire weighs 100.2 pounds 
 per 1000 feet. The following rules are approximately true 
 for B. & S. gauge wire. 
 
CALCULATION OF RESISTANCE 33 
 
 (a) A wire which is three sizes larger than another has 
 half the resistance, twice the weight, and twice the area. 
 
 (b) A wire which is ten sizes larger than another has one- 
 tenth the resistance, ten times the weight, and ten times 
 the area. 
 
 (c) To find the resistance, divide the circular-mil area by 
 10; the result is the number of feet per ohm. 
 
 (d) To find the weight per thousand feet, divide the 
 number of circular mils by 10 000 and multiply by the weight 
 of No. 10 wire. Table C, Chapter 20, gives the equivalent 
 cross-sections of different size wires. 
 
 PROBLEMS 
 
 (1) What is the circular-mil area of a wire *4 inch in 
 diameter? 
 
 Ans. 62 500 c.m. 
 
 (2) The circular-mil area of a wire is 4225. What is its 
 diameter in inches? 
 
 Ans. .065 inch. 
 
 (3) A certain rectangular piece of copper is % by Vz of 
 an inch in cross-section. What is the area of this bar in 
 square mils? 
 
 Ans. 125000 sq. mils. 
 
 (4) What is the area of the rectangular piece of copper 
 given in problem 3, in circular mils? 
 
 Ans. Approximately, 159 150 c.m. 
 
 (5) What would be the diameter of a circular con- 
 ductor in mils that would have the same actual area as the 
 rectangular piece of copper given in problem 3? 
 
 Ans. Approximately 399. mils. 
 
CHAPTEK III 
 
 SERIES AND DIVIDED CIRCUITS MEASUREMENT OF 
 RESISTANCE 
 
 43. Grouping of Conductors. The resistance of a whole or 
 a portion of a circuit will depend upon the manner in which 
 the various parts constituting the circuit are connected. 
 Two or more conductors may be combined in a number of 
 ways, and the total resistance of the combination can be 
 determined if the resistance of each part of the circuit and 
 the manner in which the various parts are connected is 
 known. The various ways in which conductors may be 
 grouped are as follows: 
 
 (a) Series grouping. 
 
 (b) Parallel or multiple grouping. 
 
 (c) Any combination of series and parallel. 
 
 44. Series Grouping. 
 When the conductors form- 
 ing a circuit are so ar- 
 ranged that the current has 
 a single path the conductors 
 are said to be connected 
 in series and such a circuit 
 is called a series circuit. 
 Fig. 6 shows three resist- 
 ances (Ri), (R 2 ),and (R 8 ), 
 connected in series to the 
 Fig - 6 terminals of the battery 
 
 (B). The current has only 
 
 one path from the positive to the negative terminal of the 
 battery. These resistances may be of widely different values 
 and composed of different materials, but the total resistance 
 of the combination is equal to the sum of the resistances of 
 the various parts. 
 
 Suppose the three resistances in Fig. 6 have values of 3, 
 4, and 5 ohms, then the total resistance of the circuit, neg- 
 
 34 
 
 ~Jn r 
 
 ,TTh i 
 
 B 
 
 
 B 
 
SERIES AND DIVIDED CIRCUITS 
 
 35 
 
 lecting the resistance of the connections and the internal 
 resistance of the battery, will be 3 + 4 + 5 = 12 ohms. 
 
 The above relation of the total resistance to the individual 
 resistances can be shown by a hydraulic analogy. Suppose 
 that in Fig. 7 (A), (B), and (C) are three pipes of different 
 size and length and that they are joined end to end, or in 
 
 Fig. 7 
 
 series, and they are to be used in conducting water from 
 the tank (Tj) to the tank (T 2 ). It is apparent that the total 
 resistance offered by the three pipes connected in series is 
 equal to the sum of their respective resistances. 
 
 45. Facts Concerning Series Circuit. There are four facts 
 concerning every series circuit: 
 
 (a) The current is uniform throughout the series circuit. 
 
 (b) The p.d.'s over any portions of the series circuit are 
 proportional to the resistances of these portions. 
 
 (c) The total resistance is the sum of the individual 
 resistances. 
 
 (d) The effective e.m.f. of the circuit is the algebraic 
 sum of all the e.m.f.'s acting in the circuit. 
 
 46. Uniformity of Current. Since there is but one path 
 for the current, the conductors being all joined in series, 
 there must be as much current at one end of the conductor 
 as at the other. If this were not the case there would be 
 an accumulation of electricity at certain points along the cir- 
 cuit, but careful experiments show no such accumulation. 
 The flow of electricity can be compared to the flow of water 
 or other incompressible fluid in a pipe, as shown in Fig. 7. 
 If there is a certain quantity of liquid entering the end 
 of the pipe, connected to the tank (Tj), in a certain time, 
 
36 PRACTICAL APPLIED ELECTRICITY 
 
 then that same quantity must pass by any cross-section of 
 the pipe and the same quantity must flow out of the other 
 end of the pipe in the same time. It is impossible for the 
 liquid to accumulate at any point as it is incompressible. 
 
 An ammeter, which is an instrument used to measure the 
 current, may then be connected at any point in a series cir- 
 cuit and there will be the same indication on its scale so long 
 as the total resistance of the circuit and the electrical pres- 
 sure acting on the circuit remain constant. It must always 
 be remembered that it is not the current in an electrical 
 circuit that is used up, but instead, it is the energy of the 
 electricity that is always utilized. 
 
 47. Relation of P.D.'s to Resistance. Ohm's Law, which 
 expresses the relation between electrical pressure, current, 
 and resistance, holds for any part of the circuit as well 
 as for the whole circuit. Consider a uniform conductor 
 
 Fig. 8 
 
 (A, B, C, D), carrying a current of (I) amperes in the direction 
 indicated by the arrow in Fig. 8. There must be a difference 
 in pressure between the points, say (A) and (B), since there 
 is a current between them and the point (A) is at a higher 
 potential or pressure than the point B when the current 
 exists in the direction indicated. Let the resistance between 
 the points (A) and (B) be represented by (Ri) and the 
 difference in pressure or drop in potential between the same 
 two points be represented by (Ej). The current is then equal 
 to (Ei) divided by (Ri), or 
 
 E! 
 I = (35) 
 
 RI 
 
 If any other section of the conductor be taken, such as 
 that between the points (C) and (D), and the drop in poten- 
 tial between the two points be represented by (E 2 ) and 
 the resistance of the section by (R 2 ) we have 
 
 E 2 
 I = - (36) 
 
 R 2 
 
SEEIES AND DIVIDED CIRCUITS 37 
 
 The currents in the two sections are equal since they are 
 in series and the right-hand portions of the above equations 
 are equal, hence 
 
 B! E 2 
 
 (37) 
 RI R2 
 
 or the drop in potential is proportional to the resistance. 
 
 Example. Two coils of 5 and 10 ohms are connected in 
 series to a battery whose e.m.f. is 6 volts. What is the poten- 
 tial drop over each coil? 
 
 Solution. From equation (37) we can determine the rela- 
 tion between (Ej) and (E 2 ), where they represent the drops 
 in potential over the two coils, by substituting the values 
 of (Ri) and (R 2 ) in the equation, which gives 
 
 5 10 
 5 E 2 = 10 E! 
 
 EO TTS 
 2 === ^ -*^1 
 
 The p.d. (E 2 ) over the 10-ohm coil is then equal to twice 
 the p.d. (EO over the 5-ohm coil. The 5-ohm coil will then 
 have % of the total pressure over it and the 10-ohm coil will 
 have %. Since the total pressure is 6 volts, the drop over the 
 5-ohm coil will be 
 
 i/, of 6 = 2 
 
 Ans. 2 volts. 
 and the p.d. over the 10-ohm coil will be 
 
 % of 6 = 4 
 
 Ans. 4 volts. 
 
 48. Resistance of Series Circuit. In a previous section 
 the statement was made that the total resistance of the series 
 circuit is equal to the sum of the various resistances com- 
 posing the circuit. This statement is practically self-evident, 
 but it may be shown to be true by an application of Ohm's 
 Law. 
 
 If a number of resistances (Rj), (R 2 ), etc., are connected 
 in series and there is a current of (I) amperes through them, 
 we have, from equation (35), 
 
38 PRACTICAL APPLIED ELECTRICITY 
 
 E 1 = R 1 I, E 2 = R 2 I, etc., (38) 
 
 where (Ej), (E 2 ), etc., represent the p.d.'s over the resist- 
 ances (Ri), (R 2 ), etc. 
 
 Let (R) represent the total resistance and (E) the total 
 pressure. Then 
 
 E = RI (39) 
 
 But we also know (E) is equal to the sum of all the p.d.'s, 
 that is, 
 
 Hence 
 
 RI = R,I + R 2 I + etc. (41) 
 
 R = R t + R 2 -f etc. (42) 
 
 The above equation states that the resistance of several 
 conductors joined in series is the sum of their individual 
 resistances. 
 
 Example. Three resistance coils of 5, 6, and 7 ohms, re- 
 spectively, are connected in series and the combination con- 
 nected to a battery whose e.m.f. is 9 volts. What is the 
 value of the current in the coils? 
 
 Solution. The total resistance (R) is equal to the sum 
 of the several resistances, or 
 
 R = 5 + 6 + 7 = 18 ohms 
 
 The current then is equal to (E) divided by (R), or 
 
 9 1 
 
 18 2 
 
 Ans. l /2 ampere. 
 
 If there are (n) equal resistances of (r) ohm each con- 
 nected in series, the total resistance (R) is 
 
 R = nr (43) 
 
 An example of this would be a number of lamps connected 
 in series and the combination then connected to the mains. 
 If there are 5 incandescent lamps connected in series each 
 having a resistance of 220 ohms, the combination will have a 
 resistance of 5 X 220, or 1100 ohms. 
 
 49. Effective E.M.F. in a Circuit. The effective e.m.f. in 
 a circuit is the e.m.f. that is really effective in causing the 
 current. Several sources of e.m.f. may be joined in series, 
 
SERIES AND DIVIDED CIRCUITS 
 
 39 
 
 but the effective e.m.f. would not necessarily be equal to the 
 sum of their values because some of the e.m.f.'s might act 
 in the opposite direction to others. If all the e.m.f.'s in 
 the circuit tend to send a current in the same direction then 
 the value of the effective e.m.f. is the sum of all the e.m.f.'s 
 acting. When they are not all acting in the same direction, 
 the effective e.m.f. is equal to the difference between the 
 sum of the e.m.f.'s acting in one direction and the sum of the 
 e.m.f.'s acting in the opposite direction, and its direction will 
 be that of the larger sum. An example of the above would 
 be a battery composed of a number of cells all connected in 
 series but the e.m.f. of some of the cells acting in the oppo- 
 site direction to the remainder. The effective e.m.f. is a 
 maximum when all the e.m.f.'s in the circuit are acting in 
 the same direction. 
 
 50. Parallel or Multiple Grouping. When the conductors 
 forming a circuit are so connected that there are as many 
 paths for the current as there are conductors, the conductors 
 are said to be connected in parallel or multiple, and such a 
 
 circuit is called a divided 
 
 circuit. Fig. 9 shows three 
 
 coils (Ri), (R 2 ), and (R 3 ) 
 connected in parallel and 
 the combination connected 
 to the battery (B). In a 
 circuit such as that shown 
 in Fig. 9, it is apparent 
 that the current cannot be 
 the same in all parts of the 
 circuit, since it divides at 
 the point (A) between the 
 
 branches, part existing in each branch. The part of the total 
 current that is in each branch will depend upon the relation 
 between the resistance of that particular branch to the re- 
 sistance of the other branches. 
 
 The total resistance is not equal to the sum of the several 
 resistances, as in the series circuit, but it will be less than 
 the resistance of the branch having the smallest resistance. 
 A simple hydraulic analogy, as shown in Fig. 10, will serve 
 to verify the above statements. Three pipes, (Pj), (P 2 ), 
 and (P 3 ) are used in conducting water from a tank (Tj) 
 
 Fig. 9 
 
40 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 to another tank (T 2 ), as shown in the figure. If the pressure 
 in the tank (Tj) is maintained constant, the pressure acting 
 on the three pipes will remain constant and it will be the 
 same for each pipe, neglecting the difference in their level. 
 
 The same pressure is act- 
 ing on each of the resist- 
 ances in Fig. 9, neglecting 
 the resistance of the con- 
 necting leads. Let this 
 pressure be represented by 
 (E). The current in each 
 of the resistances will be 
 Fig. 10 equal to the presure over 
 
 the branch, which in this 
 
 case is (E), divided by the resistance of the branch. The 
 current supplied by the battery is equal to the sum of the 
 currents in the various branches, just as the total quantity of 
 water flowing from the tank (Ti), Fig. 10, in a given time, 
 is equal to the sum of the quantities flowing in the three 
 pipes in the same time. Representing the currents in the 
 several branches by (Ii), (I 2 ), and (I 3 ), and the total current 
 by (I) we have the relation 
 
 I = I, + I 2 + 
 
 E 
 
 Ii = 
 B, 
 
 E 
 
 (44) 
 (45) 
 
 R 3 
 
 The total current (I) is equal to the electrical pressure 
 (E) acting on the combination divided by the total resist- 
 ance (R) which we want to determine, or 
 
 (46) 
 
 Substituting the values of the various currents in equation 
 (44), we have 
 
 E E E E 
 
 = - + -- + - 
 R RI R 2 RS 
 
 (47) 
 
SERIES AND DIVIDED CIRCUITS 41 
 
 Dividing both sides of the equation by (E), we have 
 
 1111 
 
 - = + -- + - (48) 
 
 R R, Ro R 3 
 
 The above equation states that the total conductance of a 
 number of resistances in parallel is equal to the sum of the 
 respective conductances regardless of the number connected. 
 This equation can be reduced to the form 
 
 RjR 2 R3 
 
 R = (49) 
 
 RiR2 ~h -^2^3 H~ RiRs 
 
 When there are only two resistances connected in parallel, 
 the combined resistance can be calculated by the use of the 
 equation 
 
 RjR 2 
 
 R = (50) 
 
 RI + R2 
 
 If the resistances (Ri) and (R 2 ) are equal, the combined 
 resistance is equal to one-half of the resistance of either 
 of them. Or, in general, if (n) equal resistances of (r) ohms 
 each are connected in parallel, the combined resistance (R) is 
 
 r 
 R = (51) 
 
 n 
 
 Example. Eight incandescent lamps, each having a resist- 
 ance of 220 ohms, are connected in parallel across a 110-volt 
 circuit. What is the total current taken by the lamps? 
 
 Solution. The total resistance of the eight lamps would be 
 equal to the resistance of one of them divided by the number 
 of lamps connected in parallel, or 
 r 220 
 
 R = = = 27^ ohms 
 
 n 8 
 
 The current taken by the lamps is equal to the applied 
 voltage divided by the resistance, or 
 E 110 
 
 I = = = 4 
 
 R 27V 2 
 
 Ans. 4 amperes. 
 
42 PEAGTICAL APPLIED ELECTRICITY 
 
 Example. Two resistances of 3 and 5 ohms, respectively, 
 are connected in parallel. What is their combined resist- 
 ance? 
 
 Solution. The combined resistance can be determined by 
 substituting directly in equation (50), which gives 
 
 3X5 15 
 
 R = = 1% 
 
 3 + 5 8 
 
 Ans. 1% ohms. 
 
 51. Series and Parallel Combinations. A number of re- 
 sistances may be connected in such a way that some of them 
 are in parallel with others, or some of them may be in series 
 with others, or a combination of series and parallel connec- 
 tions may be formed. Six resistance coils are shown con- 
 nected together in Fig. 11. 
 This is a parallel combina- 
 R^. R 5 tion of three different re- 
 
 I J\fflfo '^N^f^\ sistances, the first of 
 
 R 2 4 R,\ which consists of the re- 
 
 sistances (R 4 ) and (R r) ) 
 2X2 Re 2 3 f /2 / in series; the second con- 
 
 tyWWWV ' sists of ( R i)' ^^' and 
 
 6 (R 3 ) in series; and the 
 
 third consists of the single 
 
 Fl2 11 
 
 resistance (R 6 ). To find 
 the total resistance of the 
 
 circuit determine the resistance of each path separately and 
 combine their resistances by the use of equation (49). 
 
 Several such groups of resistances may be connected in 
 series and the total resistance would be the sum of the 
 resistances of the several groups. 
 
 Example. The six coils shown connected in Fig. 11 have 
 the resistances marked on them in the figure. What is the 
 total resistance? 
 
 Solution. The resistance of the upper branch, call it (Bj), 
 is equal to th^ sum of the resistances (R 4 ) and (R 5 ), these 
 being connected in series, or 
 
 Bi = 3 + 4 = 7 ohms 
 
 Similarly the resistance of the middle branch (B 2 ) is 
 B 2 == 2y 2 + 2 + 3V = 8 ohms 
 
SERIES AND DIVIDED CIRCUITS 43 
 
 and the resistance of the lower branch (B 3 ) is 6 ohms. Sub- 
 stituting these values for the resistances of the various 
 branches in equation (49), we obtain 
 
 7X8X6 336 
 
 R = = = 2.301 
 
 7X8 + 7X6 + 8X6 146 
 
 Ans. 2.301 ohms. 
 
 PROBLEMS ON SERIES AND DIVIDED CIRCUITS 
 
 (1) Five similar incandescent lamps are connected in 
 series across 550-volt mains, and there is a current of .5 
 ampere through them. What is the combined resistance of 
 the five lamps and the resistance of each? 
 
 Ans. Combined resistance, 1100 ohms. 
 Resistance of each lamp, 220 ohms. 
 
 (2) An adjustable resistance is connected in series with 
 the field winding of a dynamo, which has a resistance of 40 
 ohms, and a current of 2 amperes exists in the circuit when 
 the impressed voltage is 110 volts. What is the total resist- 
 ance of the circuit, and how many ohms resistance is there 
 in the circuit due to the adjustable resistance? 
 
 Ans. Total resistance, 55 ohms. 
 
 Adjustable resistance, 15 ohms. 
 
 (3) There is a current of 50 amperes in a circuit when the 
 impressed voltage is 200 volts. What resistance should be 
 added in series with the circuit in order that the current be 
 reduced to 40 amperes? 
 
 Ans. 1 ohm. 
 
 (4) What resistance should be connected in parallel with 
 the circuit in problem 3 when the current is 50 amperes in 
 order that the total current may be 80 amperes? 
 
 Ans. 6% ohms. 
 
 (5) Three resistances of 5, 6, and 7 ohms, respectively, are 
 connected in parallel. What is their combined resistance? 
 
 Ans. 1.96 ohms. 
 
 (6) If 12 similar incandescent lamps connected in parellel 
 have a combined resistance of 18% ohms, what is the resist- 
 ance of each lamp? 
 
 Ans. 220 ohms. 
 
44 PRACTICAL APPLIED ELECTRICITY 
 
 (7) Two resistances of 4 and 12 ohms, respectively, are 
 connected in parallel and the combination connected in series 
 with a 7-ohm coil. What is the current through each resist- 
 ance when a pressure of 50 volts is impressed upon the 
 circuit? 
 
 Ans. Current in 7-ohm coil, 5 amperes. 
 Current in 12-ohm coil, 1^4 amperes. 
 Current in 4-ohm coil, 3% amperes. 
 
 (8) What is the drop in potential over each resistance in 
 the above problem? What resistance should be introduced in 
 the circuit, and how, to make the value of the current 2.5 
 amperes? 
 
 Ans. Drop over 7-ohm coil, 35 volts. 
 Drop over 4-ohm coil, 15 volts. 
 Drop over 12-ohm coil, 15 volts. 
 Connect 10 ohms in series. 
 
 52. Measurement of Resistance. Practically all the meth- 
 ods employed in measuring resistance depend upon some ap- 
 plication of Ohm's law. The method to be used in any case 
 will depend upon the kind of resistance to be measured, 
 that is, whether it is capable of carrying a large or small cur- 
 rent; the accessibility of the resistance; the value of the 
 resistance to be measured; and the accuracy desired. The 
 different methods described in the following sections are, per- 
 haps, the most common ones employed in practice. 
 
 53. Drop in Potential Method. Since Ohm's Law holds 
 true for any part of an electrical circuit, it follows that 
 the value of a certain resistance can be determined by measur- 
 ing the drop in potential across the resistance when the cur- 
 rent through the resistance is known. A voltmeter for meas- 
 uring the drop in potential, an ammeter for measuring 
 the current, and some source of energy such as a battery or 
 generator are required in measuring resistance by this method. 
 The resistance (R) to be measured is connected in series with 
 the ammeter (A), and the combination then connected to 
 the source of energy such as a battery (B), indicated in Pig. 
 12. The drop in potential across the resistance can be deter- 
 mined by means of the voltmeter (V), which should be 
 connected to the terminals of the resistance, as shown in the 
 figure. The value of the resistance can be determined by 
 
SEEIES AND DIVIDED CIRCUITS 
 
 45 
 
 substituting the ammeter and voltmeter readings in equation 
 (5), which states that the resistance is equal to the differ- 
 ence in electrical pressure divided by the current. This is a 
 very simple and convenient method and will give quite accur- 
 
 Fig. 12 
 
 ate results when proper care is exercised in reading the in- 
 struments. The method is best suited for the measurement of 
 low resistances capable of carrying rather large currents, for 
 the following reason : The current in the resistance to be meas- 
 ured is not equal to that indicated on the ammeter because 
 there is a certain current through the voltmeter. The current 
 through the voltmeter will, however, be small in comparison 
 to that through the unknown resistance, if the resistance of 
 the voltmeter is large in comparison to the unknown, the cur- 
 rents in the two branches of a divided circuit being to each 
 other inversely as the resistances of the respective branches. 
 This error can be avoided by subtracting from the value of 
 the current indicated on the ammeter the value of the cur- 
 rent through the voltmeter, which gives the true value of the 
 current through the resistance to be measured. The current 
 through the voltmeter is equal to its indication in volts 
 divided by its own resistance, or 
 
 E 
 I, = (52) 
 
 Ry 
 
 The resistance of the voltmeter is usually given on the 
 lid of the containing case. If not, it can be determined by 
 
4 <; I'K.M 11. Al. Al'l'l.ll.l. l-.l,l.. TBI< II V 
 
 means of a resistan- . bridge. The current i r thrmiKh the 
 resistance then in 
 
 I r K U or 
 
 E 
 
 It -I.- (54) 
 
 R* 
 
 and tho value of the unknown resistance will \- 
 
 (55) 
 
 Care should be exercised in making a resistance measure- 
 tu. nt by thin method not to pass too large a current through 
 ilu object to be measured as you are likely to change its 
 resistance due to a change in temperature resulting from 
 xcessive current. The greater the current, however, 
 without undue heating of the conductor, the greater the volt- 
 iii.-t.-r reading and, as a UHual thiiiK. the greater the accui.-icy. 
 When very low resistances are to be measured, a low-read im; 
 \oihn--t.T or, better still, a railllvoltmeter should be u 
 
 Example. The current through a rail joint is 300 amp* ! -s 
 and the drop in potential across the joint and bonds is 18 
 millivolts or .018 volt. What is the resistance in ohms and 
 microhms? 
 
 Solution. By substituting in equation (5) we have 
 
 .018 
 
 U .000 06 
 
 300 
 
 Ans. .00006 ohm. 
 
 0.000 06 X 1 000 000 60 
 
 Ans. 60 microhms. 
 
 Example. The current through a spool of wire is .5 am- 
 pere and the drop in potential across the spool as indi- 
 cated on a (0-15) voltmeter, having a resistance of 1500 ohms, 
 is 12 volts. What is the resistance of the wire? 
 
 Solution. Substituting in equation (55) we have 
 
SERIES AND DIVIDED CIRCUITS 
 
 12 
 
 R 
 
 X 1500 = 24.39 
 
 .5 X 1500 12 
 
 Ans. 24.39 ohms 
 
 54 Measurement of Resistance by Comparison. This 
 method requires no ammeter and the value of the unknown 
 resistance (X) is determined in terms of a known resistance 
 
 Fig. 13 
 
 (R) connected in series with it, as shown in Fig. 13. The 
 drop in potential over the known and unknown resistances is 
 measured when they are both carrying the same current. 
 The proper connections of the voltmeter for making these 
 measurements is shown in the figure by the full and dotted 
 lines. Since the drop in potential across any part of a cir- 
 cuit bears the same relation to the drop across any other part 
 of the same circuit as exists between the resistances of the 
 two parts, we have the simple relation 
 
 Drop in potential over X Resistance of X 
 = (56) 
 
 Drop in potential over R 
 
 Resistance of R 
 
 or 
 
 the unknown Resistance of R X p. d. over X 
 resistance X = 
 
 (57) 
 
 p. d. over R 
 
 Example. A known resistance (R) of 10 ohms was con- 
 nected in series with an unknown resistance (X), as shown in 
 Fig. 13. The drop in potential over (R) was 5 volts and the 
 drop over X was 10 volts. What was the resistance of (X)? 
 
PEACTICAL APPLIED ELECTRICITY 
 
 Solution. Since the drop over the resistance (X) was twice 
 that over the standard, the resistance of (X) must be twice 
 that of the standard, or 
 
 X = 2 X 10 = 20 
 
 Ans. 20 ohms. 
 
 Substituting in equation (57) we have 
 
 10 X 10 
 X = = 20 
 
 Ans. 20 ohms. 
 
 55. Series Voltmeter Method. The connections for the 
 measurement of resistance by this method are made as 
 shown in Fig. 14. The terminals (T a ) and (T 2 ) represent 
 
 a source of e.m.f.; (X) is 
 
 _ _ the resistance to be meas- 
 
 I 1 o 2 ured and (V) is a direct 
 
 ^J \ ^ reading voltmeter. When 
 
 the voltmeter is con- 
 nected as shown by the 
 dotted line, the resistance 
 (X) is not in series with 
 it between the terminals 
 (Tj) and (T 2 ) and the 
 Fi 14 voltmeter indicates the 
 
 total pressure between 
 
 the two terminals. When, however, the resistance (X) is con- 
 nected in series with the voltmeter by opening the switch 
 (S), the indication of the voltmeter is no longer the total 
 pressure between the terminals (T x ) and (T 2 ) but it sim- 
 ply indicates the difference in pressure between its own 
 terminals. The drop in potential over the voltmeter (E v ) 
 or its own indication subtracted from the total pressure be- 
 tween (Tj) and (T 2 ), which we will call (E), will give the 
 value of the drop (E x ) over the resistance (X). 
 
 E x = E Ev (58) 
 
 It is assumed, of course, that the difference in pressure 
 between (T a ) and (T 2 ) remains constant. If this is not the 
 case a second voltmeter should be used, it being connected 
 across the source of supply, and the value of its indication 
 
SERIES AND DIVIDED CIRCUITS 49 
 
 should be noted at the same time the voltmeter in series with 
 the resistance is read. The current through the voltmeter 
 and the resistance (X) is the same, since they are in series. 
 The current through the voltmeter at any time is equal to the 
 voltmeter reading divided by its own resistance, or 
 
 Ev 
 Iv= (59) 
 
 Rv 
 
 The value of the resistance (X) can now be calculated, 
 since the current through it and the drop in potential across 
 it are known. Substituting in equation (5) the values of the 
 p.d. and the current given in equations (58) and (59), gives 
 
 E E v E Ev 
 R = - X Rv (60) 
 
 Ev Ev 
 
 Rv 
 
 The above equation gives the value of the resistance in 
 terms of the total pressure (E), the voltmeter reading (E v ) 
 when it is in series with the resistance, and the resistance 
 (Rv) of the voltmeter. 
 
 This method is, in general, serviceable for the measure- 
 ment of high resistances, such as the insulation of electric 
 light and power wires that are installed, insulation of trol- 
 ley lines, dynamos, transformers, etc. 
 
 The scheme of connections for the measurement of the 
 resistance of the insulation of a lighting circuit is shown in 
 Fig. 15. A small generator (G) capable of supplying an 
 e.m.f. of about 500 volts is usually used as a source of pres- 
 sure for testing. The generator may be engine- or motor- 
 driven. One terminal of the generator is connected directly 
 to the conduit or ground and the other terminal is connected 
 to the wire whose insulation resistance is to be determined, 
 with the voltmeter in circuit. The total pressure generated 
 by the machine (G) will be distributed over the resistance 
 between the wire and the conduit, or ground, and the volt- 
 meter. The voltmeter will read the drop (E v ) across itself. 
 A second voltmeter (V B ) is shown connected across the ter- 
 minals of the generator, and this voltmeter will read the 
 total pressure (E). The value of the insulation resistance 
 
50 
 
 PEACTICAL APPLIED ELECTRICITY 
 
 (X) can now be calculated by substituting the values of The 
 readings of the two voltmeters in equation (60) together with 
 the resistance of the voltmeter (V x ) and solving the equa- 
 tion. Insulation resistance is usually given as so many 
 megohms. 
 
 Exarrple. Connections were made, as shown in Fig. 15, 
 for testing the insulation resistance of a certain electric 
 light system. The resistance of the voltmeter (V x ) connected 
 in series with the resistance to be measured was 50 000 ohms. 
 The voltmeter (V g ) read 500 volts and (V x ) 10 volts. What 
 was the insulation resistance in megohms? 
 
 Solution. Substituting the voltmeter readings and the re- 
 sistance R v in equation (60) gives 
 
 500 10 
 R = - - X 50 000 = 2 250 000 
 
 10 
 2 250 000 -5- 1 000 000 = 2.25 
 
 Ans. 2.25 megohms. 
 
 56. Direct-Deflection Method. A galvanometer (G) is con- 
 nected in series with the resistance to be measured and the 
 two then connected to a source of e.m.f., as shown in Fig. 
 16. The indication produced on the galvanometer when 
 the circuit is closed should be noted. The unknown resist- 
 ance is then replaced by a known resistance and the cir- 
 
ISEBiES AND DIVIDED CIRCUITS 
 
 51 
 
 cuit again closed and the deflection again noted. The cur- 
 rent in the circuit for the two cases can be determined 
 
 from the deflections of the 
 galvanometer. Let (R g ) 
 represent the resistance of 
 
 n^ 
 
 B ft ^px> AAA/-^ battery pressure, (R) the 
 
 I I |J | s-^J - VVVW known resistance, (X) the 
 
 unknown resistance, (I r ) 
 
 Fi s- 16 the current through the 
 
 known resistance, and (I x ) 
 the current through the unknown resistance, then 
 
 and 
 
 I x = 
 
 Ir = 
 
 E 
 
 E 
 
 (61) 
 
 (62) 
 
 Since the same pressure is acting on the circuit in both 
 cases, and knowing the current in a circuit will vary in- 
 versely as the resistance, the relation may be written 
 
 Ix R g + R 
 
 (63) 
 I r R s + X 
 
 Calculating the value of (X) from the above equation we 
 have 
 
 \ Ir (Rg + R) 
 
 X = - R g (64) 
 
 I, 
 
 The resistance of the galvanometer is usually very small 
 in comparison to the resistance being measured so that it may 
 be neglected in the above equation, which gives 
 
 Ir 
 
 X = XR (65) 
 
 as the resistance of the unknown in terms of the current 
 in the two cases and the value of the known resistance (R). 
 
52 PRACTICAL APPLIED ELECTRICITY 
 
 This method is used in determining the insulation of coils of 
 wire, etc. The wire whose insulation is to be measured is 
 immersed in a salty solution (it being a better conductor than 
 ordinary water), with at least three feet of the wire out of the 
 solution at each end. One terminal of the testing circuit is 
 connected to the wire itself and the other terminal to a 
 metallic plate placed in the solution. The resistance between 
 the wire and the solution is then measured, giving the insula- 
 tion resistance for the length of wire immersed in the solution. 
 
 The insulation resistance of a wire varies inversely as its 
 length, because with an increase in length there is more 
 surface exposed, resulting in a greater leakage and less 
 resistance. 
 
 57. Principle of the Slide-Wire Wheatstone Bridge. Two 
 resistances, which may be equal or unequal, are shown con- 
 nected in parallel between the points (A) and (B), Fig. 17, 
 and the combination is connected to a source of e.m.f., such 
 
 AAAAAA/VWWWWWWV\V 
 
 Fig. 17 
 
 as the battery (B). The drop in potential across the two 
 branches of the divided circuit is the same regardless of the 
 relation of the two resistances. If the resistance in each 
 branch is the same, then the drop over a certain resistance in 
 one branch is equal to the drop over the same resistance in 
 the other branch. When the resistances of the two branches 
 are not equal, the above relation does not hold true, but there 
 are points on the two branches that have the same potential 
 with respect to (A) or (B). Select some point, such as (C) 
 on the lower branch, that will always have a potential less 
 than the point (A) and higher than the point (B) when the 
 current is in the direction indicated by the arrows. There is 
 
SERIES AND DIVIDED CIRCUITS 53 
 
 a point on the upper branch whose potential is equal to that 
 of (C) and this point can be located by means of a galvanom- 
 eter as follows: Connect one terminal of the galvanometer to 
 the point (C) and slide the other terminal along the upper 
 branch until a point is found which results in no deflection 
 of the galvanometer when the circuit is closed. This point, 
 which is marked (D) in the figure, is at the same potential as 
 the point (C), since there is no current between them, there 
 being no deflection produced on the galvanometer. 
 
 When the point (D) has been located, the drop in potential 
 across (AC) is equal to the drop across (AD), and the 
 drop across (CB) is equal to the drop across (DB). The 
 resistance (AC) bears the same relation to (AD), after a 
 balance is obtained, as the resistance (C B) bears to (DB). 
 This statement may be put into the form of a simple equa- 
 tion, thus 
 
 Resistance (AD) Resistance (DB) 
 
 (66) 
 
 Resistance (AC) Resistance (CB) 
 
 For example, suppose the resistance (AC) and the total 
 resistance of the upper branch are known and the resistance 
 (C B) is unknown. A balance is obtained, as previously de- 
 scribed, and, from the position of the point (D) on the upper 
 branch, the values of the resistances (AD) and (DB) may 
 be determined, the combined resistance of the two being 
 known. The above equation can then be changed to the form 
 
 Res. (DB) 
 Resistance (C B) = - X Res. (A C) (67) 
 
 Res. (AD) 
 
 By substituting the value of the three resistances (AC), 
 (DB), and (AD) in the above equation, the value of the 
 resistance (C B) may be determined. This type of bridge is 
 called a slide-wire pattern 'because the upper branch is usually 
 a piece of resistance wire stretched between the points (A) 
 and (B). The wire is stretched over a board divided into 
 equal parts and the relation between the two resistances 
 (AD) and (DB) can be determined in terms of their respect- 
 ive lengths, the resistance of the wire varying directly as the 
 length. The two resistances (A D) and (D B) are called the 
 
54 PRACTICAL APPLIED ELECTRICITY 
 
 ratio-arms, since their relation to each other gives the ratio 
 between the known and the unknown resistances. 
 
 58. Commercial Wheatstone Bridge. The form of Wheat- 
 stone bridge described in the previous section is not used 
 to any great extent in practice, as its operation is usually too 
 tedious, and for this reason it is confined almost entirely to 
 laboratory work. The principle of the commercial bridge is 
 the same as that of the slide-wire bridge, differing only in 
 construction and operation. A diagram of a simple form of 
 
 Fig. 18 
 
 bridge is shown in Fig. 18. The letters in the figure corre- 
 spond to those in Fig. 17. The resistances (DB) and (DA) 
 are the ratio arms, consisting of three coils each, having the 
 resistances marked in the figure. The resistance (AC), 
 called the rheostat of the bridge, consists of a number of coils 
 ranging in value from a very low resistance to several hun- 
 dred ohms, depending upon the range of the bridge. The 
 various resistance coils that form the different arms of the 
 bridge can be cut in or out of circuit by means of metallic 
 plugs that connect massive brass or copper strips on top 
 
SEKIES AND DIVIDED CIRCUITS 55 
 
 of the bridge. When a certain plug is removed the resistance 
 coil that was shorted by the plug is connected in the circuit. 
 The unknown resistance (X) is connected between the points 
 (B) and (C). When a balance is obtained on the galvanom- 
 eter, the following relation exists between the various arms of 
 the bridge 
 
 a R 
 
 (68) 
 
 or b X 
 
 b 
 
 X = R (69) 
 
 a 
 
 In making a measurement with this form of bridge the 
 relation between the ratio arms (a) and (b) remains con- 
 stant after they are adjusted to a certain value, and a balance 
 is obtained by changing the value of the resistance in the 
 rheostat (R). If (a) and (b) are made equal, then the resist- 
 ance in (R), when a balance is obtained, is equal to the 
 resistance of the unknown (X). When it is desired to measure 
 a resistance larger than the value of (R), make the ratio arm 
 
 Fig. 19 
 
 (b) greater than (a); and to measure a resistance smaller 
 than (R), make (b) less than (a). In the first case the resist- 
 ance (R) is multiplied by a certain number, which is the 
 quotient of (b-=-a), and will always be greater than unity 
 to obtain the value of (X) ; and in the second case (R) will 
 be multiplied by a number less than unity. The galvonometer 
 
56 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 and the battery connections may be interchanged without 
 interfering with the operation of the bridge. 
 
 There are a large number of different forms of bridges on 
 the market at the present time. Some of them have the gal- 
 vanometer, battery, and contact keys all mounted in the same 
 box with the resistances, and the only connection that must be 
 made is to the resistance to be measured. Fig. 19 shows a 
 good form of portable Wheatstone bridge. 
 
 59. The Ohmmeter. An Ohmmeter is an instrument for 
 measuring automatically the resistance of a circuit connected 
 to its terminals, by noting the position of a pointer on a dial 
 that is marked to read directly in ohms. The principle of 
 the Evershed instrument is as follows: The deflecting sys- 
 tem consists of a set of coils (BB^, as shown in Fig. 20, 
 rigidly fastened together, which move about a center (O) in 
 the magnetic field of strong permanent magnets (MM). The 
 nature of this construction brings the instrument into the 
 class of moving-coil permanent-magnet instruments, the ad- 
 vantages of which for reliability, accuracy under all condi- 
 tions of use, and promptness in taking deflection, are quite 
 
 Fig. 20 
 
 numerous. Springs are not used for the control of the moving 
 system, so that when not in use the needle may stand at any 
 point along the scale. 
 
 If the generator is set in motion and no resistance is con- 
 nected between the external terminals, current exists only in 
 the coils (BBj), which move at once to such location that (B) 
 is clear of the horn on the pole piece and (B^ is central 
 over the air gap in the (O) shaped centrally placed hollow 
 
SERIES AND DIVIDED CIRCUITS 57 
 
 iron cylinder. The needle then stands over Inf. on the scale, 
 showing an infinite resistance between the terminals. If a 
 measurable resistance is connected between the terminals, 
 a current exists in the stationary coil and, due to the thrust 
 experienced by it in the magnetic field, the needle moves along 
 the scale, and a direct reading of the amount of resistance 
 so connected is made. 
 
 The hand dynamo (D) operates in the field of the same per- 
 manent magnets. The armature is wound so that a rated 
 e.m.f. of 125, 250, 500, or even 1000 volts are generated for 
 some 100 r.p.m. of the crank. The design of this machine 
 is the result of a large amount of research by Mr. Evershed, 
 in his desire to make a rugged, reliable, light-weight gen- 
 erator which would require slight propelling force to drive it. 
 
 Instruments of this kind are usually used in measuring very 
 high resistances, such as insulation resistances, etc. 
 
CHAPTER IV 
 
 PRIMARY BATTERIES 
 
 60. The Voltaic Cell. If two unlike metals are immersed 
 in a solution, which is capable of acting upon one of them 
 more than upon the other, there will be a current of elec- 
 tricity between them when they are connected by a wire. 
 Such a combination constitutes a voltaic cell. This cell was 
 first discovered by an Italian physicist, Volta, in 1800, and 
 Was named after him. It is, however, often called a gal- 
 vanic cell, after Galvani, who was Volta's contemporary. 
 
 61. Simple Voltaic Cell. Two 
 pieces of metal, such as copper and 
 zinc, immersed in a solution that con- 
 tains a little sulphuric acid, or other 
 oxidizing acid, forms a simple voltaic 
 cell. Such a cell is shown in Fig. 21. 
 This cell is capable of furnishing a 
 continuous flow of electricity through 
 a wire whose ends are brought into 
 contact with the strips of copper 
 and zinc. When the electricity flows, 
 the zinc is wasted away, its con- 
 sumption furnishing the energy re- 
 quired to drive the current through 
 the cell and the connecting wire. 
 The cell might be thought of then 
 
 as a chemical furnace in which the fuel is zinc. The copper 
 strip from which the flow starts in passing through the 
 external circuit is called the positive pole of the battery, and 
 the zinc sirip is called the negative pole. These poles are 
 usually designated by the plus ( + ) and negative ( ) signs. 
 
 58 
 
 Fig. 21 
 
PKIMABY BATTEEIES 
 
 59 
 
 !t is the difference in electrical pressure between the positive 
 and the negative poles of the battery that causes a current in 
 the circuit when the poles are connected. 
 
 62. Voltaic Battery. If a number of voltaic cells are joined 
 in series the zinc plate of one joined to the copper plate of 
 the next, and so on a greater difference in electrical pressure 
 will be produced between the copper pole at one end and 
 the zinc pole at the other end. When the poles forming 
 the terminals of such a series are joined, there will be a more 
 powerful current than one cell would cause. [It is assumed 
 that the resistance 01 the circuit connecting the two poles or 
 terminals is practically the same as the resistance of the cir- 
 cuit connecting the terminals of a single cell.] Such a group- 
 ing of voltaic cells is called a voltaic battery. Four single cells 
 (Ci), (C 2 ), (C 3 ), and (C 4 ), are shown connected in series in 
 Fig. 22. The cells may be combined in other ways and these 
 
 ZCZCZCZC 
 
 Fig. 22 
 
 c, 
 
 methods will be taken up later. It is customary to represent 
 a single cell by two parallel lines, as shown in Fig. 23, 
 instead of drawing a picture of the cell each time you want to 
 show it in a diagram. The long line corresponds to the plus 
 ( + ), or positive, terminal, and the short line corresponds to 
 the minus ( ), or negative, terminal. 
 
 63. Chemical Action in a Battery. A continuous potential 
 difference is maintained between the zinc and copper in a 
 simple voltaic cell chiefly by the action of the exciting liquid, 
 say sulphuric acid, upon the zinc. Sulphuric acid is a complex 
 substance in which every molecule is made up of a group of 
 atoms, 2 of hydrogen, 1 of sulphur, and 4 of oxygen; or in 
 symbols H 2 SO 4 . The SO 4 part of the acid has a very strong 
 affinity for the zinc, and attacks it, when the plates are con- 
 nected, producing a current, and forms zinc sulphate ZnSO 4 , 
 which is dissolved in the water. There will be two parts of 
 
60 PRACTICAL APPLIED ELECTKICITY 
 
 hydrogen gas liberated for every portion of the SO 4 part of 
 the sulphuric acid that unites with the zinc. The zinc thus 
 replaces the hydrogen in the acid, when the cell is being 
 used, setting the hydrogen free. This chemical reaction is 
 expressed in the equation 
 
 Zn + H 2 SO 4 ZnSO 4 + H 2 
 
 Zinc and sulphuric acid produce zinc sulphate and hydrogen. 
 
 This chemical action continues as long as the battery is sup- 
 plying a current, the zinc gradually wasting away and the 
 power of the acid to attack the zinc gradually becoming 
 exhausted. Electrical energy is thus supplied to the external 
 circuit by the combination of zinc and acid inside the cell. 
 
 64. Local Action. When the circuit of a battery is not 
 closed, the current cannot exist, and there should be no chem- 
 ical action as long as the battery is producing no current. 
 Ordinary commercial zinc, however, contains many impurities, 
 such as tin, arsenic, iron, lead, carbon, etc., and these numer- 
 ous foreign particles form local voltaic cells on the surface of 
 the zinc inside the cell, with the result that the zinc is being 
 continuously eaten away whether the cell is supplying current 
 to an external circuit or at rest. These small cells weaken the 
 current the main cell is capable of supplying under proper 
 conditions. Often local action is caused by a difference in 
 density of the liquid at different parts of the cell. This 
 causes the zinc at the top of the cell to waste away and it 
 may be entirely eaten off. 
 
 65. Amalgamation. To do away with this local action, and 
 thus abolish the wasting of the zinc while the battery is at 
 rest, it is usual to amalgamate the surface of the zinc plates 
 with mercury. The surface to be amalgamated should be thor- 
 oughly cleaned by dipping it into acid and then a few drops of 
 mercury should be rubbed into the surface. The mercury 
 unites with the zinc at the surface forming pasty amalgam. 
 The foreign particles do not dissolve in the mercury, but float 
 to the surface, and they are carried away by the hydrogen bub- 
 bles. As the zinc in the pasty amalgam dissolves into the 
 acid, the film of mercury unites with fresh portions of zinc, 
 and a clean, bright surface is always presented to the liquid. 
 
 66. Polarization. When there is a current through a cell, 
 the hydrogen that is liberated from the acid appears upon 
 
PRIMARY BATTERIES 61 
 
 the surface of the copper, and the copper plate becomes prac- 
 tically a hydrogen plate. If a cell were made having a hydro- 
 gen and zinc plate, there would be a current from the hydro- 
 gen to the zinc inside the cell and from the zinc to the hy- 
 drogen outside the cell. The hydrogen collecting on the copper 
 plate tends to send a current through the cell opposite to that 
 produced by the copper and zinc current. This results in the 
 current supplied by the battery decreasing as the hydrogen 
 on the copper plate increases, or the plate becomes more 
 nearly covered with the hydrogen gas. A cell that has become 
 weakened in this way is said to be polarized, and the phe- 
 nomenon is called polarization. Hence, polarization is an evil, 
 and if it could be overcome by preventing the hydrogen bub- 
 bles collecting on the copper plate, the cell would be capable 
 of supplying a current of almost constant strength as long as 
 zinc remained to be acted upon and the acid was not ex- 
 hausted. Various attempts to prevent polarization have given 
 rise to many different types of cells on the market at the 
 present time. 
 
 67. Prevention of Polarization. Various remedies have 
 been practiced to reduce or prevent the polarization of cells. 
 These may be classed as mechanical, chemical, and electro- 
 chemical. 
 
 (a) Mechanical Means. If the hydrogen bubbles be sim- 
 ply brushed away from the surface of the positive pole, the 
 resistance they cause will be diminished. If air be blown 
 into the acid solution through a tube, or if the liquid be 
 agitated or kept in constant circulation by syphons, the re- 
 sistance is also diminished. If the surface be rough or cov- 
 ered with points, the bubbles collect more freely at the 
 points and are quickly carried up to the surface and got 
 rid of. This remedy is used in the Smee cell, which con- 
 sists of a zinc and a platinized silver plate dipping into 
 dilute sulphuric acid; the silver plate, having its surface 
 thus covered with a rough coat of finely divided platinum, 
 gives up the hydrogen bubbles freely, nevertheless in a bat- 
 tery of Smee Cells the current falls off greatly after a few 
 minutes. 
 
 (b) Chemical Means. If a strongly oxidizing substance 
 be placed in the solution it will combine with the hydrogen 
 and thus will prevent both the increase in internal resistance 
 
62 PBACTJCAL APPLIED ELECTEICITY 
 
 and the opposing electromotive force. Such substances are 
 bichromate of potash, nitric acid, and bleaching powder (so- 
 called chloride of lime). These substances, however, would 
 attack the copper in the zinc-copper cell. Hence, they can 
 only be used in a zinc-carbon or zinc-platinum cell. 
 
 (c) Electro-chemical Means. It is possible by employing 
 double cells to so arrange matters that some solid metal, such 
 as copper, shall be liberated, instead of hydrogen bubbles, 
 at the point where the current leaves the liquid. This elec- 
 tro-chemical exchange entirely obviates polarization. 
 
 68. Internal Resistance. The resistance offered by a cell 
 to a current through it from one plate to the other is called 
 its internal resistance. The value of the internal resistance 
 of any cell will depend upon the area of the two plates, the 
 distance between the two plates, the specific resistance of 
 the liquid, and the degree of polarization. As the polariza- 
 tion of a cell increases, the internal resistance increases, 
 since the effective area of the plates exposed to the action 
 of the liquid is decreased due to the accumulation of the 
 hydrogen gas. This increase in internal resistance of a cell 
 causes the difference in potential between its terminals to 
 decrease, as a larger part of the electromotive force of the 
 cell is required to force the current through its own resist- 
 ance and the available electrical pressure is decreased. 
 . 69. Factors Determining the Electromotive Force of a Cell. 
 When two plates of the same material, such as zinc, are 
 immersed in an acid solution and are connected by a 
 wire, there will be no current in the wire, because there is 
 a tendency to opposite currents and these two tendencies 
 neutralize each other. In other words, the difference in elec- 
 trical potential between one zinc plate and the solution is 
 the same as that between the other zinc plate and the solu- 
 tion, and these two potentials are opposite in direction when 
 the two plates are connected by a conductor which results in 
 no current through the circuit when it is closed. The essential 
 parts of any cell, therefore, are two dissimilar materials 
 immersed in a solution, one of which is more readily acted 
 upon by the solution than the other. The greater this 
 difference in intensity in chemical action, the greater the 
 difference in potential between the terminals of the cell. 
 
 Copper, platinum, silver, and zinc are the only metals 
 
PEIMAKY BATTEEIES 63 
 
 that have been mentioned up to the present time, but other 
 metals may be used, and since the intensity of chemical 
 action will be different for different metals, there will be 
 combinations that will produce better results than others. 
 For example, a cell composed of zinc and tin would not 
 produce as large an electromotive force as one composed 
 of zinc and copper the same size, because there is a greater 
 difference of electrical potential between the zinc and the 
 copper than there is between the zinc and the tin. 
 
 The solution used in the cell also determines the value 
 of the difference in potential between any combination of 
 plates. There will be a different value for the potential 
 difference between any two plates when they are immersed 
 in different liquids. 
 
 When the same kinds of metals and solution are used, the 
 potential difference between the plates will be the same, 
 regardless of the areas of the plates. A small battery will 
 have the same electromotive force as a large one composed 
 of the same materials. 
 
 In the following list, the substances are arranged in order 
 depending upon the degree of chemical action when placed 
 in dilute sulphuric acid: Zinc, Iron, Tin, Lead, Copper, 
 Silver, Platinum, and Carbon. 
 
 70. Classification of Cells. (a) If a cell is capable of 
 producing a current directly from the consumption in it of 
 some substance, such as zinc, it is a primary cell. If, how- 
 ever, a current must first be sent through the cell to bring 
 it to such a condition that it is capable of producing a cur- 
 rent, it is called a secondary, or storage, cell. The funda- 
 mental distinction then between a primary and a secondary, 
 or storage, cell is that, with the latter type the chemical 
 changes are reversible, while with the former type this is not 
 practical even when possible. The discussion of the storage 
 cell will be taken up in a later chapter. 
 
 (b) Cells are also classified into closed- and open-circuit 
 types, depending upon whether they are or are not capable 
 of furnishing a current continuously. This classification is 
 entirely dependent upon the polarization the cell which 
 does not polarize being able to maintain its current until 
 its chemical substances are exhausted. 
 
 The Grenet and the Leclanche are perhaps the best exam- 
 
64 
 
 PKACTICAL APPLIED ELECTRICITY 
 
 pies of the open-circuit cells, while the Daniell, the Lalande, 
 and the Fuller are good examples of the closed-circuit cell. 
 
 (c) All cells must be made up of two substances im- 
 mersed in a liquid, but in some cases there are different 
 liquids separated by gravity or a porous cup. Cells may then 
 be classified, as to their construction, into single-fluid cells 
 and double-fluid cells. The Grenet, Leclanche, and Lalande 
 are good examples of single-fluid cells, while the Bunsen, 
 Fuller, Daniell, and Grove are perhaps the best examples 
 of the double-fluid type. 
 
 71. Forms of Primary Cells. The various cells given in 
 Table No. V are the principal ones that are used to any 
 extent and the construction of a few of these will be given in 
 detail in the following sections. 
 
 TABLE NO. V 
 PRIMARY CELLS 
 
 Names of 
 Cell 
 
 Negative 
 Pole 
 
 Positive 
 Pole 
 
 Solution 
 
 Depolariz- 
 ing Agent 
 
 E.M.F. 
 in 
 Volts 
 
 Internal 
 Resistance 
 in Ohms 
 
 Smee 
 
 Zinc 
 
 Platinized 
 
 Solution of 
 
 None 
 
 .65 
 
 0.5 
 
 
 
 Silver 
 
 Sulphuric 
 Acid 
 
 
 
 
 Grenet 
 
 Zinc 
 
 Graphite 
 (Carbon) 
 
 Solution of 
 Sulphuric 
 Acid 
 
 Potassium 
 Bichro- 
 mate 
 
 2.1 
 
 2 to .5 
 
 Leclanche. 
 
 Zinc 
 
 Graphite 
 (Carbon) 
 
 Ammoni'm 
 Chloride 
 
 Manganese 
 Dioxide 
 
 .5 to 
 
 1.6 
 
 1.5 
 
 Daniell.... 
 
 Zinc 
 
 Copper 
 
 Zinc Sul- 
 phate 
 
 Copper 
 Sulphate 
 
 1.079 
 
 2 to 6 
 
 Lalande... 
 
 Zinc 
 
 Graphite 
 (Carbon) 
 
 Caustic 
 Potash or 
 Potassium 
 Hydrate 
 
 Cupric 
 Oxide 
 
 0.8 to 
 0.9 
 
 1.3 
 
 Fuller 
 
 Zinc 
 
 Graphite 
 (Carbon) 
 
 Sulphuric 
 Acid 
 
 Potassium 
 Bichro- 
 mate 
 
 2.0 
 
 0.5 to 0.7 
 
 Bunsen.. .. 
 
 Zinc 
 
 Graphite 
 (Carbon) 
 
 Dilute 
 Sulphuric 
 Acid 
 
 Nitric 
 Acid 
 
 1.8 to 
 1.98 
 
 .08 to. 11 
 
 Grove 
 
 Clark 
 Standard,. 
 
 Zinc 
 Zinc 
 
 Platinum 
 Mercury 
 
 Dilute 
 Sulphuric 
 Acid 
 
 Zinc 
 Sulphate 
 
 Nitric 
 Acid 
 
 Mercurous 
 Sulphate 
 
 1.96 
 1.434 
 
 .lto.12 
 .3 to .5 
 
 Weston.... 
 
 Cadmium 
 
 Mercury 
 
 Cadmium 
 Sulphate 
 
 Mercurous 
 Sulphate 
 
 1.01830 
 
 
PRIMARY BATTERIES 65 
 
 72. Chemicals Used in Cells and Their Symbols. 
 
 Sulphuric Acid, H 2 SO 4 . 
 
 Chromic Acid, CrO 3 . 
 
 Manganese Dioxide, MnO. 
 
 Zinc Chloride, ZnCl 2 . 
 
 Lead Oxide, PbO. 
 
 Zinc Sulphate, ZnSO 4 . 
 
 Nitric Acid, HNO 3 . 
 
 Hydrochloric Acid, HC1. 
 
 Silver Chloride, AgCl. 
 
 Copper Oxide, CuO. 
 
 Lead Peroxide, PbO 2 . 
 
 Sodium Chloride, NaCl. 
 
 Caustic Potash or Potassium Hydrate, KOH. 
 
 Copper Sulphate (blue vitriol), CuSO 4 . 
 
 Zinc Sulphate (white vitriol), ZnSO 4 . 
 
 Ammonium Chloride (sal-ammoniac), NH 4 C1. 
 
 Bichromate of Potassium, K 2 Cr 2 O 7 . 
 
 Bichromate of Soda, Na 2 Cr 2 O 7 . 
 
 Mercurous Sulphate, Hg 2 SO 4 . 
 
 Cadmium Sulphate, CdSO 4 . 
 
 73. Mechanical Depolarization. The Smee cell has been 
 mentioned in section (67) as a good example of a mechanical 
 means of preventing polarization. This cell was used com- 
 mercially a number of years ago, but it was not very suc- 
 cessful. A Smee cell is shown in Fig. 24. 
 
 There are a number of cells used for intermittent work, 
 such as ringing door bells, that depend entirely upon the 
 use of a large positive plate surface to lessen the rapidity 
 of polarization. They consist usually of zinc and carbon 
 plates immersed in a solution of sal ammoniac (ammonium 
 chloride), see section (72). The carbons for such cells are 
 made in almost endless variety and with very large surface. 
 
 74. Chemical Depolarization. Bichromate Cells. There 
 are a number of different forms of bichromate cells, the 
 principal ones of which are perhaps the Grenet and Fuller. 
 
 (a) Grenet Cell. In this form a zinc plate is suspended 
 by a rod between two carbon plates, see Fig. 25, so that 
 it does not touch them, and when the cell is not in use the 
 zinc can be removed from the solution by raising and fasten- 
 
66 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 ing the rod by means of a set screw, as the acid acts on 
 the zinc when the cell is not in use. Sulphuric acid and 
 water is the solution used in this cell, to which is added 
 potassium bichromate that acts as the depolarizer. The 
 bichromate is rich in oxygen, which readily combines with 
 the liberated hydrogen and thus prevents polarization. This 
 
 Fig. 24 
 
 Fig. 
 
 cell gives a large e.m.f. and is capable of supplying a 
 strong current for a short time, but the liquid soon becomes 
 exhausted. 
 
 (b) Fuller Cell. This form of bichromate cell is a double 
 fluid type, and has the advantage over the Grenet type in 
 that the zinc is always kept well amalgamated and it is not 
 necessary to remove it from the solution. A pyramidal block 
 of zinc is placed in a. small porous cup ; Fig. 26, and a 
 small quantity of mercury poured in. The cup is then filled 
 with a diluted solution of sulphuric acid and placed in a 
 glass jar containing a solution of potassium bichromate 
 and the carbon plate (P). A conductor, covered with a suit- 
 able insulation, is attached to the block of zinc and serves as 
 one terminal of the cell. The zinc is well amalgamated by 
 the mercury and there is practically no local action. The 
 
PKIMAKY BATTERIES 
 
 67 
 
 cell gives a large e.m.f. and may be used for open circuit 
 or semi-closed circuit work. 
 
 75. Chemical Depolarization. Leclanche. This cell con- 
 sists of a zinc plate in a solution of ammonium chloride and 
 a carbon plate placed inside a porous cup which is packed 
 full of manganese dioxide and powdered carbon. The action 
 of the manganese dioxide on the hydrogen is not quick 
 enough to prevent polarization entirely when large currents 
 
 Zinc 
 
 Fig. 26 
 
 Fig. 27 
 
 are taken from the cell. The cell, however, will recover 
 when allowed to stand on open circuit. A great advantage of 
 this type of cell lies in the fact that the zinc is not acted 
 on at all by the ammonium chloride when the cell is on 
 open circuit, and as a result it can be left for almost an 
 indefinite period when the circuit is open without deteriora- 
 tion. These cells are usually used for intermittent work, 
 such as ringing door bells, and will supply quite a large 
 current for a short time. Their e.m.f. is about 1.5 volts. 
 Leclanche cells are called open-circuit cells on account of 
 the very slight chemical action that takes place when the 
 circuit is open. A Leclanche cell is shown in Fig. 27. 
 
 76. Electro-Chemical Depolarization. Daniel! Cells. This 
 type of cell consists of a zinc plate immersed in a solu- 
 tion of zinc sulphate and a copper plate immersed in a 
 
68 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 solution of copper sulphate. The two liquids may be kept 
 apart either by gravity or by a porous earthen cup, as shown 
 in Fig. 28. When the solutions are kept separated by grav- 
 ity, the cell is called the gravity, or crowfoot type. A cross- 
 section of a Daniell cell, in which the liquids are separated 
 by a porous cup, is shown in Fig. 29. The gravity cell is 
 
 "t* PorousCup 
 
 Fig. 28 
 
 Fig. 29 
 
 shown in Fig. 30. The copper sulphate being the heavier 
 of the two liquids remains at the bottom about the plate 
 of copper, while the zinc sulphate remains at the top about 
 the zinc plate. This cell will give a very constant e.m.f. of 
 about 1.08 volts. It has a large internal resistance (two 
 to six ohms) and as a result is not capable of supplying 
 a very large current. The current supplied, however, is con- 
 stant, and it will operate for a great length of time without 
 renewal. 
 
 The Daniell cell is a closed-circuit cell and it should 
 never be allowed to stand on open circuit, but a resistance 
 (thirty to fifty ohms) should always be connected across 
 its terminals. 
 
 77. Dry Cells. The dry cell is a special form of the 
 Leclanche cell first described. The cell is not altogether 
 dry, since the zinc and carbon plates are placed in a moist 
 paste which consists usually of . ammonium chloride, one 
 part; plaster of Paris, three parts; zinc chloride, one part; 
 
PRIMARY BATTERIES 69 
 
 zinc oxide, one part, and sawdust. These various materials*, 
 composing the above mixture are thoroughly mixed and then 
 moistened with a small quantity of water. The paste thus 
 formed is packed around a carbon rod, placed inside a zinc 
 cup lined with moistened blotting paper, and the cup is sealed 
 with some kind of wax to prevent evaporation. There are a 
 large number of different makes of dry cells on the market 
 at the present time but the chemical action in each is prac- 
 tically the same. The dry cell is a very convenient form 
 of cell and its operation is very satisfactory for work requir- 
 ing an intermittent current. Fig. 31 shows a cross-section 
 through a dry cell. 
 
 Paste Board 
 Covering 
 
 Pitch 
 ; Zinc Cup 
 
 filling 
 
 Carbon 
 Blotting 
 Paper 
 
 
 Fig. 30 
 
 Fig. 31 
 
 78. Standard Cells. A standard cell is one whose e.m.f. 
 can be accurately calculated and will remain constant. The 
 Clark Standard cell and the Weston cell are the two best 
 examples of standard cells. The Clark cell has an e.m.f. of 
 1.434 volts at 15 C. and a correction must be made in this 
 value when the cell is used at some other temperature. 
 
 The Weston normal cell has an e.m.f. of 1.01830 volts and 
 there is practically no change in its e.m.f. due to a change 
 in temperature. A Weston standard cell, as manufactured by 
 the Weston Electrical Instrument Company, is shown in 
 Fig. 32. The e.m.f. of different Weston cells is not exactly 
 the same, but they are standardized in the factory and a 
 certificate accompanies each cell. The average e.m.f. of a 
 
70 PRACTICAL APPLIED ELECTK1CITY 
 
 number of cells tested by the Bureau of Standards at Wash- 
 ington, D. C., was 1.01869 volts. 
 
 A great amount of care is exercised in assembling standard 
 cells, to see that the materials used are the very best and 
 that they are all constructed alike. 
 
 79. Requirements of Good Cell. 
 A good cell should fulfill all, or 
 the greater part, of the following 
 conditions: 
 
 (a) Its electromotive force 
 should be high and constant. 
 
 (b) Its internal resistance should 
 be small. 
 
 (c) It should be capable of sup- 
 plying a constant current, and, 
 therefore, entirely free from polari- 
 zation, and not liable to rapid 
 
 32 exhaustion, requiring frequent re- 
 
 newals of the liquid or plates. 
 
 (d) It should be free from local action. 
 
 (e) It should be cheap and of durable materials which 
 results in a low cost for renewals when they are required. 
 
 (f) It should be easily managed, and, if possible, should 
 not emit corrosive fumes. 
 
 No particular cell fulfills all of the above conditions, how- 
 ever, and some cells are better for one purpose than others. 
 Thus, for telegraph work over a long line, a cell of consid- 
 erable internal resistance is no great disadvantage; while a 
 large internal resistance is a great disadvantage when the 
 cell is supplying current to a circuit of corresponding low 
 resistance. An open-circuit cell would not operate satisfac- 
 torily in driving a small motor, but would be quite satisfac- 
 tory for intermittent work; while the closed-circuit type 
 would be very unsatisfactory for intermittent work. 
 
 80. Series Connection of Cells. Any number of cells are 
 said to be connected in series when the positive terminal 
 of one is connected to the negative terminal of another, 
 and so on. When all of the cells are connected, there remains 
 a positive and a negative terminal which form the terminals 
 of the battery. If (n) cells are connected in series, as shown 
 in Fig. 33, and they each have an e.m.f. of (e) volts, the 
 
PRIMARY BATTERIES 
 
 71 
 
 combination will have an e.m.f. of (ne) volts. The internal 
 resistance of the battery will be equal to (nr) ohms where 
 (r) is the internal resistance of each cell. If the external 
 resistance or the resistance of the circuit to which the battery 
 is connected is (R) ohms, then the current produced by the 
 combination will be 
 
 ne 
 
 1 = (70) 
 
 R-f-nr 
 
 In the above equation (R + nr) represents the total resist- 
 ance of the entire circuit and (ne) the total electromotive 
 
 Fig. 34 
 
 force acting in the circuit. Fig. 33 sho\\rf three cells con- 
 nected in series and the battery thus formed connected to 
 a resistance (R). 
 
 Fig. 34 shows a hydraulic analogy similar to the connection 
 of cells in series. The pumps (Pi) and (P 2 ) are so arranged 
 that their pressures are added, the total pressure acting in 
 the circuit being equal to the sum of the pressures produced 
 by the respective pumps. If there is no water flowing and 
 the gauge (G^ reads zero, then (G 2 ) reads the pressure 
 produced by the pump (Pj). The difference in the readings 
 of (G 3 ) and (G 2 ) is the pressure produced by the pump 
 (P 2 ). Hence (G 3 ) reads the total pressure produced by the 
 two pumps combined when (Gi) reads zero and no water is 
 flowing. When there is a flow of water, however, part of the 
 pressure produced by the pumps is used in causing the water 
 to pass through them or to overcome their internal resistance, 
 and as a result the indication on (G ;} ) is reduced. 
 
 Example. Six cells having an e.m.f. of 1.5 volts each and 
 an internal resistance of .6 ohm each are connected in series 
 
72 PRACTICAL APPLIED ELECTRICITY 
 
 with a resistance of 10 ohms. -What is the current in 
 the resistance when the circuit is closed? 
 
 Solution. By a direct substitution in equation (70) we 
 have 
 
 6 X 1.5 9 9 
 
 I = = 6.62 
 
 10 + (6 X .6) 10 + 3.6 13.6 
 
 Ans. 6.62 amperes. 
 
 81. Parallel Connection of Cells. When (n) cells, all 
 having the same e.m.f., are all connected in parallel, then 
 the e.m.f. of the combination is only that of a single cell. 
 The internal resistance of a battery formed of a number of 
 cells connected in parallel is less than the internal resistance 
 
 I vwww i 
 
 Fig. 35 
 
 Fig. 36 
 
 of a single cell. If (r) is the internal resistance of each cell, 
 and there are (n) cells in parallel, then the total internal 
 
 resistance will be \^~J. If the resistance of the external 
 circuit is (R) ohms, then the current produced by the com- 
 bination will be 
 
 r 
 
 R + - 
 n 
 
 (71) 
 
 In the above equation 
 
 ~ is the total resistance of 
 
PKIMAEY BATTERIES 73 
 
 the entire circuit, and (e) is the electromotive force acting 
 on this resistance. 
 
 Fig. 35 shows three cells connected in parallel and the 
 battery thus formed connected to a resistance (R). 
 
 Fig. 36 shows a hydraulic analogy similar to the con- 
 nection of cells in parallel. The pumps (Pj) and (P 2 ) are 
 so connected that their pressures are not added, but the 
 quantity of water supplied will be equal to that supplied 
 by both pumps. 
 
 Example. Six cells having an e.m.f. of 1.5 volts each and 
 an internal resistance of .6 ohm each are connected in 
 parallel, and the combination is then connected to a resist- 
 ance of 10 ohms. What current exists in the resistance when 
 the circuit is closed? 
 
 Solution. By a direct substitution in equation (71) we 
 have 
 
 1.5 1.5 
 
 I = - = -- = 0.148+ 
 
 .6 10.1 
 10 + 
 6. 
 
 Ans. 0.148+ ampere. 
 
 82. Series and Parallel Combinations. A very common 
 grouping of cells is a combination of the series and the par- 
 allel groups. Suppose there are (P) groups of cells and each 
 group consists of (S) cells in series. The total number of 
 cells is then equal to (SP). The e.m.f. will be (Se) volts, 
 the internal resistance of each set will be (Sr) ohms, and 
 the internal resistance of the (P) sets combined will be 
 
 ohms. If the external resistance is (R) ohms, then 
 
 the total resistance will be (R^^p) ohms, and the current 
 produced by the combination will be 
 
 Se PSe 
 
 (72) 
 PR + Sr 
 
74 PRACTICAL APPLIED ELECTRICITY 
 
 Fig. 37 shows a battery composed of three groups of cells 
 and there are three cells connected in series in each group. 
 The battery is connected to a resistance (R). 
 
 Example. A battery is composed of nine cells connected, 
 as shown in Fig. 37, to an external resistance of 10 ohms. 
 The e.m.f. of each cell is 1.5 volts; each cell has an internal 
 resistance of .5 ohm. What current will the battery supply 
 when the circuit is closed? 
 
 Solution. Substituting directly in equation (72), we have 
 
 3 X 3 X 1.5 13.5 
 
 1 = - = 0.428 + 
 
 (3 X 10) + (3 X .5) 31.5 
 
 Ans. 0.428+ ampere. 
 83. Advantage of Series and Par- 
 
 ^_ I | I allel Connections. -Cells are con- 
 
 ' | r~| r~| I ^ nected in parallel when it is desired 
 to obtain a large current through 
 a low external resistance. When the 
 cells are so grouped they are equiva- 
 lent to one large cell, and will have 
 a very low internal resistance, and 
 when connected to a low external 
 resistance, as compared to the inter- 
 Fig. 37 nal resistance, the current will be 
 large. If the external resistance 
 
 is large, the current will be small, as the electromotive 
 force acting is small. The series connection is employed 
 when the external resistance is the principal resistance to 
 overcome and the maximum current strength is desired in 
 the circuit. 
 
 PROBLEMS ON GROUPING OF CELLS 
 
 (1) How many cells should be connected in series to 
 cause a current of 1.5 amperes in an external resistance of 
 8 ohms. The e.m.f. of each cell is 1.5 volts, and its internal 
 resistance is .2 ohm. 
 
 Ans. 10 cells. 
 
 (2) How many cells must be connected in parallel to 
 cause a current of 2 amperes in an external resistance of .6 
 
 HHH 
 -HHH 
 
PRIMARY BATTERIES 75 
 
 ohm. The e.m.f. of each cell is 1.5 volts and its internal 
 resistance is 1.2 ohms. 
 
 Ans. 8 cells. 
 
 (3) Ten cells, each having an e.m.f. of 2.2 volts and an 
 internal resistance of .07 ohm, are connected in series to a cir- 
 cuit whose resistance is 4.3 ohms. What current exists in the 
 circuit? 
 
 Ans. 4.4 amperes. 
 
 (4) Twenty storage cells are connected in series-multiple, 
 there being five groups in parallel and four cells in series 
 in each group. The e.m.f. of each cell is 2.2 volts and its 
 internal resistance is .05 ohm. What current will the com- 
 bination produce through an external resistance of .4 ohm? 
 
 Ans. 20 amperes. 
 
 (5) Five cells are connected in series. Each cell has an 
 e.m.f. of 2 volts and an internal resistance of .2 ohm. What 
 is the terminal voltage of the battery on open circuit and 
 also when it is connected to an external resistance of 4 
 ohms? 
 
 Ans. Open-circuit voltage = 10 volts. 
 Closed-circuit voltage = 8 volts. 
 
 Note. (There will be a drop in terminal voltage when the 
 circuit is closed on account of the internal resistance.) 
 
 (6) Twenty cells, each having an e.m.f. of 2 volts and an 
 internal resistance of .2 ohm, are to be connected so that 
 they will give the maximum current through an external 
 resistance of 1 ohm. What combination should be used? 
 Ans. Two groups, in parallel, each group having ten cells 
 
 in series. 
 
 Note. (The maximum current is obtained from any com- 
 bination of cells when they are so connected that their 
 combined internal resistance is equal to the external resist- 
 ance to which they are connected). 
 
 Solution. Let (S) equal the number of cells in series in 
 any one group and then (n -t- S) will equal the number of 
 groups in parallel. Then in order that the maximum cuir- 
 rent be obtained from the battery 
 
76 PBACTICAL APPLIED ELECTKICITY 
 
 SXr 
 must equal 1.0 
 
 (n-K.8) 
 
 or 
 
 S X .2 .282 2S2 S2 
 
 20 20 200 100 
 
 
 
 8 
 
 S2 = 100 
 
 S= 10 
 
 (7) How many cells, each having an e.m.f. of 2.2 volts 
 and an internal resistance of .005 ohm, must be connected 
 in series in order that the terminal voltage may be at least 
 44 volts when the current through tLe battery is 40 amperes? 
 
 Ans. 22 cells. 
 
 (8) The terminal voltage of a battery drops from 1.8 
 volts on open circuit to 1.5 volts when there is a current 
 of 6 amperes through the battery. What is the internal 
 resistance of the battery? 
 
 Ans. .5 ohm. 
 
CHAPTER V 
 
 MAGNETISM 
 
 84. The Magnet. The name magnet was given by the 
 ancients to certain black stones, found in various parts of 
 the world, principally at Magnesia in Asia Minor, which 
 possessed the property of attracting to them small pieces 
 of iron or steel. This magic property, as they deemed it, 
 made the magnet-stone famous; but it was not until about 
 the twelfth century that such stones were discovered to have 
 the still more remarkable property of pointing approximately 
 north and south when freely suspended by a thread. This 
 property of the magnet-stone led to its use in navigation, 
 and from that time the magnet received the name of "lode- 
 stone," or "leading stone." The natural magnet, or lodestone, 
 is an ore of iron, and is called magnetite. Its chemical, 
 composition is Fe 3 O 4 . This is found in quite large quantities 
 in Sweden, Spain, and Arkansas, U. S. A., and other parts 
 of the world, but not always in the magnetic state. 
 
 85. Artificial Magnets. If a piece of iron, or, better still, 
 a piece of hard steel, be rubbed with a lodestone, it will be 
 found to possess the properties or characteristic of the mag- 
 net, viz, it will attract light 
 
 bits of iron; it will point ap- 
 proximately north and south 
 if hung up by a thread; 
 and it can be used to magne- 
 tize another piece of iron Fig. 38 
 or steel. Magnets made in 
 this manner are called artificial magnets. 
 
 Strong artificial magnets are not made from lodestone, 
 as its magnetic force is not strong, but by methods as de- 
 scribed under "Electromagnetism." Figs. 38 and 39 show, 
 respectively, a natural and an artificial magnet, each of which 
 
 77 
 
78 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 has been dipped into iron filings; the filings are attracted 
 and adhere in tufts at the ends. 
 
 86. Poles of a Magnet. Certain parts of a magnet possess 
 the property of attracting iron to a greater extent than do 
 other parts. These parts are called the poles of the magnet. 
 
 The poles of a bar magnet, 
 for example, are usually 
 situated at or near the 
 ends of the bar, as shown 
 in Fig. 38. 
 
 87. Magnetic Needle.- 
 The magnetic needle con- 
 Fig. 39 sists of a light needle cut 
 
 out of steel, and fitted 
 
 with a cap of glass, or agate, by means of which it can be 
 supported on a sharp point, so as to turn with very little 
 friction. This needle is made into a magnet by being rubbed 
 on a magnet; and when placed on its support will turn into 
 the rorth-and-south position, or, as we should say, will set 
 itself in the "magnetic meridian." The end of the needle 
 that points toward the north geographical pole is called the 
 North Pole, and is usually marked with the letter N, while 
 the other end is the South Pole. 
 
 By the term polarity is 
 meant the nature of the 
 magnetism at some particu- 
 lar point, that is, whether it 
 is north or south-seeking 
 magnetism. The compass 
 sold by opticians consists of 
 such a needle balanced 
 above a card marked with 
 the "points of the compass" 
 
 and the whole placed in a suitable containing case. A com- 
 mon form of the magnetic needle is shown in Fig. 40. 
 
 88. Magnetic Attraction and Repulsion. When the two 
 poles of a magnet are presented in turn to the north-pointing 
 pole of a magnetic needle, it will be observed that one pole 
 of the magnet attracts it, while the other repels it. If the 
 magnet is presented to the south-pointing pole of the mag- 
 netic needle, it will be. repelled by one pole and attracted 
 
 
MAGNETISM 79 
 
 by the other. The same pole that attracts the north-pointing 
 end of the magnetic needle repels the south-pointing end. 
 As the needle and the magnet attract each other when unlike 
 poles are presented, and repel each other when like poles 
 are presented, it follows that like poles always repel each 
 other and unlike poles always attract each other. Fig. 41 
 shows the results of presenting two like poles and Fig. 42 
 shows the result of presenting two unlike poles. 
 
 Fig. 41 Fig. 42 
 
 Two equal and like poles are said to have unit strength 
 when there is a force of repulsion between them of one 
 dyne when placed one centimeter apart in air. 
 
 89. Magnetizable Metals. The principal magnetic metals 
 used in practice are steel and iron. There are other metals, 
 such as nickel, cobalt, chromium, and cerium, that are at- 
 tracted by a magnet, but very feebly. Of this last class 
 cobalt and nickel are the best, but very inferior to iron or 
 steel. All other substances, such as wood, lead, gold, copper, 
 glass, platinum, etc., may be regarded as unmagnetizable, 
 or nonmagnetic substances. Magnetic attraction or repul- 
 sion will, however, take place through these substances. 
 
 90. Magnetic Force. The force with which a magnet 
 attracts or repels another magnet, or any piece of iron or 
 steel, is termed its magnetic force. The value of this mag- 
 netic force is not the same for all distances, the value being 
 greater when the magnet is nearer, and less when the magnet 
 is further off. The value of this force of attraction or repul- 
 sion decreases inversely as the square of the distance from 
 the pole of the magnet. The force is mutual, that is, the 
 
80 
 
 PBACTICAL APPLIED ELECTRICITY 
 
 iron attracts the magnet just as much as the magnet attracts 
 the iron. 
 
 91. Magnetic Lines of Force. The magnetic force pro- 
 duced by a magnet emanates in all directions from the mag- 
 net. The direction of the magnetic force at any point 
 near a magnet can be determined by means of a small 
 compass needle suspended at the point in such a way that it 
 is free to move in any direction. The direction at any other 
 point can be determined by changing the position of the 
 needle with respect to the magnet. Starting with the needle 
 near one end of the magnet, it may be carried toward the 
 other end and an imaginary line, drawn in such a way that 
 its direction at any point corresponds to the direction as- 
 sumed by the needle at that point, corresponds to what is 
 termed a line of force, or it is the path taken by a north 
 magnetic pole in moving from the north to the south pole 
 of a magnet. These lines of force start at the north pole 
 of a magnet and terminate at the south pole. Fig. 43 shows 
 such a line. 
 
 92. Magnetic Field. The region surrounding a magnet 
 which is permeated by magnetic lines of force is called a 
 
 Fig. 43 
 
 Fig. 44 
 
 magnetic field of force, or a magnetic field. The lines of 
 force forming a magnetic field emanate from the N-pole 
 of a magnet, pass through the medium surrounding the 
 magnet, re-enter the S-pole and complete their path by 
 passing from the S-pole to the N-Pole inside the magnet 
 itself. The magnetic field surrounding a bar magnet is 
 shown in Fig. 44. All magnetic lines form closed circuits 
 and there must be two or more magnetic poles (always even) 
 associated with each of these circuits except in the case of a 
 ring magnetized by a current, which will be discussed later. 
 
MAGNETISM 
 
 81 
 
 The region we speak of as a magnetic field is capable of 
 acting upon magnets, magnetic materials, and conductors 
 carrying a current of electricity. The lines of force forming 
 any magnetic field are assumed to have two properties: 
 First, they tend to contract in length; second, they repel 
 each other. The attraction and repulsion of unlike and like 
 poles can be accounted for by assuming the lines to possess 
 the above properties. 
 
 93. Making Magnetic Fields. A graphical representation 
 of a magnetic field may be made by placing a piece of card- 
 board over the magnet or magnets whose field you want to 
 produce, and sprinkle iron filings on the paper, tapping it 
 gently at the same time. The iron filings are composed of 
 a magnet material and arrange themselves in the direction 
 of the lines of force or magnetic field, and as a result produce 
 a graphical representation of the field. This representation 
 of the field can be made permanent by using a piece of paper 
 that has been dipped in paraffine instead of the cardboard. 
 
 N 
 
 Fig. 45 
 
 Fig. 46 
 
 The paraffine can be heated by means of a warm soldering 
 iron, or other warm non-magnetic material, which permits 
 the filings to imbed themselves in the wax and they will be 
 held firmly in place when the paraffine has cooled. 
 
 The magnetic field that exists between unlike poles is 
 shown in Fig. 45, and the field between like poles is shown 
 in Fig. 46. 
 
 94. Distortion of Magnetic Field. The direction of a mag- 
 netic field is influenced by the presence of magnetic material 
 or magnets. When a magnetic material is placed in any 
 magnetic field that exists in air, the form of the field will be 
 changed because the material is a better conductor of mag- 
 netic lines than air and the lines of force crowd into the 
 material. There will be a greater number of magnetic lines 
 
82 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 in a given area in the iron than there is in a corresponding 
 area in the air. A magnetic field that has been distorted, 
 due to the presence of a piece of iron, is shown in Fig. 47. 
 All materials that conduct magnetic lines better than air 
 are called paramagnetic, and those that do not conduct as 
 well as air are called diamagnetic substances. 
 
 Fig. 47 
 
 Fig. 48 
 
 95. Magnetic Induction. Magnetism may be communicated 
 to a piece of iron without actual contact with the magnet. 
 If a short, thin, unmagnetized bar of iron be placed near 
 some filings, and a magnet brought near to the bar, the 
 presence of the magnet will induce magnetism in the bar, and 
 it will now attract the iron filings, Fig. 48. The piece of 
 iron thus magnetized has two poles, the pole nearest to the 
 pole of the inducing magnet being of the opposite kind, while 
 the pole at the farther end of the bar is of the same kind as 
 the inducing pole. Magnetism can, however, only be induced 
 in those bodies that are composed of magnetic materials. 
 It is now apparent why a magnet should attract a piece of 
 iron that has never been magnetized; it first magnetizes it 
 by induction and then attracts it; as the nearest end will 
 be a pole of opposite polarity, it will be attracted with 
 a force exceeding that with which the more distant end is 
 repelled. 
 
 96. Retention of Magnetization. Not all of the magnetic 
 substances can be used in making permanent magnets, as 
 some of them do not retain their magnetism after being mag- 
 netized. The lodestone, steel, and nickel, retain permanently 
 the greater part of the magnetism imparted to them. Cast 
 iron and many impure qualities of wrought iron also retain 
 magnetism imperfectly. Pure, soft iron is, however, only 
 
MAGNETISM 83 
 
 temporarily magnetic. The above statements can be illus- 
 trated by the following experiment: Take several pieces 
 of soft iron, or a few soft iron nails, and place one of them 
 in contact with the pole of a permanent magnet, allowing it 
 to hang downward from the magnet, as shown in Fig. 49. 
 The piece of iron or nail is held to the magnet because it 
 has become a temporary magnet, due to the .process of mag- 
 netic induction. Another piece can be hung to the first, and 
 another to the second, etc., until a chain of four or five 
 pieces is formed. If now the steel magnet be removed from 
 the first piece of iron, or nail, all the remaining pieces drop 
 off and are no longer magnets. A similar chain formed of 
 steel needles will act in the same way, but they will retain 
 their magnetism permanently. 
 
 It is harder to get the magnetism into steel than into 
 iron, and it is harder to get the magnetism out of steel than 
 out of iron, because steel resists magnetization or demagneti- 
 zation to a greater extent than soft iron. This power of resist- 
 ing magnetization or demagnetization is called hysteresis. 
 
 97. Molecular Theory of Magnetism. There are quite a 
 number of experimental facts that lead to the conclusion that 
 magnetism has something to do with the molecules of the 
 
 Fig. 49 Fig. 50 
 
 substance, since any disturbance of the molecules causes a 
 change in the degree of magnetization. If a test tube full 
 of hard steel filings be magnetized, it will behave toward a 
 compass needle or other magnet as though it were a solid 
 bar magnet, but it will lose practically all of its magnet- 
 ism as soon as the fillings are rearranged with respect to 
 each other by giving the tube several good shakes. A 
 needle that has been magnetized will lose its magnetism 
 when heated. A magnet may be broken into any number of 
 
84 PRACTICAL APPLIED ELECTRICITY 
 
 different pieces and there will appear at each break an N- 
 pole and an S-pole, as shown in Fig. 50. The strength of 
 the poles of any magnet will be greatly reduced by ham- 
 mering, twisting, or bending it. A theory often used to explain 
 certain magnetic phenomena is as follows: In an unmagne- 
 tized bar it is assumed that the molecules are each a tiny 
 
 magnet, and that these 
 molecules or magnets are 
 arranged in no definite way, 
 
 except that the opposite 
 poles neutralize each other 
 throughout the bar. The 
 theoretical arrangement of 
 
 the molecules in an unmagnetized bar is shown in Fig. 
 51. When the bar is brought into a magnetic field, the tiny 
 magnets are turned, due to the action of the outside force, 
 so that the N-poles tend to point in one direction and their 
 S-poles in the other. The arrangement of the molecules after 
 the bar has been magnetized is shown in Fig. 52. The 
 opposite poles neutralize each other in the middle of the bar 
 but there will be an N^pole found at one end and an S-pole 
 at the other. 
 
 The ease with which any 
 
 material may be magnetized 
 
 as compared to some other 
 
 material will depend upon 
 
 what might be termed the 
 
 molecular friction of the ma- Fig - 52 
 
 terial. Thus, the molecules in 
 
 a bar of steel offer a greater resistance to a change in their 
 
 position than do the molecules in cast iron. Steel, as a result, 
 
 is harder to magnetize than cast iron, and it will also retain 
 
 its magnetism after once magnetized better than cast iron for 
 
 the same reason. 
 
 98. Application of Permanent Magnets. Permanent mag- 
 nets are made to assume many different forms, depending 
 upon the particular use to which they are to be placed. In 
 the majority of cases the bar forming the magnet is bent 
 into such a form that both poles will produce an effect 
 instead of only one pole. Thus, instead of using a straight bar 
 magnet in picking up a piece of iron, as shown in Fig. 53, the 
 
MAGNETISM 
 
 85 
 
 bar can be bent into a U-shape and both poles presented to 
 the piece to be picked up as shown in Fig. 54. The effect 
 of the two poles in the second case will, of course, be greater 
 
 Fig. 53 
 
 Fig. 54 
 
 than the single pole in the first. A magnet such as that shown 
 in Fig. 54 is called a horseshoe magnet. 
 
 Permanent magnets are used for numerous different pur- 
 poses, such as in telephone receivers, relays, ringers, measur- 
 ing instruments, etc. 
 
CHAPTER VI 
 
 ELECTRON! AGNETISM 
 
 99. Magnet Field Around a Conductor Carrying a Current. 
 In 1819, Oersted discovered that a magnetic needle was dis- 
 turbed by the presence of a conductor carrying a current, 
 and that the needle always tended to set itself at right an- 
 gles to the conductor. If a magnetic needle be placed below 
 
 Fig. 55 
 
 a wire, as shown in Fig. 55, the current in the wire being 
 from left to right, as indicated by the arrow, the needle 
 will tend to move in the direction indicated by the curved 
 arrows. If the current in the conductor be reversed, the 
 direction of the magnetic needle will be reversed. It is thus 
 seen that there is a magnetic field set up about a conductor 
 carrying a current and that the direction of this magnetic 
 field will depend upon the direction of the current in the 
 conductor. Magnetism set up in this way by an electric 
 current is called electromagnetism. 
 
 100. Direction of an Electromagnetic Field. Remembering 
 that the direction of a magnet field may be determined 
 by placing a compass needle in the field -and determining 
 the direction in which the N-pole of the needle will point 
 this being taken as the positive direction you can determine 
 the direction of the magnetic field surrounding a conductor, 
 produced by a current in the conductor. The small circle 
 
 86 
 
ELECTBOMAGNETISM 
 
 8? 
 
 in Fig. 56 represents the cross-section of a conductor that 
 can be imagined as passing through the paper. The direc- 
 tion of current in this conductor is away from the observer, 
 and this fact is indicated by the plus sign ( + ) inside the 
 circle. A compass needle placed below this conductor will 
 set itself in such a position that the N-pole is toward the 
 left and the S-pole is toward the right. If the compass needle 
 be placed above the conductor, as shown in Fig. 57, the N- 
 pole will point toward the right and the S-pole toward the 
 
 Fig. 5(5 
 
 left. When the current is reversed in direction, that is, the 
 flow is toward the observer which is indicated by the minus 
 sign ( ) inside of the circle the positions assumed by the 
 compass needle will be just the reverse of those shown in 
 Figs. 56 and 57. 
 
 Fig. 58 
 
 If a conductor is passed through a small opening in the 
 center of a piece of cardboard that is supported in a hori- 
 zontal position, as shown in Fig. 58, and a current is passed 
 through the conductor, the field may be explored by means 
 of a small compass needle. When the current in the con- 
 
88 
 
 PBACTICAL APPLIED ELECTKICITY 
 
 ductor is down through the cardboard, as indicated by the 
 arrow (I) in the figure, the needle will assume a position 
 at right angles to the conductor (neglecting the effect of 
 the earth's magnetic field) and the N-pole will point, when 
 you are looking down upon the cardboard, in the direction 
 the hands of a clock move. The dotted line drawn on the 
 surface of the cardboard indicates the path that an N-pole 
 
 would move in, in passing 
 around the conductor. The 
 arrow on the dotted line 
 indicates the direction in 
 which the pole would 
 move. If the current in 
 the conductor were re- 
 versed, the direction of 
 motion, or the direction of 
 the field, would be reversed. 
 Iron filings may be 
 sprinkled on the cardboard 
 and they will form con- 
 Fig. 59 centric circles about the 
 conductor which corre- 
 spond to the lines of magnetic force produced by the cur- 
 rent. A field formed in this way is shown in Fig. 59. 
 
 101. Rules for Determining the Direction of a Field About 
 a Conductor Carrying a Current. There are a number of 
 different ways of remembering the relation between the di- 
 rection of a magnetic field and the direction of the cur- 
 rent producing it. A very simple rule that is known as 
 the "right-hand rule" is as follows: Grasp the conductor 
 carrying the current with the right hand, the thumb being 
 placed along the wire and the fingers being wrapped around 
 the wire; then the fingers point in the direction of the 
 magnetic field produced by the current in the wire when 
 the thumb points in the direction in which the current passes 
 through the wire. 
 
 If a person looks along a conductor, carrying a current, 
 in the direction of the current, the direction of the magnetic 
 field surrounding the conductor will be clockwise. 
 
 Another rule known as the "right-hand screw rule" is as 
 follows: Consider a right-handed screw which is being 
 
ELECTEOMAGNETISM 
 
 89 
 
 screwed into or out of a block, as shown in Fig. 60. If 
 an electric current is supposed to exist through the screw 
 in the direction in which the screw moves through the block, 
 then the direction of the magnetic field will correspond to 
 the direction in which the screw turns. 
 
 102. Strength of Magnetic Field. The strength of any 
 magnetic field is measured in terms of the number of lines 
 of force per unit area, usually one square centimeter per- 
 pendicular to the direction of the field. The symbol used 
 to indicate field strength is the letter (H). The properties 
 of the magnetic field surrounding a conductor carrying a 
 current are the same as those possessed by the magnetic 
 field produced by a permanent magnet. The strength of a 
 
 Fig. 60 
 
 Fig. 61 
 
 magnetic field at a certain point, due to a current in a con- 
 ductor or a permanent magnet, will depend directly upon 
 the strength of the current in the conductor, or the strength 
 of the permanent magnet, and inversely as the square of the 
 average distance the point is from the conductor or perma- 
 nent magnet. 
 
 103. Solenoid. A little consideration will show that if a 
 current be carried below a compass needle in one direction, 
 and then back in the opposite direction above the needle 
 by bending the wire around, as shown in Fig. 61, the forces 
 exerted on the needle, due to the current in the upper and 
 lower portions of the wire, will be in the same direction. 
 If the needle is the same distance from each portion of the 
 circuit the effect of the two parts will be just double that 
 
90 PRACTICAL APPLIED ELECTRICITY 
 
 produced by either part acting alone. Hence, if the wire 
 be coiled about the needle, each additional turn will produce 
 an additional force tending to turn the needle from its nor- 
 mal position. The magnetic effect of any current can be 
 greatly increased in this way. 
 
 A cross-section through a single turn of wire is shown in 
 
 Fig. 62. The current is 
 away from the observer in 
 
 /' / /' ,''"^x \ \ ' the upper part of the con- 
 
 , ductor > and toward the 
 ''' observer in the lower part, 
 as indicated by the ( + ) 
 and ( ) signs. The direc- 
 * tion o f the magnetic field 
 ^ surrounding the upper 
 '\ \ V _",-'' ' ) \ cross-section will be clock- 
 wise, as indicated by the 
 
 Fig- C'J arrows on the curves 
 
 drawn about it, while the 
 
 direction of the field surrounding the lower cross-section will 
 be counter clockwise, as indicated by the arrows, since the 
 current is in the opposite direction in the lower cross-section 
 of the conductor to what 
 it is in the uppe~ cross- 
 section. It will be seen ,-***' '*"*-, 
 that the magnet field be- ./ .-''',-"- .--. ,--. "j^N. 
 tween the two cross-sec- "x 
 tions of the conductor -^I:* w 
 or through the center of ^ 
 the turn is toward the left ''^ r -'' 
 and it is the resultant of /' ( 
 the two fields about the >x v. '--.."".. 
 two cross-sections. The .,,---'' 
 field is stronger between Fi s- 63 
 the two cross-sections than 
 
 it is outside, which is indicated by a larger number of lines 
 of force per unit of area, as shown in the figure. 
 
 Increasing the number of turns forming the coil will in- 
 crease the strength of the magnetic field inside the coil, 
 since the lines of force that surround each turn seem to 
 join together and pass around the entire winding instead 
 
ELECTEOMAGNETISM 
 
 91 
 
 N 
 
 of passing around the respective conductors. A cross-sec- 
 tion through a coil composed of several turns is shown in 
 Fig. 63. A few of the lines encircle the different conductors, 
 but the greater portion pass entirely through the center of 
 the coil and around the total number of turns. Such coils 
 are called solenoids. 
 
 104. Polarity of Solen- 
 oids. A solenoid carrying 
 a current exhibits all the 
 magnetic effects that are 
 shown by permanent mag- 
 nets. If a solenoid that 
 is carrying a current be 
 suspended so that it is 
 free to swing about a ver- 
 tical axis, its own axis 
 being horizontal, it will 
 move into an approxi- 
 mately north and south 
 position, exactly like a 
 permanent magnet. A so- 
 lenoid supported in this 
 way is shown in Fig. 64. 
 They attract and repel 
 magnets, pieces of iron, Fig. 64 
 
 and other solenoids. See 
 Fig. 65. 
 
 The polarity of any solenoid may be determined, when 
 the direction of the current is known, by a simple application 
 of any one of the rules given in section (101). The lines of 
 magnetic force inside the solenoid pass from the S-pole 
 to the N-pole and outside the solenoid from the N-pole to 
 the S-pole. Referring to Fig. 63, you see that the end of 
 the solenoid toward the left will be the S-pole and the end 
 toward the right, the N-pole. 
 
 A simple rule by which the polarity of a solenoid may be 
 determined, if the direction of the current around the wind- 
 ing is known, is as follows: If you face one end of the 
 solenoid and the current is around the winding in a clock- 
 wise direction, the end nearest you will be the S-pole and 
 the other end will be the N-pole. If the direction of the cur- 
 
92 PRACTICAL APPLIED ELECTRICITY 
 
 rent around the winding is counter clockwise, the end near- 
 est you will be the N-pole and the other end, the S-pole. 
 
 Another simple rule is to grasp the solenoid with the right 
 hand with the fingers pointing around the coil in the direc- 
 tion of the current, the thumb will then point toward the 
 N-pole of the coil, as shown in Fig. 66. 
 
 Fig. 65 
 
 Fig. 66 
 
 105. The Toroid. If a solenoid is bent around until its 
 two ends meet, or if a winding is placed on a ring, the 
 arrangement thus produced will be a toroid. By winding 
 the various turns closely and uniformly over the entire 
 periphery of the ring, the lines of force produced inside 
 the ring by a current in the winding will form closed curves 
 whose paths are entirely with- 
 in the turns composing the 
 
 winding; consequently, there 
 are ro external magnet poles. 
 Such a coil is shown in Fig. 67. 
 
 106. Permeability. The 
 number of magnetic lines pro- 
 duced inside a solenoid, with 
 an air core, can be greatly in- 
 creased by introducing a piece 
 of iron, even though the cur- 
 rent in the winding of the so- 
 lenoid remains constant. This 
 
 is due to the fact that the iron is a better conductor 
 of magnetic lines than air. The relation between the num- 
 ber of lines of force per unit area inside the solenoid after 
 the iron has been introduced, designated by (/3), to the 
 
 Fig. 6' 
 
ELECTKOMAGNETISM 
 
 93 
 
 number of lines per unit of area for an air core, which is 
 the field strength, designated by (#), is called the permea- 
 bility, designated by (/*). 
 
 fi 
 M = (73) 
 
 H 
 
 The permeability of a given sample of iron is not constant 
 because the value of (/3) does not increase at the same 
 rate (H) increases. Curves showing the relation between 
 the two quantities for wronght iron, cast iron, and cast steel 
 
 ZO 30 40 SO 60 70 80 90 . 100 110 IZO 150 140 150 160 
 
 Fig. 68 
 
 are shown in Fig. 68. The permeability of these different 
 kinds of iron can be determined for any value of (0) or 
 (H) by dividing the value of (/3) for any point on the 
 curve by the corresponding value of (fl). 
 
 The sharp bend in the curve is called the "knee" of the 
 curve. The iron is very nearly saturated at this point be- 
 cause any further increase in (H) produces a small increase 
 in (j8) as compared to what a corresponding increase in 
 (H) would do below the knee of the curve. 
 
 107. Magnetomotive Force. The magnetomotive force 
 (abbreviated m.m.f.) of a coil carrying a current is its total 
 magnetizing power. When a current passes around a core 
 several times, as shown in Fig. 69, the magnetizing power 
 
94 PRACTICAL APPLIED ELECTRICITY 
 
 is proportional both to the strength of the current and the 
 number of turns in the coil. The product of the current in 
 the coil and the number of turns composing the coil is 
 called the ampere-turns. The magnetizing power of the 
 current is independent of the size of the wire, the area of 
 
 the coils, or their shape, and re- 
 mains the same whether the 
 turns are close together or far 
 apart. It has been found by 
 experiment that one ampere 
 Fig. 69 turn sets up 1.2566 units of mag- 
 
 netic pressure. Hence, if (n) 
 
 represents the number of turns in the coil and (I) represents 
 the current in amperes through each turn, the magnetomotive 
 force is 
 
 m.m.f. = 1.2566 X n X I (74) 
 
 The gilbert is the unit in which magnetomotive force is 
 measured. One gilbert is equal to (1 -=- 1.2566) ampere-turn. 
 Magnetomotive force or magnetic pressure corresponds to 
 electromotive force and electrical pressure in the electrical 
 circuit. 
 
 The m.m.f. acting in any magnetic circuit encounters a 
 certain opposition to the production of a magnetic field, 
 just as an electrical pressure encounters a certain opposi- 
 tion in the electrical circuit to the production of a current. 
 The opposition in the magnetic circuit is called the reluc- 
 tance, represented by (E), of the circuit and its value will 
 depend upon the materials composing the circuit and the 
 dimensions of the circuit. 
 
 The total number of magnetic lines of force, called the 
 magnetic flux, represented by ($), produced in any magnetic 
 circuit will depend upon the m.m.f. acting on the circuit 
 and the total reluctance of the circuit, just as the current 
 in an electrical circuit depends upon the electrical pressure 
 acting upon the resistance of the circuit. The unit of mag- 
 netic flux is the maxwell, and it is equal to one line of force. 
 The gauss is the unit of flux density, and it is equal to one 
 line of force per unit of area. 
 
 Magnetomotive force 
 
 Number of lines = (75) 
 
 Reluctance 
 
ELECTKOMAGNETISM 95 
 
 (76) 
 
 108. Reluctance. The reluctance of any magnetic cir- 
 cuit depends upon the dimensions of the circuit and the 
 kind of material composing the circuit. It varies directly 
 as the length of the circuit and inversely as the area, all 
 other conditions remaining constant. The reluctance of any 
 given volume varies inversely as the permeability of the 
 material filling the volume. 
 
 Length in centimeters 
 Reluctance = 
 
 Permeability X cross-section in sq. cm. 
 
 I 
 E = (77) 
 
 The unit in which reluctance is measured is called the 
 oersted and it is equal to the reluctance of a cubic centi- 
 meter of air. 
 
 Reluctances can be added in the same way as resistances. 
 If a magnetic circuit, such as that of the dynamo, is com- 
 posed of a number of different kinds of materials, such as 
 cast iron, wrought iron, air, etc., calculate the reluctance 
 of each part by the above equation, and add these reluc- 
 tances together to give the total reluctance of the entire 
 magnetic circuit. The value of the permeability to use in 
 the above equation will, of course, depend upon the number 
 of magnetic lines the various parts of the circuit are to 
 conduct per unit of area. The permeability of air is always 
 unity. 
 
 Example. An iron ring has a rectangular cross-section of 
 four square centimeters and a mean length of 20.5 centi- 
 meters. A slot is cut in this ring .5 centimeters wide and 
 the ring is wound with 1000 turns of wire. What current 
 must there be in the winding in order that there will be 
 100000 magnetic lines produced in the air gap? Take the 
 permeability of the iron equal to 1000. 
 
 Solution. The reluctance of the iron portion of the cir- 
 cuit can be determined by substituting in equation (77) : 
 
PBACTICAL APPLIED ELECTKICITY 
 
 20 1 
 
 E = = oersted 
 
 1000 X 4 200 
 The reluctance of the air gap will be 
 
 '.5 
 
 E = = y s oersted 
 
 1X4 
 
 Total reluctance is 
 
 11 13 
 
 1 = = .13 oersted 
 
 8 200 ICO 
 
 Substituting the values of (E), (n), and ($) in equations 
 (74) and (76) gives 
 
 L2566 X 1000 X I 
 
 100 000 = 
 
 .13 
 
 1.2566 X 1000 X I = 13 000 
 1256.61 = 13000 
 1 = 10.34 
 
 Ans. 10.34 amperes. 
 
 Example. The magnetic 
 circuit, shown in Fig. 70, 
 is rectangular in cross-sec- 
 tion, the dimensions per- 
 pendicular to the paper be- 
 ing 3 centimeters. The 
 permeability of the iron is 
 1000. The armature (A) 
 is .5 centimeter from eacii 
 magnet core. There are 
 500 turns in each coil and 
 each turn is carrying a 
 current of 10 amperes. 
 What is the value of the 
 total number of magnetic 
 lines produced in the air 
 gaps? 
 
 Fig. 70 
 
 Solution. The total length of path in air is 
 2 x .5 = 1 cm. 
 
ELECTROMAGNETISM 97 
 
 The area of the magnetic circuit is the same throughout 
 and is equal tc 
 
 2 X 3 = 6 sq. cm. 
 
 The reluctance of the air gaps is equal to 
 
 I 1 1 
 
 E = = = 
 
 A* A 1X6 6 
 
 The length of the magnetic circuit in the iron is 
 
 TT X d 
 
 (2 X 5) + (2 X 10) + 4 ( ) = 33.1416 cm. 
 4 
 
 (Note The circuit is taken as a curve about the corners.) 
 The reluctance of the iron portion of the magnetic circuit 
 will be 
 
 33.1416 
 
 E = = .005 523 6 oersted 
 
 1000 X 6 
 
 The total reluctance will be 
 
 h .0055236 = .17219 oersted 
 
 6 
 
 Substituting the values of (I), (n), and (E) in equation (76) 
 gives 
 
 1.2566 X 2 X 500 X 10 
 
 * = =72970. 
 
 .17219 
 Ans. 72970. maxwells (approx.). 
 
 PROBLEMS ON MAGNETISM 
 
 (1) A magnetic circuit is 40 cm. in length, has a cross- 
 section of 4 square centimeters, and is composed of a material 
 whose permeability is 1500. What is the reluctance of the 
 circuit? 
 
 1 
 
 Ans. oersted. 
 
 150 
 
98 PEACTICAL APPLIED ELECTRICITY 
 
 2. What is the m.m.f. in gilberts produced by a current 
 ' 7.5 amperes thr 
 cuit of 1200 turns? 
 
 of 7.5 amperes through a winding around a magnetic cir- 
 
 Ans. 11 309. + gilberts. 
 
 (3) A magnetic circuit is composed of three parts con- 
 nected in series, having reluctances of .032, .015, and .053 
 oersted, respectively. What m.m.f. would be required to 
 produce a flux of 10 000 maxwells? 
 
 Ans. 1000 gilberts. 
 
 (4) How many turns would be required in a coil to pro- 
 duce the above m.m.f., if each turn is to carry a current of 
 1 ampere? 
 
 Ans. 795 turns (approx.). 
 
 (5) It is desired to magnetize a piece of iron until there 
 are 6000 lines per square centimeter. What cross-section is 
 required to have a total of 100000 lines? 
 
 Ans. 16% sq. cm. 
 
 (6) Two magnetic circuits are acting in parallel and they 
 have reluctances of .05 and .04 oersted respectively. What 
 is the total reluctance of the two combined? 
 
 Ans. .0222 oersted. 
 
 (Note: Add reluctances in parallel the same as resist- 
 ances.) 
 
 109. Electromagnet. A simple electromagnet consists of 
 a piece of iron about which is wound an electrical con- 
 ductor through which a current of electricity may be passed. 
 Commercial electromagnets assume numerous different forms 
 depending upon the particular use to which they are to be 
 placed. They are used in electric bells, telephones, relays, 
 circuit breakers, generators, motors, lifting magnets, etc. 
 The use of the electromagnet in handling magnetic materials 
 has become quite common in recent years. A magnet manu- 
 factured by the Electric Controller and Supply Company, 
 Cleveland, Ohio, which is used for the above purpose, is shown 
 in Fig. 71. 
 
 110. Hysteresis. If a piece of iron be magnetized, then 
 
ELECTEOMAGNETISM 
 
 99 
 
 demagnetized and magnetized in the opposite direction and 
 again demagnetized it will be found that the degree of 
 magnetization will be different for the same value of (H) 
 depending upon whether the field is increasing or decreasing 
 in strength. The magnetization of the iron lags behind the 
 magnetizing force and, as a result, the values of (/3) for 
 
 Fig. 71 
 
 certain values of (H) will be greater when the magnetizing 
 force is decreasing than they will be for the same values of 
 (H) when the magnetizing force is increasing. Fig. 72 
 shows the relation between (/3) and (H) when the iron 
 is carried through what is termed a complete cycle; that is, 
 it is magnetized to a maximum positive (/3), as at (a) in 
 the figure; then demagnetized and magnetized to a maximum 
 negative (/3), as at (b) in the figure, which gives the upper 
 curve (acb). The lower curve (b d a) is obtained in a 
 similar way by demagnetizing the sample from a negative 
 (/3) to zero and then magnetizing it to a maximum posi- 
 tive (|3), returning the iron to its original magnetic condition, 
 which completes the cycle. 
 
 111. Hysteresis Loss. When a piece of iron is carried 
 through a magnetic cycle, as described in the previous sec- 
 
100 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 tion, all the energy spent in magnetizing it is not returned to 
 
 the circuit when the iron is demagnetized, which results in 
 
 a certain amount of electrical 
 energy being expended to 
 carry the iron through the 
 cycle. This energy appears 
 in the iron as heat. The en- 
 ergy lost per cycle depends 
 upon the kind of iron being 
 tested, the volume of the 
 sample, and the maximum 
 value of (]8) raised to the 1.6 
 power. 
 
 Joules (energy per cycle) = 
 V X jSi.e X -n X 10-7 (78) 
 The constant (77) takes into 
 account the kind of iron being 
 Fig 72 tested and (V) is the volume 
 
 in cubic centimeters. If the 
 
 iron is carried through (f) cycles per second, the loss of power 
 
 in watts is given by the equation 
 
 Wh = 77XfXVX ,3i.c x 10-7 watts (79) 
 
 TABLE NO. VI 
 
 VALUE OF HYSTERETIC CONSTANT (77) FOR DIFFERENT 
 MATERIALS 
 
 Best annealed transformer sheet metal. . ......... 001 
 
 Thin sheet iron (good) ................. ......... 003 
 
 Ordinary sheet iron ............................. 004 
 
 Soft annealed cast steel ......................... 008 
 
 Cast steel ..... ................................. 012 
 
 Cast iron ....................................... 016 
 
 Example. A piece of iron is magnetized to a maximum (0) 
 of 9000 lines per sq. cm. It is carried through 60 complete 
 cycles per second. What is the power lost in 10 cubic centi- 
 meters if the hysteretic constant (77) is .003? 
 
 Solution. In order to raise the value of (/3) to the 1.6 
 power you must make use of logarithms. (A description of 
 the use of logarithms is given in Chapter 20.) In the table 
 of logarithms you will find opposite the number 900 the 
 mantissa 95424. (The mantissa of the logarithm of 900 is 
 
ELECTROMAGNETISM 101 
 
 the same as the mantissa of the logarithm of 9000.) 
 Place the figure 3, the characteristic, before this num- 
 ber, which is one less than the number of significant figures 
 in 9000 and you have the log 9000 = 3.95424. Multiply 
 this log by 1.6 and you have 6.326 784. Now 6.326 78 is the 
 log of the result you want to obtain. Looking up the man- 
 tissa 32678 in the table, you find it corresponds to 2122. 
 The result must contain seven figures before the decimal 
 point (because the characteristic is six), hence, the result 
 is 2.122 X 106. Substituting this value in equation (79), 
 together with the values of (f), (V), and (77), gives 
 
 Wh = .003 X 60 X 10 X 2.122 X 106 X 10-7 
 
 = .18 X. 2.122 = .38 
 
 Ans. .38 watts. 
 
 112. Law of Traction. The formula for the pull of, or lift- 
 ing power of, an electromagnet when it is in actual contact 
 with the object to be lifted is 
 
 /32 A 
 Pull in pounds = - (80) 
 
 72 134 000 
 
 In the above equation (/3) is the number of lines per square 
 inch and (A) is the area of contact in square inches. The 
 value of (/3) required to produce a given pull, when the area 
 of contact is known, can be calculated by the use of the 
 equation 
 
 Pull in pounds 
 
 - (81) 
 
 Area in square inches 
 In the above equation (/3) will be lines per square inch. 
 
CHAPTEE VII 
 
 ELECTROMAGNETIC INDUCTION FUNDAMENTAL 
 THEORY OF THE DYNAMO 
 
 113. Electromagnetic Induction. In 1831, Michael Faraday 
 discovered that an electrical pressure was induced in a con- 
 ductor that was moved in a magnetic field, when the direction 
 of motion of the conductor was such that it cut across the 
 lines of force of the field. If this conductor forms part of a 
 closed electrical circuit, the electromotive force induced in it 
 will produce a current. Currents that are produced in this 
 way are called induction currents and the phenomenon is 
 termed electromagnetic induction. In this great discovery 
 lies the principle of the operation of many forms of commer- 
 cial electrical apparatus, such as dynamos, induction coils, 
 transformers, etc. 
 
 114. Currents Induced in a Conductor by a Magnet. If a 
 conductor (AB), Fig. 73, that is connected in series with a 
 galvanometer (G), located so that it is not influenced to any 
 great extent by the permanent magnet, be moved in the 
 field of the magnet, the moving system of the galvanometer 
 will be deflected to the right or left of the zero position. 
 This deflection is due to a current in the circuit which is 
 caused by the induced e.m.f. in the conductor that was 
 moved in the magnetic field. When the movement of the 
 conductor in the field ceases, the galvanometer system will 
 return to its zero position, which indicates there is no cur- 
 rent and hence no induced e.m.f. in the circuit. Hence, the 
 conductor must be actually cutting the magnet lines of force 
 in order that there be an induced e.m.f. produced in the 
 circuit. If the conductor was moved downward across the 
 field in the above case and the deflection of the galvanom- 
 eter needle was to the right, it will be found, upon moving 
 the conductor upward across the field or in the opposite direc- 
 
 102 
 
ELECTEOMAGNETIC INDUCTION 
 
 103 
 
 tion to its motion in the first case, that the galvanometer 
 needle will be deflected to the other side of its zero posi- 
 tion. Since the direction in which the needle of the galva- 
 nometer is deflected depends upon the direction of the current 
 through its winding, it is apparent the current in the circuit 
 in the second case is in 
 the opposite direction to 
 what it was in the first 
 case; and since the current 
 is due to the induced 
 e.m.f. in the conductor 
 (AB), it must also be in 
 the opposite direction. If 
 the motion of the conduc- 
 tor in the magnetic field is 
 continuous, up and down 
 past the end of the mag- 
 net, there will be a current FJ g- 73 
 through the galvanometer 
 
 first in one direction and then in the opposite direction, and 
 the galvanometer needle will swing to the right and left of 
 its zero position. The motion of the conductor, however, 
 may be rapid enough so that the galvanometer needle has 
 not sufficient time to take its proper position with respect 
 to the current in the conductor and as a result it remains 
 practically at zero, the vibration or deflection to the right 
 or to the left being very small. 
 
 The same results can be obtained by using the opposite 
 pole of the magnet, except the deflection of the galvanometer 
 needle due to a given direction of motion of the conductor 
 will be just the reverse of what it was with the other pole. 
 This shows that there is some definite relation between the 
 direction of motion of the conductor, the direction of the mag- 
 netic field, and the direction in which the induced e.m.f. acts. 
 If the wire were held stationary and the magnet moved, the 
 same results would be obtained as though the wire were 
 moved past the magnet. Hence, it is only necessary that 
 there be a relative movement of the conductor and the 
 field; either may remain stationary. An electromagnet may 
 be used instead of the permanent magnet and the same 
 results will be obtained under similar conditions. 
 
104 PRACTICAL APPLIED ELECTKICITY 
 
 If the conductor were moved very slowly across the mag- 
 netic field, the galvanometer needle would be deflected 
 through a much smaller angle than it would be if the con- 
 ductor were moved faster across the field. The deflection 
 of the galvanometer needle depends upon the value of the 
 current through its winding and since the deflection is 
 smaller when the conductor is moved slowly than it is when 
 the conductor is moved fast, it must follow that the induced 
 e.m.f. for a slow movement of the conductor is less than it 
 is for a fast movement, even though all the magnetic 
 lines of force forming the magnetic field be cut by. the con- 
 ductor. The above results show that the value of the 
 e.m.f. induced in a conductor, due to the relative motion of 
 the conductor and a magnetic field, depend upon the rate 
 at which the conductor is moving. If a second conductor 
 be connected in series with the first, so that their induced 
 e.m.f.'s act in the same direction, the resultant e.m.f. is 
 increased. This is equivalent to increasing the effective 
 length of the conductor in the magnetic field. 
 
 The induced e.m.f. may be increased by placing a second 
 magnet along the side of the first so that their like poles 
 are pointing in the same direction. This second magnet in- 
 creases the strength of the magnetic field and the conductor 
 cuts more lines of force due to any movement. 
 
 If the conductor be moved in a path parallel to the lines of 
 force forming the magnetic field or along its own axis, there 
 will be no deflection of the galvanometer needle, which indi- 
 cates there is no current in the circuit and hence, no in- 
 duced e.m.f. Then, in order that there be an induced e.m.f. 
 set up in a conductor due to Us movement with respect to a 
 magnetic field, the path in which the conductor moves must 
 make some angle with the direction of the magnetic lines of 
 force. The value of the induced e.m.f. due to the movement 
 of a conductor in a magnetic field will increase as the angle 
 between the direction of the lines of force and the path 
 in which the conductor moves increases, and it will be a 
 maximum when the conductor moves in a path perpendicular 
 to the direction of the magnetic field and perpendicular to 
 itself. 
 
 There will be an induced e.m.f. set up in the conductor 
 even though the circuit of which the conductor, forms a part 
 
ELECTED MAGNETIC INDUCTION 105 
 
 be open. This induced e.m.f. will exist between the ter- 
 minals of the circuit where it is opened, just the same as an 
 e.m.f. exists between the terminals of a battery that is on 
 open circuit. 
 
 The question naturally arises: Is the magnet weakened 
 when it is used in producing induced currents in a conductor 
 as previously described, and if not, what is the source of 
 energy that causes the current to exist in the conductor? 
 The magnet is in no way weakened when it is used as pre- 
 viously described, and the induced current is produced by 
 the expenditure of muscular energy just as an expenditure 
 of chemical energy in a cell produces an electrical current 
 in a closed circuit to which the cell is connected. When 
 a conductor with a current in it is located in a magnetic 
 field in a position other than parallel to the field, there is 
 a force produced which tends to cause the conductor to move 
 across the field. The direction of this force is just oppo- 
 site to the one that must be applied to the conductor to 
 cause it to move so there will be an induced e.m.f. set up 
 which will produce the current. In other words, the induced 
 e.m.f. set up in a conductor will always be in such a direc- 
 tion that the current produced by it will oppose the motion 
 of the conductor. 
 
 115. Currents induced in a Coil 
 by a Magnet. If a coil of wire (C) 
 be connected in series with a gal- 
 vanometer (G), as shown in Fig. ?Ail JM 
 74, a deflection of the galvanom- 
 eter needle can be produced by 
 thrusting a magnet (M) in and out 
 
 j of the coil. When the magnet is 
 thrust into the coil, a deflection of 
 
 the needle will be produced, say, to 
 the right, and when the magnet is 
 
 withdrawn a deflection of the needle will be produced to the 
 left. If the magnet be turned end for end, the deflections of 
 the galvanometer needle will be just the reverse of what 
 
 'they were for the previous arrangement. If the coil (C) be 
 turned through an angle of 180 degrees so that the side that 
 was originally toward the magnet will now be away from it 
 and the magnet be placed in its original position, the deflec- 
 
106 PEACT1CAL APPLIED ELECTKICITY 
 
 tions of the galvanometer needle produced by a movement 
 of the magnet in or out of the coil will correspond in direc- 
 tion to those produced when the coil was in its original 
 position and the magnet had been turned end for end. 
 
 If the coil be moved on or off of the magnet, the same effect 
 is produced as would be produced by moving the magnet in or 
 out of the coil. The e.m.f. in this case, as in the previous 
 one, will depend upon the rapidity of the movement of the 
 magnetic field with respect to the coil, or vice versa. 
 
 If the number of turns of wire composing the coil be 
 increased or decreased, there will be a corresponding increase 
 or decrease in the e.m.f. induced in the winding due to a 
 given movement of the coil or magnet with respect to the 
 other. The induced e.m.f. in the various turns all act in 
 the same direction, they are all equal, and the resultant 
 e.m.f. is equal to their sum. 
 
 116. Magnitude of the Induced E.M.F. and Factors upon 
 Which It Depends. From the discussion in the two previous 
 sections it is seen that the induced e.m.f. in a circuit de- 
 pends upon the following factors: 
 
 (a) The rate of movement of the conductor and the mag- 
 netic field with respect to each other. The more rapid 
 the movement the greater the e.m.f. induced, all other 
 quantities remaining constant. 
 
 (b) The strength of the magnetic field or the number of 
 lines of force per square centimeter. The stronger 
 the field the greater the e.m.f. induced, all other 
 quantities remaining constant. 
 
 (c) Upon the angle the path, in which the conductor moves, 
 makes with the direction of the lines of force. The 
 nearer this path is to being perpendicular to the mag- 
 netic field and the position of the conductor, the greater 
 the induced e.m.f. 
 
 (d) The length of the wire that is actually in the magnetic 
 field. The more wire there is in the magnetic field, the 
 greater the induced e.m.f. 
 
 The above facts can be condensed into the following 
 simple statement: The magnitude of the induced e.m.f. 
 in any circuit depends upon the rate at which the conductor, 
 
ELECTEOMAGNETIC INDUCTION 1Q7 
 
 forming part of the circuit, cuts magnetic lines of force; that 
 is, it depends upon the total number of lines of force cut per 
 second by the conductor. When the conductor cuts one hun- 
 dred million (100 000 000) lines in each second during its mo- 
 tion, an electrical pressure of one volt is induced in the con- 
 ductor. If the conductor cuts lines of force at the rate of 
 two hundred million (200 000 000) in each second, the in- 
 duced pressure is equal to two volts; and if the conductor cuts 
 eleven thousand million (11 000 000 000) lines in each second, 
 there will be an induced e.m.f. of 110 volts. If the circuit of 
 which this conductor forms a part be closed, there will be a 
 current in the conductor, which has a strength equal to the 
 induced pressure divided by the total resistance of the 
 circuit. 
 
 Example. A conductor cuts across a magnetic field of 
 110 000 000 lines of force 100 times per second. (The con- 
 ductor always moves across the field in the same direction.) 
 How many volts are induced in the wire? 
 
 Solution. A conductor cutting 11 000 000 lines of force 
 100 times per second would be equivalent to cutting 
 (11000000X100), or 1100000000 lines once per second. 
 Cutting 1 100 000 000 lines of force per second will induce in 
 a conductor (1 100 000 000 -i- 100 000 000), or 11 volts. 
 
 Ans. 11 volts. 
 
 117. Direction of Induced E.M.F. From the previous dis- 
 cussion it is seen that the direction of the induced e.m.f. 
 depends upon the direction of the magnetic field and the 
 direction in which the conductor is moved with respect to 
 the field. 
 
 If a piece of copper be bent into the form shown by 
 (ECDF), Fig. 75, and a second piece (AB) be placed across 
 the first and the combination placed in a magnetic field as 
 shown by the vertical arrows in the figure, there will be a 
 current around the metallic circuit thus formed when the con- 
 ductor (AB) is moved to the right or to the left of its initial 
 position. When the conductor (AB) is moved it cuts across 
 some of the lines of force and there is an induced pressure set 
 up in it which .produces a current. The direction of this 
 current will be reversed when the direction of motion of 
 (AB), or the direction of the magnetic field, is reversed. 
 
108 
 
 PEACTICAL APPLIED ELECTKICITY 
 
 When the wire is moved in the direction indicated by the 
 arrow (K) in the figure, the end (B) is positive and the other 
 end (A) is negative, or the potential of (B) is higher than that 
 of (A). This difference in pressure between (B) and (A) 
 will cause a current in the circuit, from (B) through (C) 
 and (D) to (A) and from (A) to (B). The wire (AB) is the 
 part of the circuit in which the electrical pressure is gen- 
 erated and the electricity passes from a lower to a higher 
 potential through this part of the circuit, just as the elec- 
 tricity passes from the negative to the positive pole of the 
 battery through the battery itself. 
 
 A simple way of determining the direction of induced 
 e.m.f. in a circuit, when the direction of motion of the con- 
 
 E B 
 
 A 
 
 Fig. 75 
 
 Fig. 76 
 
 ductor and the direction of the magnetic field are known, is 
 as follows: Suppose a conductor (C), Fig. 76, is moved to 
 the -right, as indicated by the arrow, in a magnetic field whose 
 direction is downward, as shown by the small arrow heads 
 at the lower part of the figure. The lines of force might be 
 thought of as elastic bands that are pushed aside when the 
 conductor is moved in the field, but finally break and join 
 again on the left side of the conductor, leaving a line linked 
 around the conductor, as shown by the small circle (c). The 
 direction of this line of force about the conductor is clock- 
 wise, or it corresponds to a line produced by a current toward 
 the paper. Hence, the current in the conductor is from the 
 observer toward the paper. It must be remembered that the 
 current is from a point of relatively low potential to one of 
 higher potential in this part of the circuit. 
 
ELECTROMAGNETIC INDUCTION 
 
 109 
 
 118. Rules for Determining Direction of Induced E.M.F. 
 There are a number of different ways of remembering the 
 relation between the direction of the electrical current, the 
 direction of the conductor's motion, and the direction of the 
 magnetic field. One of the best rules is what is known as 
 Fleming's "Right-Hand Rule," and it is as follows: Place 
 the thumb and the first and second fingers of the right hand 
 all at right angles to each other. Now turn the hand into 
 such a position that the thumb points in the direction of 
 motion of the conductor, and the first finger points in the 
 direction of the lines of force, then the second, or middle, 
 finger will point in the direction of the current that is set 
 up in the conductor by the induced pressure. An illustra- 
 tion of the "Right-Hand Rule" is shown in Fig. 77. 
 
 Inducedemf 
 Fig. 77 
 
 Fig. 78 
 
 119. Primary and Secondary Coils. If a coil of wire 
 be connected in series with a galvanometer (G), as shown in 
 Fig. 78, and a second coil (C 2 ) that has its winding con- 
 nected to a battery (B) be moved into or out of the coil 
 (Ci), there will be a deflection produced on the galvanometer, 
 just as though a permanent magnet had been used instead of 
 the coil (C 2 ). The coil (Cj), in which the induced e.m.f. is 
 produced, is called the secondary and the coil (C 2 ), in which 
 the inducing current exists, is called the primary. 
 
 There are a number of different ways of producing an 
 induced e.m.f. in the secondary coil besides moving one coil 
 with respect to the other. Four of 'these methods are as fol- 
 lows: (Both coils are stationary and one surrounds the 
 other, or they are both wound around the same magnetic cir- 
 cuit). 
 
 (a) By making or breaking the primary circuit. Imagine 
 
HO PRACTICAL APPLIED ELECTRICITY 
 
 two conductors (AB) and (CD), Fig. 79, that are parallel to 
 each other and very near together but are connected in 
 two electrically independent circuits. The conductor (AB) 
 is in series with the galvanometer (G) and constitutes the 
 secondary circuit. The conductor (CD) is connected in se- 
 ries with a battery (B) and a switch (S) that can be used 
 in opening and closing the primary circuit. When the primary 
 circuit is completed by closing the switch (S), there will be 
 a current through the conductor (CD) from (C) to (D), 
 This current will produce a magnetic field about its path 
 and the field around the conductor (CD) will cut the con- 
 ductor (AB) which will result in an 
 induced e.m.f. being set up in the 
 secondary circuit that will send a 
 current through the circuit from (B) 
 to (A). The direction of this in- 
 duced e.m.f. can be determined by 
 
 means of the "Right-Hand Rule." 
 
 B ' 
 
 L_| |J d | ^^ \ ) There will be an e.m.f. set up in the 
 
 secondary for a period of time cor- 
 
 Fi s- 79 responding to the time required to 
 
 establish the current in the primary. 
 
 As soon as the primary current ceases to change in value, 
 there will be no movement of the magnetic field and the con- 
 ductor TAB) with respect to each other. 
 
 If now the primary circuit be broken, the magnetic field 
 surrounding the conductor (CD) will collapse, and as a result 
 the conductor (AB) will cut the field again, but in the oppo- 
 site direction to what it did when the current in the circuit 
 (CD) was being established. There will be a current pro- 
 duced in the secondary that is practically constant in dura- 
 tion if the primary circuit is made and broken a sufficient 
 number of times. The conductors forming the primary and 
 secondary circuits are usually wound into coils, and they 
 may be placed side by side or one outside the other. The 
 e.m.f. induced in the secondary, due to a certain change of 
 current in the primary, can be greatly increased by winding 
 the two coils on an iron core. The magnetic field that 
 passes through the two windings, due to the current in the 
 primary is a great deal stronger when they are placed on 
 the iron core than it is when an air core is used and, as a 
 
ELECTEOMAGNETIC INDUCTION 
 
 111 
 
 O o=^0=CD 
 
 Secondary] 
 
 \/V/V/V I i 
 
 result, a greater number of lines of force will cut the second- 
 ary winding when the primary circuit is completed or broken. 
 
 The induction coil consists of two windings, a primary and 
 a secondary, placed upon an iron core with some sort of 
 a device connected in the primary circuit for interrupting 
 the primary current. See Fig. 80. The relation between the 
 primary and the secondary e.m.f. is practically the same as the 
 relation between the number of turns of wire in the primary 
 and in the secondary windings. 
 
 (b) Varying the strength of current in the primary. This 
 in reality is practically the same as the previous method, 
 except the circuit is not entirely broken. Any change in the 
 value of the primary current will result in a change in the 
 magnetic field surrounding 
 the primary winding, and 
 as this field expands or 
 contracts it will cut the 
 conductor composing the 
 secondary and, as a result, 
 there will be an induced 
 e.m.f. set up in the sec- 
 ondary winding. The di- 
 rection of this induced III 1 r ' 
 e.m.f. will depend upon 
 
 whether the field is ex- Fig. 80 
 
 panding or contracting, 
 
 which, in turn, depends upon the change of current in the 
 primary whether it be increasing or decreasing. The 
 telephone induction coil is a good application of this 
 means of producing an alternating current in the secondary 
 due to a change in the value of the current in the primary. 
 The connections of a telephone coil are shown in Fig. 81. 
 (S) and (P) represent the secondary and the primary wind- 
 ings of the induction coil, which are usually wound, one out- 
 side of the other, on an iron core composed of a bundle of 
 small iron wires. (R) is the receiver that is connected in 
 series with the telephone line and the secondary winding. The 
 transmitter (T) is connected in series with the battery (B) 
 and the primary winding. The construction of the trans- 
 mitter is such that when the air is set in vibration about the 
 transmitter, due to any cause, there will be a change in the 
 
112 
 
 PRACTICAL APPLIED ELECTEICITY 
 
 Pig. 81 
 
 value of the resistance it offers to the current in the circuit 
 of which it is a part. The vibration of the air then causes 
 a varying current through the primary winding of the induc- 
 tion coil, which, in turn, produces an e.m.f. in the secondary 
 winding and as a result of this e.m.f. there will be a current 
 over the telephone line that produces an effect on the re- 
 ceivers both at the sending and the receiving stations. It must 
 be understood that the diagram, Fig. 81, does not show the 
 complete circuit of the telephone. 
 
 (c) Reversing the cur- 
 rent in the primary. If a 
 switch were constructed 
 so that its operation would 
 reverse the current in the 
 primary winding, there 
 would be an e.m.f. induced 
 in the secondary winding 
 due to a change in the 
 magnetic field surrounding 
 the two windings. This 
 
 method is applied in practice in what is called a transformer. 
 The switch, however, is not used, as the current in the pri- 
 mary winding is an alternating current a current that is re- 
 versing in direction at regular intervals. The operation of the 
 transformer will be taken up under the subject "Alternating 
 Current." 
 
 (d) Moving the iron core about which the windings are 
 placed. The magnetic field produced by a given value 'of 
 current in the winding of a coil will depend upon the kind of 
 material composing the magnetic circuit, whether it be a 
 material of high or low permeability. If the iron core upon 
 which the windings are placed be moved so as to increase the 
 reluctance in the magnetic circuit, there will be a decrease 
 in the lines of force, and, as a result, there will be an induced 
 e.m.f. set up in the secondary winding. If the core be moved 
 so as to decrease the reluctance of the circuit, there will be 
 an increase in the number of magnetic lines, or an increase 
 in field strength, and an induced e.m.f. will be produced 
 in the secondary winding in the opposite direction to that 
 produced when the field strength decreased. This principle 
 is employed in what is called the inductor type of alternating- 
 
ELECTROMAGNETIC INDUCTION 
 
 113 
 
 current generator. An e.m.f. is produced by rotating iron 
 poles between the primary and the secondary windings, which 
 changes the number of the lines of force through the sec- 
 ondary due to the current in the primary. 
 
 120. Mutual Induction. The reaction of two independent 
 electrical circuits upon each other is called mutual induction. 
 These circuits of course must be so placed with respect to 
 each other that the magnetic field due to the current in 
 either of them will produce an effect in the other. A good 
 practical example of mutual induction is that of a telephone 
 wire that runs parallel to, say, an electric-light circuit. 
 The magnetic field surrounding the electric-light circuit cuts 
 the telephone conductor and sets up in it an induced e.m.f. 
 This induced e.m.f. will 
 
 produce a current in the 
 telephone circuit which in- 
 terferes with the satisfac- 
 tory operation of the tele- 
 phone line. Often the 
 conversation on one tele- 
 phone circuit can be heard 
 on another circuit due to 
 
 this same cause. The wires composing the circuits should have 
 their positions interchanged, as shown in Fig. 82. The e.m.f.'s 
 induced in the two wires composing the telephone circuit are 
 opposite in direction with respect to the telephone circuit 
 and they will all exactly neutralize each other when the two 
 wires are properly changed in position. The changing of the 
 position of two wires is called a transposition. 
 
 121. Self-Induction. If the value of the current in a wire 
 forming a coil be changed in any way, there will be a change 
 in the strength of the magnetic field surrounding the wire. 
 This change in strength of the magnetic field will produce an 
 e.m.f. in the conductor in which the current is changing just 
 the same as though the field were changed in strength by a 
 current in an independent electrical circuit. This cutting of 
 the wire by the magnetic field produced by a current in 
 the wire itself is called self-induction. When a coil carry- 
 ing a current has its circuit broken, there will be a spark 
 formed at the break due to the induced e.m.f. This induced 
 e.m.f. will depend upon the form of the coil and the kind 
 
 Tel 
 ^ a > 
 
 
 
 i > 
 
 uit 
 k a v 
 
 ephoneCirc 
 
 k ' sa > 
 Fig. 82 
 
114 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 of material associated with the coil. A straight conductor 
 will have a small e.m.f. induced in it when the circuit is 
 broken, as the magnetic field surrounding the conductor is 
 not very strong. If the conductor be bent into a coil the 
 induced e.m.f. will be greater than that for the straight 
 conductor, as very nearly all the magnetic lines of force 
 produced by each turn cut all the other turns composing the 
 coil, and the total number of lines that cut the winding is 
 greatly increased. This induced e.m.f. can be further in* 
 creased by providing the coil with an iron core, which in- 
 creases the field strength due to a given current in the 
 winding. 
 
 In electric-gas lighting it is desired 
 
 r - --' , to have a circuit of large self-induc- 
 
 tion so that there will be a good 
 spark formed when the circuit is 
 broken at the gas jet. The heat of 
 this spark is sufficient to ignite the 
 gas. The self-induction of such a 
 circuit is increased by connecting in 
 series with the battery and other 
 parts of the circuit a coil wound upon 
 an iron core. This kind of a coil is 
 often spoken of as a "kick coil." 
 
 If a lamp (L) be connected across 
 the terminals of an electromagnet 
 (M), as shown in Fig. 83, the lamp will 
 
 burn very bright just for an instant after the battery circuit is 
 opened. This is due to the induced e.m.f. set up in the winding 
 of the electromagnet when the field contracts and cuts the 
 various turns. The e.m.f., of course, is only momentary, as the 
 field soon disappears when the circuit is broken by opening 
 the switch (S). The voltage the lamp is constructed to 
 operate on and the battery voltage should be practically the 
 same in order to give the best results. 
 
 122. inductance. The inductance of any circuit depends 
 upon the form of the circuit and the kind of material sur- 
 rounding the circuit. There is an increase in the value of the 
 inductance of a coil with an increase in the number of turns 
 and an increase in the permeability of the material com- 
 posing the magnetic circuit. A coil is said to have unit 
 
 Fig. 83 
 
ELECTKOMAGNETIC INDUCTION 115 
 
 inductance when an induced e.m.f. of one volt will be produced 
 due to a change in the current in the winding of one ampere 
 in one second. That is, if the current changes, say, from 
 two to three amperes in one second and there is an induced 
 e.m.f. of one volt, the coil is said to have unit inductance. 
 The unit of inductance is the henry, and inductance is usually 
 represented by the symbol (L). 
 
 The inductance of any coil can be calculated by the use 
 of the following equation when the dimension of the coil 
 and other quantities are known: 
 
 (82) 
 
 109 X I 
 
 In the above equation (n) is the number of turns of wire 
 on the coil, (ju) is the permeability of the material composing 
 the magnetic circuit, (A) is the area of the magnetic circuit 
 in square centimeters, and (Z) is the length of the magnetic 
 circuit in centimeters. 
 
 123. Lentz's Law. A careful consideration of the ways by 
 which induced currents may be produced, whether it be due 
 to self or mutual induction, will result in the following sim- 
 ple fact. In all cases of electromagnetic induction, the cur- 
 rent produced by the induced e.m.f. will always be in such a 
 direction as to tend to stop the cause producing it. Thus, 
 if a magnet be moved toward a coil, the current in the coil 
 will be in such a direction that the side of the coil toward 
 the magnet will be of the same polarity as the end of the 
 magnet toward the coil. This results in the induced current 
 tending to stop the motion of the magnet. When the magnet 
 is moved away from the coil, the current in the coil will be 
 in the opposite direction to what it was before and the 
 side of the coil toward the magnet is of the opposite polarity 
 to the end of the magnet toward the coil, and as a result 
 they attract each other, which tends to prevent the magnet 
 being moved. 
 
 If a coil of wire (Cj), in which there is a current, be moved 
 toward a second coil (C 2 ), that is, connected in series with 
 a galvanometer (G), Fig. 84, there will be an induced e.m.f. 
 set up in the coil (C 2 ), which will cause a current through 
 
116 PRACTICAL APPLIED ELECTRICITY 
 
 the galvanometer and thus produce a deflection of its needle. 
 The current produced in the second coil (C 2 ) will be in such 
 a direction as to make the sides of the two coils toward each 
 other of the same polarity. These two poles repel each 
 other and thus there is a force opposing the movement of the 
 coils toward each other. When the coil (C^ is moved away 
 from (C 2 ), the sides of the two coils 
 adjacent to each other are of opposite 
 polarity and they attract each other. 
 This results in a force which tends to 
 prevent the coils moving apart. It 
 must be remembered that this force 
 of attraction or repulsion between the 
 two coils is present only when there 
 F[ s- 84 i s a current in both coils. 
 
 If the two coils be wound on an iron 
 
 core and the value of the current in the primary winding be 
 changed, there will be a current in the secondary in such a 
 direction as to oppose any change in the value of the magnetic 
 field produced by the current in the primary. 
 
 124. General Rules for Direction of Induced Pressures. 
 
 (a) If a primary coil be moved into a secondary coil, the 
 
 current in the secondary, due to the induced e.m.f., 
 will be in the opposite direction to the primary current. 
 
 (b) If a primary coil be moved out of a secondary coil, the 
 
 current in the secondary, due to the induced e.m.f., will 
 be in the same direction as the primary current. 
 
 (c) Where the current is increasing in value in the primary 
 
 coil, there will be a current in the secondary coil, due 
 to the induced e.m.f. that is in the opposite direction 
 to that in the primary coil. 
 
 (d) When the current is decreasing in value in the primary 
 
 coil, there will be a current in the secondary coil, 
 due to the induced e.m.f. that is in the same direction 
 as that in the primary coil. 
 
 In the above cases the secondary is closed. If the secondary 
 be open there will be an induced e.m.f. set up, which would 
 produce a current in the direction indicated above, if the 
 circuit was closed. Rules (c) and (d) apply when the 
 
ELECTROMAGNETIC INDUCTION 
 
 117 
 
 primary and the secondary are stationary and the current is 
 changing in value in the primary. 
 
 125. Eddy Currents. If a disk of copper, or other conduct- 
 ing material, be rotated below a suspended magnet, as shown 
 in Fig. 85, currents will be produced in the disk, which cir- 
 culate in paths similar to those shown by the dotted lines 
 in the figure. These currents tend to oppose the motion pro- 
 ducing them and, as a result, the magnet, if it is free to move, 
 
 B, 
 
 Fig. 85 
 
 Fig. 86 
 
 will be rotated in the same direction as the disk. If, how- 
 ever, the magnet is held in position and the disk is rotated, a 
 greater force must be applied to cause the disk to rotate than 
 is required when the magnet is free to turn. 
 
 Currents induced in masses of metal that are moved in a 
 magnetic field, or are cut by a moving magnetic field, are 
 called eddy currents. 
 
 Faraday's dynamo, as shown in Fig. 86, consisted of a disk 
 
 ' of copper (D) rotated between the poles of a permanent 
 
 magnet (M), the electrical connection to the machine being 
 
 made by means of brushes (Bj) and (B 2 ) that rested upon the 
 
 center and edge of the disk. 
 
 126. Application of Eddy Currents. A good example of 
 the practical application of the fact that eddy currents are 
 set up in a mass of metal revolved in a magnetic field, is found 
 in almost all types of integrating wattmeters. A disk of copper 
 
118 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 is fastened on the same shaft as the rotating portion of the 
 meter is mounted upon, and this disk revolves between the 
 poles of several permanent magnets, as shown in Fig. 87. 
 This combination of disk and magnets constitutes a small 
 generator and serves as a load for the motor part of the 
 meter. The torque required to drive the disk in the field 
 
 of the magnets is propor- 
 tional to the speed, and 
 since the driving torque of 
 the motor is proportional 
 to the product of the im- 
 pressed voltage and the 
 load current, or the watts, 
 the speed of the moving 
 part of the meter must be 
 proportional to the watts. 
 The integrating meter will 
 be taken up more in detail 
 In the chapter on "Electric- 
 al Measuring Instruments." 
 127. Eddy-Current Loss. 
 The energy expended in 
 producing eddy currents 
 is converted into heat and 
 represents a loss. These 
 losses are quite large in 
 dynamos, motors, trans- 
 formers, etc., and it is 
 always best to reduce 
 Fig. 87 them to a minimum when 
 
 it is possible. The best 
 
 way of reducing them is to split the mass of metal up into 
 sheets, the plane of these sheets being parallel to the direction 
 of the lines of force. It is customary to build up all volumes 
 of metal that are likely to have eddy currents produced in 
 them from thin sheets, or laminations, as they are called. 
 Induction-coil cores are made from short lengths of small wire 
 instead of using a solid core. Armature cores and the cores of 
 transformers are laminated so as to reduce the loss due to 
 eddy currents. These laminae are usually between .014 and 
 .025 inch in thickness for dynamos, and the space between 
 
ELECTKOMAGNETIC INDUCTION 119 
 
 them that is taken up by the oxide that forms on their surface 
 is about .002 inch. Losses due to eddy currents could be re- 
 duced to an inappreciable value by decreasing the thickness of 
 the laminae, but there is a practical limit on account of the 
 decrease in effective iron area, caused by the waste of space 
 taken up by the insulation between adjacent lamin.ne. 
 
 When the laminae are perfectly insulated from each other, 
 the following equation can be used in calculating the power 
 in watts lost in iron due to eddy currents: 
 
 We = k X V X f2 x t2 x 2 (83) 
 
 In the above equation (k) is a constant, depending upon 
 the resistance of the iron per cubic centimeter, which is 
 usually about 1.6 X 10-H; (V) is the volume of the iron in 
 cubic centimeters; (t) is the thickness of one lamina in 
 centimeters; (f) is the frequency of magnetic cycles per 
 second; and (/3) is the maximum number of lines per square 
 centimeter to which the iron is magnetized. 
 
 Example. Find the eddy-current loss in 1000 cubic centi- 
 meters of iron, composed of laminations .04 cm. thick (in- 
 cluding insulation), that is subject to a maximum (/3) of 
 10 000 lines per square centimeter and a frequency of 60 
 cycles per second. 
 
 Solution. Taking the value of (k) = 1.6 X 10-n and sub- 
 stituting in equation (83) gives 
 
 1000 X 602 X (.04)2 x 10 0002 
 
 1.6 X 1011 
 1000 X 3600 X .0016 X 100 000 000 
 
 We = 
 
 1.6 X 1011 
 
 Ans. 3.6 watts. 
 
 128. Non-inductive Circuit. In the construction of certain 
 coils it is desired to have them as nearly non-inductive as 
 possible. This is accomplished by winding the coil with two 
 
120 
 
 PEACTICAL APPLIED ELECTKICITY 
 
 wires laid side by side, as shown in Fig. 88, their inner ends 
 being joined electrically. When the winding is completed, 
 the two outside ends form the terminals of the coil. The cur- 
 rent in such a coil is in one direction in one- 
 half of the turns and in the remaining half 
 of the turns in the opposite direction. The 
 result is that the magnetic effect of the 
 current in one-half of the turns is equal 
 and opposite to the other half and they 
 
 Fig. 88 
 
 exactly neutralize, and the inductance of the coil will be zero, 
 or the coil will be non-inductive. 
 
CHAPTEE VIII 
 
 ELECTRICAL INSTRUMENTS AND EFFECTS OF A 
 CURRENT 
 
 129. Classification of Instruments. No attempt will be made 
 in this chapter to describe all of the various forms of instru- 
 ments on the market at the present time, it being deemed 
 best to confine the description in almost every case to 
 those that are in most common use. Electricity is not a 
 material substance like water and cannot be measured in 
 the same way since it has no dimensions such as length, 
 breadth, or weight. An electrical current is studied and meas- 
 ured by the effects it produces in an electrical circuit. The 
 operation of all instruments depends upon some effect pro- 
 duced by the current and this leads to the classification of 
 instruments into four groups depending upon the particular 
 effect employed in their operation. These effects are: 
 
 (a) Electro-chemical effect. 
 
 (b) Magnetic effect. 
 
 (c) Heating effect. 
 
 (d) Electrostatic effect. 
 
 Note: The electrostatic effect is not an effect of a cur- 
 rent primarily, but of electrical pressure. 
 
 In addition to the above classification, instruments may 
 be divided into the following groups: 
 
 (a) Instruments suitable for direct-current measurements 
 only. 
 
 (b) Instruments suitable for alternating-current measure- 
 ments only. 
 
 (c) Instruments suitable for both direct- and alternating- 
 current measurements. 
 
 In the following discussion of instruments, they will be 
 grouped according to the effect upon which their operation 
 
 121 
 
122 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 depends, and their adaptability to the measurement of direct 
 or alternating current will be pointed out at the same time. 
 
 Ammeters, Galvanometers, and Voltmeters 
 
 130. Distinction between Ammeters, Galvanometers, and 
 Voltmeters. An ammeter is an instrument to be used in 
 measuring the current in a circuit, and for that reason am- 
 meters will always be connected in series with that part of 
 the circuit in which it is desired to ascertain the value of 
 the current. 
 
 A galvanometer is an instrument used in detecting the 
 presence of a current in a circuit, or for measuring the 
 value of the current. It is really the same as an ammeter 
 as far as construction and operation are concerned, but 
 it is usually used in measuring very small currents as com- 
 pared to those measured by ammeters. 
 
 Fig. 89 Fig. 90 
 
 In Fig. 89, the ammeter (A) is connected in series with 
 the battery (B) and the two resistances (Ri) and (R 2 ), 
 which are in parallel. The ammeter in this case reads 
 the total current in the main circuit but it does not give 
 the current in either of the resistances (R!> or (R 2 ). If, 
 however, the instrument be connected, as shown in Fig. 90, 
 it will indicate the current in the resistance (Ri). By chang- 
 ing the instrument to the branch containing the resistance 
 (R 2 ), the current in this branch can likewise be determined. 
 
 A voltmeter is an instrument for measuring the difference 
 in electrical pressure between any two points to which 
 its terminals may be connected. Thus, if it is desired to 
 know the difference in electrical pressure between the ter- 
 
ELECTKICAL INSTRUMENTS 123 
 
 minals of any part of an electrical circuit, such as the differ- 
 ence in pressure between the terminals of a lamp that is 
 connected to some source of electrical energy, as shown in 
 Fig. 91, the voltmeter is connected to the two terminals and 
 its indication is a measure of the pressure over the lamp. The 
 ammeter and the voltmeter both operate on the same prin- 
 ciple, that is, their indications depend upon the current pass- 
 ing through them. The voltmeter indication depends upon the 
 pressure between its terminals, because the current through 
 it varies with this difference in pressure, the resistance of 
 the instrument remaining constant. 
 
 The resistance of an ammeter should be very low for the 
 following reason: An ammeter will always be connected 
 directly in the circuit and there will be a difference in elec- 
 trical pressure between its terminals when there is a cur- 
 rent through it, which is at any instant numerically equal 
 to the product of the current and the resistance of the instru- 
 ment. This drop across the ammeter should be small in 
 order that the power required to operate the instrument be 
 low in value, it being equal to the product of the current 
 through the ammeter and the difference in pressure between 
 ammeter terminals. If the ammeter in Fig. 89 had a resist- 
 ance whose value was something near the value of the com- 
 bined resistance of the two coils (Rj) and (R2) in parallel, 
 practically half the output of the battery would be consumed 
 in the ammeter and would represent a loss. If, on the other 
 hand, the ammeter had a very low resistance, a very small 
 part of the output of the battery would be consumed in it. 
 The division of the current between the two branches of 
 the circuit shown in Fig. 90 would be quite different after 
 the ammeter was introduced in either branch to what it was 
 before, if the ammeter had a large resistance. If the am- 
 meter had a small resistance in comparison to that of either 
 of the branches, the change in the division of the current 
 between the two branches when the ammeter was introduced 
 in either of them would be a great deal less than in the pre- 
 vious case. 
 
 The resistance of a voltmeter, on the other hand, should be 
 as large as possible for the following reason: The loss 
 of power in the voltmeter is equal to the product of the 
 current through it and the difference in pressure between its 
 
124 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 terminals, and since it is to indicate the difference in pres- 
 sure, the only way this loss can be reduced is to increase the 
 resistance of the instrument, which results in a smaller cur- 
 rent. Suppose the voltmeter (V), shown in Fig. 91, had a re- 
 sistance equal to that of the lamp (L), then the power 
 required to operate the voltmeter would be equal to that 
 required to operate the lamp, since there would be the 
 same value of current in each, and the same difference in 
 pressure between their terminals. This condition of affairs 
 would result in a considerable loss and it could be reduced 
 by increasing the resistance of the voltmeter. An ammeter 
 
 connected in the line lead- 
 ing from the generator 
 (G) .to this lamp would in- 
 dicate the combined cur- 
 
 rent in the lamp and the 
 voltmeter circuits. Hence, 
 in order to get the current 
 in the lamp circuit, the 
 value of the current in the 
 
 circuit should be subtracted from the value of 
 current. If the resistance of the voltmeter be 
 
 Fig. 91 
 
 voltmeter 
 the total 
 
 large in comparison to that of the lamp, the current in its 
 circuit will be small in comparison to the lamp current and 
 the ammeter indication will be practically equal to that in the 
 lamp circuit. The above discussion leads to the conclusion 
 that an ammeter and a voltmeter need differ only in their 
 resistance, the principle of operation being the same. 
 
 131. Ammeter Shunts. In the construction of ammeters it 
 is usually customary to make them with two circuits between 
 their terminals. One circuit has a very low resistance and 
 carries the greater portion of the current to be measured, 
 while the other circuit has a comparatively large resistance 
 and carries a small current. The current in the branch of 
 larger resistance usually produces the deflection of the mov- 
 ing system of the instrument. The other branch constitutes 
 what is termed the ammeter shunt. The shunt and moving 
 system are usually mounted in the same case, when the 
 instrument is used in measuring currents ranging from a 
 very low value to perhaps 600 amperes. For large currents 
 they are usually constructed separately. 
 
ELECTEICAL INSTEUMENTS 
 
 125 
 
 If the resistance of the shunt is known, the current through 
 it can be determined by measuring the difference in pres- 
 sure between its terminals by means of a suitable voltmeter, 
 usually a millivoltmeter and then dividing this difference 
 in pressure in volts by 
 the resistance gives the 
 value of the current. 
 Instruments used on 
 switchboards as a rule 
 have their shunts con- 
 nected directly in the 
 line, and small leads 
 run from the terminals 
 of this shunt to the 
 moving system, which 
 is mounted in a conven- 
 ient place on the face 
 of the board. An instru- 
 ment and its shunt are 
 chown in Fig. 92. The 
 needle of this instru- 
 ment comes to rest in 
 the center of the scale 
 when there is no cur- 
 rent in its winding, and the direction of its deflection will 
 depend upon the direction of the currents in the shunt. 
 
 Fig. 92 
 
 Instruments Whose Operation Depends Upon Electro-Chemical 
 Effect of a Current 
 
 132. Electrolysis. If two conducting plates, such as plati- 
 rum, be immersed in acidulated water and a current of elec- 
 tricity be passed through the solution from one plate to the 
 other, the water will be decomposed into its two constituents, 
 oxygen and hydrogen. Such a combination of plates and 
 solution constitutes what is called an electrolytic cell, and 
 the process of decomposing the liquid is called electrolysis. 
 The solution through which the electricity is being conducted 
 is called the electrolyte, and the two plates that are im- 
 mersed in the solution are called electrodes. The plate by 
 
126 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 which the electricity enters the solution is called the positive 
 electrode, or anode, and the plate by which the electricity 
 leaves the solution is called the negative electrode, or cathode. 
 The parts into which the electrolyte is decomposed are 
 called ions. The ion liberated at the positive electrode is 
 called the anion, and the one liberated at the negative pole 
 is called the oath ion. The vessel, plates, and other appa- 
 ratus used in electrolysis constitute what is termed a 
 voltameter, when such apparatus is used to measure quantity 
 or current. When water is decomposed, hydrogen appears 
 at the negative plate, or it is the cathion, and oxygen ap- 
 pears at the positive plate, or it is the anion. A simple 
 
 Electrolyte 
 
 Cathode 
 
 Fig. 93 
 
 Fig. 04 
 
 electrolytic cell is shown in Fig. 93. The gas liberated at 
 the two electrodes in this case passes off into the air. The 
 voltameter, however, can be so constructed that the liberated 
 gas will collect in an enclosed U-shaped tube, as shown in 
 Fig. 94. The direction of the current in the circuit is indi- 
 cated in the figure by the arrow. The oxygen will collect 
 in the tube (A) and force the water down, while the hydrogen 
 will collect in (B) and force the water down. The weight of 
 the oxygen gas liberated by a certain quantity of electricity 
 will be about eight times that of the hydrogen gas, but the 
 oxygen gas will occupy only half the space that the hydrogen 
 gas occupies, since a given volume of hydrogen gas is 
 approximately one-sixteenth as heavy as the same volume 
 
ELECTKICAL INSTRUMENTS 127 
 
 of oxygen gas, and as a result the volume of gas collecting 
 in the (B) tube will be practically twice the volume of gas 
 in the (A) tube. 
 
 133. Electrolysis of Copper Sulphate. When a current ex- 
 ists between two platinum plates immersed in a solution of 
 copper sulphate CuSO 4 made by dissolving copper sulphate 
 crystals (bluestone) in water, the solution will be broken up 
 by electrolysis into Cu (metallic copper) and SO 4 (sulphion). 
 The hydrogen gas liberated at the negative electrode takes 
 the place of the Cu in the CuSO 4 forming H 2 SO 4 (sulphuric 
 acid) and the Cu is deposited on the negative plate. Oxygen 
 will be liberated at the positive electrode as in the previous 
 case. All of the Cu contained in the solution will be de- 
 posited on the negative plate if the current be allowed 
 to pass through the electrolytic cell for a considerable time. 
 When the Cu has all been removed from the solution it will 
 be practically colorless. The reaction taking place in the cell 
 can be represented as follows: 
 
 CuSO 4 = Cu + SO 4 (84) 
 
 Copper sulphate is decomposed into copper and sulphion. 
 The Cu is deposited on the negative plate. 
 
 S0 4 + H 2 = H 2 S0 4 + O (85) 
 
 The sulphion and water combine forming sulphuric acid and 
 oxygen. The oxygen is liberated and passes off into the 
 air and the sulphuric acid remains in the solution. 
 
 In the above case the negative plate will increase in 
 weight due to the deposit of copper upon it and this increase 
 in weight is proportional to the quantity of electricity pass- 
 ing between the two electrodes. 
 
 If copper plates be substituted for the platinum plates, 
 the sulphuric acid will attack the positive electrode and 
 just as much copper will be thrown into solution as is 
 deposited upon the negative electrode. This results in no 
 change in the electrolyte, but there is a wasting away of the 
 positive plate and an equal increase in weight of the negative 
 plate as the electrolytic action continues. 
 
 134. Electroplating. The principles of electrolysis are ap^ 
 plied in coating objects with a layer of metal and the proc, 
 ess is called electroplating. The object to be plated always 
 
128 PRACTICAL APPLIED ELECTRICITY 
 
 forms the cathode of the electrolytic cell and the metal to 
 be deposited is held in solution and as the process con- 
 tinues metal is supplied to the solution from a plate which 
 forms the anode of the cell. This plate should, of course, 
 be of the same material as the metal in the solution. All 
 articles cannot be coated with certain metals without having 
 first been coated with some other metal. As an example, 
 articles composed of iron, tin, lead, and zinc cannot be silver- 
 or gold-plated without first being copper-plated. 
 
 135. Electrotyping. An electrotype of a column of stand- 
 ing type is made as follows: First, an impression in wax 
 is made, then the surface of this impression is dusted over 
 with powdered graphite to make the surface a conductor. 
 This mold is then placed in a copper-plating bath, it forming 
 the cathode, and receives a thin coating of metallic copper. 
 When sufficient copper has been deposited, the mold is re- 
 moved from the solution and the copper plate that was formed 
 is separated from the mold and backed with type metal to a 
 thickness of about % inch, and then mounted on a wooden 
 block. It is necessary to back the copper plate with type 
 metal because it is so thin that it would not stand the pres- 
 sure to which it is subjected in the printing press. 
 
 136. Polarity Indicator. The polarity of a direct-current 
 circuit can be determined as follows: Immerse the ends of 
 two wires that are connected to the line wires, whose polarity 
 it is desired to determine, into a vessel of water, taking 
 care that the two ends do not come into contact with each 
 other. Since approximately twice as much hydrogen gas 
 (by volume) is liberated at the negative electrode as oxygen 
 gas at the positive electrode, the polarity of the circuit being 
 tested is easily determined. A simple polarity indicator can 
 be constructed as follows: Place in a small glass tube a 
 solution of iodide of potassium, to which a little starch has 
 been added. Two short pieces of wire should be sealed 
 into the ends of the tube. When a current is passed through 
 this solution iodine is liberated at the positive terminal and 
 the solution is turned blue around this terminal. 
 
 137. Prevention of Electrolytic Action. Electrolytic action 
 is oftentimes the source of a great deal of trouble, especially 
 in the deterioration of underground metals, such as gas, 
 water, and sewer pipes, and the lead covering on telephone 
 
ELECTEICAL INSTRUMENTS 129 
 
 and power cables. Electricity takes the path of least resist- 
 ance in completing its circuit and, as a result, all conductors 
 that are buried in the ground and not insulated from it, 
 usually conduct some electricity, especially in localities where 
 street car and power companies are operating with grounded 
 circuits. There will be no decomposition of the pipe or 
 lead sheath where the electricity flows onto them, but at the 
 point where it leaves, an electrolytic action will take place 
 which results in the metal of the pipe or cable sheath being 
 carried away. This, of course, means that the pipe or cable 
 sheath will be greatly damaged or completely destroyed 
 if the action is allowed to continue. To prevent this action, 
 one end of a conductor is electrically connected to the pipe 
 or cable sheath at the points where the electricity tends 
 to leave them ard the other end of the conductor is buried, 
 or grounded. The electrolytic action still continues but it 
 takes place at the end of the conductor in the ground and 
 the damage is not serious. In some cases the pipes are 
 wrapped with an insulating tape or coated with an insu- 
 lating compound, which tends to prevent the electricity pass- 
 ing on or off of them, thus reducing the electrolytic action. 
 The connecting of a cable sheath or pipe to the ground is 
 called bonding. Rail joints are bonded by connecting the 
 ends of the rails electrically by means of a flexible copper 
 conductor. 
 
 138. Weight Voltameter. Since the weight of a metal 
 deposited or the weight of water decomposed by a given 
 quantity of electricity is known, the electrolytic cell may be 
 used as a quantity measuring instrument. Thus, if two cop- 
 per plates be immersed in a solution of copper sulphate and 
 a quantity of electricity passed between them, there will be a 
 change in weight of the two plates. This change in weight 
 of the plates can be determined and from it the quantity of 
 electricity that passed between them can be calculated. An 
 instrument of this kind can be used in measuring the current 
 in a circuit, If it remains constant in value for a certain 
 time. Thus, if a unit quantity of electricity pass between 
 the two plates in one second, there will be a current of one 
 ampere in the circuit. If ten units of quantity of electricity 
 pass between the plates in ten seconds, there will still be a 
 current of one ampere, or if ten units of quantity pass in 
 
130 PRACTICAL APPLIED ELECTRICITY 
 
 two seconds, there will be a current of five amperes. Hence, 
 in order to measure a current that is constant in value, with 
 the voltameter, it is only necessary to note the time taken 
 to produce a certain deposit. The weight of the total deposit 
 divided by the time gives the weight of the deposit per sec- 
 ond and this value divided by the weight each coulomb will 
 deposit gives the current in amperes, since the current is 
 the number of coulombs per second. Call the total gain in 
 weight in grams (W), the time in seconds taken to produce 
 the gain in weight (t), and the deposit produced by one 
 coulomb (K). Then 
 
 gain in weight in grams 
 
 Amperes = 
 
 gain in grams per coulomb X time in seconds 
 or (86) 
 
 (87) 
 
 Table No. VII gives the weight in grams that one coulomb 
 or one ampere in one second will deposit (called the electro- 
 chemical equivalent). 
 
 TABLE NO. VII 
 ELECTRO-CHEMICAL EQUIVALENTS IN GRAMS PER COULOMB 
 
 K for silver 001118 gram 
 
 K for copper 000329 gram 
 
 K for zinc 000338 gram 
 
 K for lead 001071 gram 
 
 K for nickel 000304 gram 
 
 A commercial form of voltameter is shown in Fig. 95. The 
 two outside plates form the anode and they are connected 
 electrically. There will be a metallic deposit on both sides 
 of the middle plate which form the cathode, due to the pres- 
 ence of the two outside plates. 
 
 Example. The increase in weight of a platinum plate in 
 a silver voltmeter was 4.0248 grams when the circuit in 
 which the voltameter was connected was closed for 15 min- 
 utes. What current was there in the circuit? 
 
ELECTEICAL INSTEUMENTS 131 
 
 Solution. Substituting in equation (87) gives 
 4.0248 
 
 = 4 
 
 .001118 X 15 X 60 
 
 Ans. 4 amperes. 
 
 139. Adaptability of Voltameters. The voltameter is really 
 a quantity-measuring instrument and it will only measure the 
 current when the rate of flow of electricity is constant and, as 
 a result, it is not suitable for ordinary work. Determinations 
 
 Fig. 95 
 
 of the value of a current made by this instrument are very 
 accurate, when properly made, and they are used as pri- 
 mary standards in checking up the indications of other cur- 
 rent-measuring instruments. 
 
 The voltameter is not suitable for pressure measurements, 
 since its resistance is not constant and, as a result, the cur- 
 rent through it would not always be proportional to the pres- 
 sure impressed upon the circuit of which it is a part. 
 Voltameters can not be used in the measurement of an alter- 
 nating current, since there would be a reversal of chemical 
 action each time there was a change in the direction of the 
 
132 PEACTICAL APPLIED ELECTRICITY 
 
 current. If the same quantity passed through the voltameter 
 in one direction as passed through it in the other, there 
 would be no metallic deposit on either electrode. 
 
 Instruments Whose Operation Depends Upon Magnetic Effect 
 of a Current 
 
 140. Magnetic Effect of a Current. The magnetic effect 
 of a current was discussed in detail in the chapter on "Electro- 
 magnetism" and it is only necessary to bear in mind the 
 following facts: 
 
 (a) There is a magnetic field about a conductor in which 
 there is a current. 
 
 (b) The direction of the magnetic field will depend upon 
 the direction of the current in the conductor. 
 
 (c) The strength or intensity of this field will vary with 
 the value of the current in the conductor and the distance 
 from the conductor. 
 
 Instruments whose operation depends upon the magnetic 
 effects of a current in a conductor may be classified as 
 follows : 
 
 A. Those in which permanent magnets are used, they 
 being acted upon by the magnetic field produced by the cur- 
 rent. Either the magnet or the conductor carrying the cur- 
 rent may form the moving part. 
 
 B. Those having soft iron parts which are moved due to 
 the magnetic effect produced by the current in the con- 
 ductor. 
 
 C. Those in which no iron is used, but having two coils, 
 one of which is movable. This coil is moved due to a mag- 
 netic force that is exerted between them when there is 
 a current in both coils. 
 
 CLASS "A" 
 
 141. Tangent Galvanometer or Ammeter. If a magnetic 
 needle be supported in the center of a coil of wire, as shown 
 in Fig. 96, there will be a force tending to turn the needle 
 from its position of rest in the earth's magnetic field when 
 there is a current in the coil. This force will increase with 
 an increase in current in the coil and, as a result, the needle 
 
ELECTRICAL INSTRUMENTS 133 
 
 will be deflected more and more as the current is increased 
 until it occupies a position that is almost at right angles 
 to its initial position. If a suitable scale be mounted, as 
 shown in the figure, so that the ends of the needle, or a 
 pointer that is fastened to the needle, will move over the 
 scale, the deflection of the needle from the position of rest, 
 due to a certain current, can be determined. 
 
 The force which tends to return 
 the needle to its initial position is 
 due to the magnetic field of the 
 earth. In using the instrument, the 
 coil carrying the current should be 
 placed with its plane parallel to the 
 plane of the needle and allowed to 
 remain in this position while all the 
 readings are being taken. Such an 
 instrument is usually called a tan- 
 gent galvanometer, or ammeter, 
 because the value of the current Fig. 96 
 
 through the coil is equal to some 
 
 constant times the tangent of the angle through which the 
 needle moves. The indications of an instrument of this kind 
 are disturbed by the presence of magnetic fields other than 
 that of the earth, or the current in the coil of the instrument 
 itself, and as a result its operation is not very saisfactory 
 except under ideal conditions. 
 
 142. D'Arsonval Instrument. In the D'Arsonval type of 
 instrument, the permanent magnet is the stationary portion 
 and the conductor carrying the current forms the movable 
 part of the instrument. The instrument is named after a 
 French scientist, who first put it into a useful form. The 
 cor.ductor carrying the current to be measured is bent into 
 the form of a coil and may be either suspended or supported 
 in the magnetic field of the permanent magnet. In the most 
 sensitive forms of the instrument the coil is usually sus- 
 pended by a conducting thread, such as phosphor-bronze or 
 plated quartz fiber. The electricity is conducted to and 
 from the coil by means of this support and another electrical 
 connection at the bottom of the coil which may consist of 
 a second fiber of the same material as the upper one or 
 it may be a very fine wire coiled into a spiral, or a wire 
 
134 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 may dip into a cup of mercury. A D'Arsonval galvanometer 
 is shown in Fig. 97. The deflections of the coil are measured 
 by means of a telescope and suitable scale, together with 
 a small mirror mounted on the moving system of the instru- 
 ment. The image of the scale in the mirror may be read 
 by means of the telescope, and as the mirror turns, the part 
 of the scale visible through the telescope changes. 
 
 Fig. 97 
 
 An instrument of this kind can be constructed so that it is 
 very sensitive and will respond to extremely small currents. 
 It is not subject to outside disturbances to any great extent, 
 such as stray magnetic fields, changes in the strength of the 
 earth's magnetic field, etc. This instrument can be con- 
 structed and adjusted so that it may be used in measuring 
 either current or pressure. 
 
 143. D'Arsonval Ammeters and Voltmeters. The Weston 
 ammeter and voltmeter are both good examples of D'Arson- 
 val instruments. The moving coil in these instruments is 
 mounted on pointed pivots that are extremely hard and 
 rest in agate jewels, which results in a very small frictional 
 resistance to the movement of the coil. A light pointer is 
 attached to the coil and so arranged that it moves over a 
 suitable scale properly graduated and lettered so that the 
 indication of the instrument may be easily determined. A 
 sectional view of the moving system of a Weston instrument 
 
ELECTBICAL INSTEUMENTS 
 
 135 
 
 is shown in Fig. 98, with a portion of the instrument cut 
 away so as to show the construction. The permanent magnet 
 is of the horseshoe type and has two pole pieces fastened 
 to its ends by means of heavy screws. The inner surface 
 of each of these pole pieces is cut so it forms an arc, the cen- 
 ter of which is midway between the two inner surfaces of the 
 magnet. A soft iron cylinder is mounted between the two 
 pole pieces and serves to improve the magnetic circuit. This 
 
 Fig. 98 
 
 cylinder is mounted on a piece of brass that is fastened to 
 the two pole pieces, as shown in the figure, there being a 
 small gap between the cylinder and the pole pieces. The 
 coil is mounted so that it can turn about the cylinder. The 
 force tending to return the coil to its zero position is sup- 
 plied by two springs. These springs are so arranged that 
 one winds up when the other unwinds, due to a movement 
 of the coil. The electrical connection to the coil is made 
 through these two springs. 
 
 Practically the same moving system is employed in the 
 construction of ammeters and voltmeters. In the ammeter, a 
 low resistance, capable of carrying the current the instru- 
 ment is supposed to measure, is connected between the bind- 
 ing post on the instrument case; and the moving system is 
 
136 
 
 PRACTICAL APPLIED ELECTEICITY 
 
 connected in parallel with this resistance. Binding posts 
 are provided of ample size to carry the current. A We&tori 
 portable ammeter is shown in Fig. 99. 
 
 In the voltmeter, a re- 
 sistance coil is con- 
 nected in series with 
 the moving system be- 
 tween the terminals of 
 the instrument. The 
 value of the resistance 
 to be placed in series 
 with a moving system 
 will depend upon the 
 voltage a full scale 
 reading of the instru- 
 ment indicates. The 
 range of any voltmeter 
 may be increased by 
 
 connecting additional resistances in series with it. Thus, if a 
 resistance equal to that of the voltmeter itself be connected 
 in series with the instrument, the voltmeter will indicate only 
 half the pressure between the two points to which the 
 
 Fig. 09 
 
 100 
 
 terminals of the combination are connected. Resistances, 
 called multipliers, can be obtained from companies manufac- 
 turing instruments to be used in increasing the range of a 
 voltmeter. 
 
 A contact key is usually mounted on each voltmeter case 
 and so arranged that the circuit of the instrument may be 
 opened or closed by manipulating the key. The instrument 
 
ELECTRICAL INSTRUMENTS 
 
 137 
 
 can be made so that a maximum scale deflection will cor- 
 respond to one or more voltages. Thus an instrument may 
 be constructed so that one connection will measure (0-3) 
 volts and another will measure (0-150) volts. The resist- 
 ance of these two circuits should be in the ratio of 3 to 
 150. A Weston portable voltmeter is shown in Fig. 100. 
 
 Instruments of the D'Arsonval type are suitable for gen- 
 eral use because they are "dead-beat"; that is, the coil or 
 moving system goes immediately to its proper position with- 
 out swinging back and forth, as in many of the other types. 
 
 144. Adaptability of Instruments with Permanent Mag- 
 nets. Instruments whose operation depends upon a perma- 
 nent magnet can be used only in direct-current measure- 
 ments, because the direction of the deflections is dependent 
 upon the direction of the current through them. 
 
 CLASS "B" 
 
 145. Plunger Type Ammeter or Voltmeter. The construc- 
 tion of a plunger type ammeter or voltmeter is shown in 
 Fig. 101. The coil (C) carries the current to be measured. 
 There will be a magnetic force exerted on the rod of iron 
 (R), when there is a current in the coil (C), which will tend 
 
 T, 
 
 prmg 
 Vane 
 Co 1 1 CO 
 
 Fig. 101 
 
 Fig. 102 
 
 to draw the rod into the coil, and thus cause the pointer 
 (P) to move over the graduated scale (S). Gravity is the 
 controlling force against which the magnetic force of the coil 
 acts. The rod (R) and the coil (C) are both formed to the 
 same curvature. The rod (R) is composed of very soft iron 
 and it becomes a magnet due to the action of the current 
 
138 PRACTICAL APPLIED ELECTRICITY 
 
 in the coil and, as a result, is drawn inside the coil. The 
 distance the rod moves will depend upon the value of the 
 controlling force and the ampere turns on the coil at any 
 instant. In an ammeter, the coil (C) is wound with a few 
 turns of large wire, while in a voltmeter it is wound with a 
 large number of turns of small wire, the ampere-turns pro- 
 ducing a given deflection in the two cases being the same. 
 
 146. Magnetic Vane Ammeter or Voltmeter. Instruments 
 of this type operate on the principle that a piece of soft iron 
 placed in a magnetic field and free to move will always 
 move into such a position that it will conduct the maximum 
 number of lines of force, or it will tend to move into the 
 strongest part of the field and parallel to the field. Fig. 102 
 shows a diagram of an instrument of this kind. The current 
 to be measured is passed around the coil (C) producing a 
 magnetic field through the center of the coil. A small piece 
 of soft iron called the vane is mounted on a shaft that is 
 supported in jewel bearings. This shaft is not in the exact 
 center of the coil so that the distance the vane is from the 
 inner edge of the coil will change as it moves about the 
 shaft. The magnetic field inside the coil is strongest near 
 the inner edge and, as a result, the vane will move so that 
 the distance between it and the inner edge of the coil would 
 be as small as possible, if it were not for a restoring force 
 supplied by a coiled spring. The tendency of this vane 
 to rotate increases with the current in -the coil and, as a 
 result, the pointer attached to the moving system moves 
 over the scale with an increase in current. 
 
 In some types of instruments there is both a stationary and 
 a movable vane. They both become magnetized to the same 
 polarity and, as a result, repel each other. This force causes 
 the moving system to be deflected. Ammeters and volt- 
 meters operating on this principle differ only in the size 
 of wire and the number of turns in the coil (C). 
 
 147. Thomson Inclined-Coil Instruments. The construe- 
 tion of a Thomson instrument is shown in Fig. 103. The coil 
 (C) carrying the current is mounted at an angle to the 
 shaft (S) supporting the pointer (P). A strip or bundle of 
 strips of iron (I) are mounted on the shaft (S) and held by 
 a spring, when there is no current in the coil, so that its posi- 
 tion is nearly parallel to the plane of the coil. When a cur- 
 
ELECTEICAL INSTRUMENTS 
 
 139 
 
 rent is passed through the coil, the iron tends to take up a 
 position with its longest dimension parallel to the magnetic 
 field, which results in the shaft being rotated and the pointer 
 moved over the scale. The degree of this movement will 
 depend upon the value of the current in the coil. 
 
 148. Adaptability of Instruments with Soft Iron Parts. 
 The instruments described in the previous three sections may 
 be used in measuring either direct or alternating currents and 
 pressures;. Their indications, however, are not reliable when 
 used in direct-current work because they are influenced by 
 outside fields and masses of iron. There is also a lag of the 
 magnetic condition of the piece of soft iron behind the mag- 
 netizing force, which results in their indications being lower 
 than the true value as the current is increasing, and higher 
 
 P Spring 
 
 Scale 
 
 Fig. 103 
 
 as the current is decreasing. With alternating currents, 
 these objections are not present and the operation of the 
 instruments will be found to be quite satisfactory, provided 
 the outside field does not change at the same frequency as 
 the current to be measured. 
 
 CLASS "C" 
 
 149. Electrodynamometer. The electrodynamometer is, per- 
 haps, the best example of an instrument whose operation 
 depends upon the magnetic force exerted between two coils, 
 both of which have a current in them. The two coils are 
 usually placed at right angles to each other, as shown in 
 Fig. 104, one of them being fastened rigidly to the frame of 
 the instrument, while the other is supported or suspended and 
 its position controlled by a spring. When a current exists in 
 
140 
 
 PEACTICAL APPLIED ELECTRICITY 
 
 both coils, the movable one tends to turn into such a position 
 that its magnetic field is parallel to the magnetic field pro- 
 duced by the current in the stationary coil. This movable 
 coil, however, is brought back to its zero position by turning 
 the thumb screw, which is connected to the upper end of the 
 spring, causing the spring to be twisted in the opposite direc- 
 tion to that in which the coil tends to move. The tortion in 
 the spring exactly balances the tendency for the coil to turn 
 when the thumb screw has been turned through the proper 
 
 Fig. 104 
 
 angle. A pointer is fastened to this thumb screw and moves 
 over a graduated scale. The effect produced by a given cur- 
 rent through the two coils, which are connected in series, is 
 then read as so many divisions on the scale. 
 
 When the instrument is used as an ammeter, the two coils 
 consist of a few turns of large wire, depending, of course, 
 on the current capacity of the instrument. Quite often the 
 stationary coil is divided into two parts, only part of the 
 turns being used in series with the movable coil for one 
 
ELECTKICAL INSTRUMENTS 141 
 
 connection, while all the turns may be used if desired. The 
 current required to produce a full scale deflection when 
 all the turns in the stationary coil are in use will be less 
 than the current required when only a portion of the turns 
 are used. 
 
 When the instrument is used as a voltmeter, the coils are 
 composed of a large number of turns of small wire. Often an 
 additional resistance is provided to be used in series with the 
 instrument, which increases its range as a voltmeter. 
 
 150. Adaptability. The indications of instruments of the 
 electrodynamometer type are influenced by stray magnetic 
 fields and, as a result, they are not altogether satisfactory 
 for direct-current measurements. This error, however, can 
 be reduced to practically zero, if the disturbing effect remains 
 constant which is not very often the case by taking the 
 average of two readings of the instrument with the current 
 through it in opposite directions in the two cases. The above 
 errors do not occur when instruments of the electrodyna- 
 mometer type are used in alternating-current measurements 
 unless frequency of the distributing field is the same as the 
 frequency of the current in the instrument as the current 
 is continuously reversing in direction. 
 
 Instruments Whose Operation Depends Upon Heating Effect 
 of a Current 
 
 151. Heat Generated in a Conductor Carrying a Current. 
 When there is a current produced in a conductor, the 
 energy expended in overcoming the conductor's resistance is 
 manifested in the form of heat. Dr. Joule discovered that the 
 heat developed in a conductor carrying a current was pro- 
 portional to 
 
 (a) The resistance of the conductor. 
 
 (b) The square of the current in the conductor. 
 
 (c) The time the current exists in the conductor. 
 
 He also determined by experiment that 778 foot-pounds 
 of work would raise the temperature of 1 pound of water 
 1 Fahrenheit. This quantity, 778 foot-pounds, is called the 
 mechanical equivalent of heat, or Joule's equivalent. A pound 
 of water can be heated electrically by immersing a conductor 
 carrying a current in the water until its temperature is raised 
 
142 PRACTICAL APPLIED ELECTRICITY 
 
 1 Fahrenheit, or the same work will be done electrically 
 as was previously done mechanically. Joule found by experi- 
 ment that 1 ampere under a pressure of 1 volt in a circuit for 
 1 second, or 1 watt expended, would do the same work as 
 '0.7373 foot-pound expended in 1 second, or 
 
 1 watt = 0.7373 foot-pound per second (88) 
 
 The British thermal heat unit (abbreviated b.t.u.) is de- 
 fined as the amount of heat required to raise one pound o 
 water 1 Fahrenheit at its maximum density (39.1 Fahren- 
 heit). Since 778 foot-pounds of work is equivalent to 1 
 b.t.u. and 1 watt is equal to .7373 foot-pound per second, then 
 1 watt acting for 1 second will develop .000 947 7 b.t.u., or 
 
 b.tu. = .000 947 7 X (E X I) X t (89) 
 
 Substituting for (E) its value, (I X R), gives 
 b.tu. = .000 947 7 X I2R X t 
 
 Example. What current must be passed through a resist- 
 ance of 100 ohms immersed in 10 pounds of water in order 
 that its temperature be raised 80 Fahrenheit in 5 minutes? 
 
 Note: (All losses due to radiation are to be neglected and 
 all the energy is supposed to be converted into heat). 
 
 Solution. There will be 80 b.t.u. required for each pound 
 of water or a total of 80x10 = 800 b.t.u. Substituting in 
 equation (89) gives 
 
 800 = .000 947 7 X 12 X 100 X (5 X 60) 
 800 8 
 
 12 = _ 
 
 .0009477X100X300 .28431 
 
 12 = 28.13 
 I ='5.3+ 
 
 Ans. 5.3-f- amperes. 
 
 152. Commercial Applications of the Heating Effect of a 
 Current. Numerous practical applications are made of the 
 heating effect of a current in a conductor, such as electric 
 irons, cooking stoves, heaters, lamps, electric welding, fuses, 
 etc. Since the heat generated in any part of a circuit is 
 proportional to the resistance of the part considered, it fol- 
 lows that it is always desirable to have all conductors used 
 
ELECTKICAL INSTRUMENTS 143 
 
 in transmitting electrical energy of as low resistance as pos- 
 sible in order that the loss in transmission be a minimum. 
 On the other hand, when it is desired to generate heat, resist- 
 ance is introduced and the value of the heat generated can be 
 determined by the use of equation (89). If none of the 
 heat generated in a circuit were carried away, the temperature 
 of the conductor would continue to rise as long as there 
 was a current in it. As a matter of fact, however, the tem- 
 perature of a conductor will rise until the heat radiated is 
 exactly equal to the heat generated in a given time. This 
 rise in temperature may be excessive and for that reason 
 the Fire Underwriters limit the value of the current a con- 
 ductor should carry. Table G, in Chapter 20, gives the cur- 
 rent-carrying capacity of different sized wires. These 
 values may be exceeded without any injurious effect, but 
 it is always essential to keep within the values allowed by 
 the Underwriters as the likelihood of a fire due to an over- 
 heated or burnt-out circuit is less than it would be if the 
 circuit were overloaded. The size of the conductor used in 
 electrical heating utensils is just sufficient to carry the 
 current without being injured. 
 
 In electric welding a large current is passed between the 
 surfaces that it is desired to weld together and the heat 
 generated is sufficient to raise the materials to a welding 
 temperature. The heat generated in an incandescent lamp 
 raises the temperature of the filament to such a value that 
 it will emit light. 
 
 The electric fuse is a device whose function is to auto- 
 matically open a circuit in which there is an excessive cur- 
 rent. The fuse usually consists of a material that will melt 
 at a much lower temperature than the material compos- 
 ing the remainder of the circuit. It is nothing more than 
 a weak spot in the circuit which is capable of conducting 
 the current the circuit is supposed to carry, but will melt 
 when the current through it becomes excessive. The val- 
 ues of the current required to fuse different sizes of wires 
 is given in Table H, in Chapter 20. 
 
 153. Hot-Wire Instruments. The heat generated in a con- 
 ductor due to a current in it will cause the conductor to 
 expand. The amount of this expansion will depend upon 
 the rise in temperature, which, in turn, depends upon the cur- 
 
144 
 
 PEACTICAL APPLIED ELECTRICITY 
 
 rent in the conductor. The principle on which hot- 
 wire instruments operate is shown diagrammatically 
 in Fig. 105. A wire (AB) of comparatively high re- 
 sistance, low temperature coefficient, and non-oxidizable 
 metal, has one end attached to the plate (C), then passed 
 around a pulley (P) that is secured to a shaft (S), and its free 
 end is brought back and mechanically, though not electrically, 
 attached to the plate (C). The spring (F) keeps the wire 
 under tension, it being attached to the plate (C), which is 
 so guided that it can move in a direction at right angles to 
 the shaft (S). An arm (G) is also 
 attached to the shaft (S), it being coun- 
 terweighted at the upper end and bifur- 
 cated at the lower end. A fine silk thread 
 (T) has ore end attached to one of the 
 arms of (G), then passed around a small 
 pulley (H), which is mounted on a shaft 
 that carries a pointer (I), and finally has 
 its other end attached to the second arm 
 of (G). The material composing the arms 
 of (G) is springy and serves to keep 
 the silk fiber in tension. The current 
 to be measured passes through the wire 
 (A), entering and leaving through two 
 twisted conductors, as shown in the 
 figure. When a current is passed through 
 (A) it is heated and expands, which 
 results in the tension in (A) being 
 
 less than that in (B) they were originally the same and 
 equilibrium can be restored only by the pulley (P) rotating 
 in a clockwise direction. This rotation of the pulley (P) 
 causes the lower end of the arm (G) to move toward the left, 
 and the silk thread that passes around the pulley (H) causes 
 it to rotate in a clockwise direction and, as a result, the 
 pointer (I) is deflected to the right, it being rigidly attached 
 to the pulley (H). The operation of this instrument is 
 quite satisfactory, as any change in the temperature of the 
 room in which it is used does not affect the correctness of 
 its indications, since both parts of the wire (AB) are af- 
 fected to the same extent, which results in no movement of 
 the pointer. In a great many instruments no adjustment or 
 
ELECTEICAL INSTBUMENTS 145 
 
 compensation is provided for errors due to changes in room 
 temperatures. In the case of ammeters, a low-resistance in- 
 strument is usually used in parallel with a suitable shunt, 
 while in the case of voltmeters a high resistance instrument 
 is employed. 
 
 154. Adaptability of Hot-Wire Instruments. Hot-wire in- 
 struments may be used equally well in both alternating and 
 direct-current measurements, the heating effect of the cur- 
 rent being independent of its direction. 
 
 Instruments Whose Operation Depends Upon the Electro- 
 static Effect 
 
 155. Condenser. Two conductors separated by an insu- 
 lator, which is called the dielectric, constitute what is called 
 a condenser. When the terminals of a condenser are con- 
 nected to some source of electrical energy, such as a bat- 
 tery or a dynamo, there will be a certain quantity of elec- 
 tricity stored in the condenser. The value of the quantity 
 
 Plates Dielectric 
 
 
 Fig. 106 Fig. 107 
 
 stored will depend upon the capacity of the condenser and 
 the electrical pressure to which its terminals are subjected. 
 A condenser is said to have a capacity equal to unity, or 1 
 farad, when a unit of quantity, 1 coulomb, will produce 
 a difference in pressure between its terminals of 1 volt. 
 A simple form of condenser is shown in Fig. 106, which con- 
 sists of two metallic plates separated by a sheet of paraf- 
 fine paper. The capacity of such a condenser will depend 
 upon the area of the plates used in the construction, the 
 number of plates, the distance between the plates, or the 
 thickness of the dielectric, and the kind of material com- 
 posing the dielectric. The value of an insulating material 
 as a dielectric is called its specific indoctive capacity. The 
 
146 PEACTICAL APPLIED ELECTEICITY 
 
 inductive capacity of different materials varies considerably, 
 but it is less through air than it is through any solids or 
 liquids. As a result, a condenser that has air for a dielec- 
 tric will have less capacity than one that has a solid or 
 liquid dielectric, the dimensions of the condensers being 
 the same. The specific inductive capacity of a material is 
 measured in terms of air as a standard, and it is the ratio 
 of the capacities of two condensers, one of which has the 
 material, whose dielectric constant is to be determined, as 
 a dielectric, and the other has air as a dielectric. The di- 
 mensions of the two condensers must be the same. Table 
 No. VIII gives the value of the specific inductive capacity of 
 some of the materials that are commonly used in the con- 
 struction of condensers. 
 
 TABLE NO. VIII 
 
 SPECIFIC INDUCTIVE CAPACITIES 
 
 Specific 
 Inductive 
 Capacity 
 4.38 
 2.52 
 2.30 
 3.35 
 
 2.50 to 3.80 
 2.20 
 2.17 
 
 Condensers used in practice usually consist of more than 
 two plates, as shown in Fig. 106. An arrangement similar 
 to that shown in Fig. 107 is usually used where alternate 
 plates are connected together and form one terminal, while 
 the remaining plates are connected together and form the 
 other terminal. The capacity in farads of such a combina- 
 tion of plates as that shown in B'ig. 107 can be calculated 
 by the use of the equation 
 
 K (n 1) a 
 
 C = (90) 
 
 4.452 X 1012 x d 
 
 where (n) represents the total number of plates used in the 
 construction of the condenser, (K) represents the constant of 
 the dielectric, (a) represents the area of each plate in square 
 inches, and (d) is the distance between the plates in inches. 
 
 Material 
 
 Air 
 Alcohol (Amyl) 
 Glass (Plate) 
 Gutta-percha 
 Mica 
 Parafflue 
 Petroleum 
 
 Specific 
 Inductive 
 Capacity 
 1.00 
 15.50 
 3.00 to 7.00 
 2.50 
 6.70 
 1.90 to 2.40 
 2.10 
 
 Material 
 
 Porcelain 
 Resin 
 Rubber 
 Shellac 
 Sulphur 
 Turpentine 
 Vaseline 
 
ELECTEICAL INSTRUMENTS 
 
 147 
 
 Example. Determine the capacity of a condenser of 100 
 sheets of tinfoil 10 X 10 inches, that are separated by plate 
 glass whose dielectric constant is 5. and 0.1 of an inch in 
 thickness. 
 
 Solution. Substituting the values of the above quantities 
 in equation (90) gives 
 
 5 X (100-1) X 10 X 10 
 
 C (in farads) = = .000 000 111 2 
 
 4.452 X 1012 X 0.1 
 
 Ans. .000 000 111 2 farads. 
 
 The farad is a unit of capacity entirely too large for prac- 
 tical use so a smaller unit, or the microfarad, is used. The 
 microfarad is equal to one-millionth of a farad. 
 
 Fig. 108 
 
 Fig. 109 
 
 156. Connection of Condensers in Series and Parallel. 
 Condensers may be connected in series or in parallel, or in any 
 combination of series and parallel, just as resistances. The 
 capacity of a combination of condensers may be calculated 
 by the use of one of the following equations. When a num- 
 ber of condensers are connected in series, as shown in Fig. 
 108, the total capacity (C) of the combination will be given by 
 the equation 
 
 1111 
 
 -H h-- + etc. 
 
 C G C C 
 
 (91) 
 
 This results in the combined capacity of several condensers 
 in series being less than the capacity of any one of them. 
 
148 PRACTICAL APPLIED ELECTRICITY 
 
 If there are only two connected in series, the combined ca- 
 pacity will be equal to 
 
 CiC 2 
 C = -- (92) 
 
 It is seen that the above equation is similar to the one used 
 in calculating the combined resistance of a number of re- 
 sistances in parallel. 
 
 When a number of condensers are connected in parallel, 
 as shown in Fig. 109, the total capacity (C) of the combina- 
 tion will be equal to 
 
 C = Ci + C 2 + C 3 + etc. (93) 
 
 The combined capacity of several condensers in parallel 
 will be greater than the capacity of any single condenser. 
 This equation is similar to the one used in calculating the 
 combined resistance of several resistances in series. 
 
 157. Relation of Impressed Voltage, Quantity, and Con- 
 denser Capacity. If a condenser is said to have unit capacity 
 when 1 coulomb of electricity will produce a difference 
 in electrical pressure between its terminals of 1 volt, then 
 1-volt pressure applied at the terminals will produce a charge 
 of unit quantity, 1 coulomb, if the capacity is 1 farad. If 
 1-volt pressure produces a charge of 2 coulombs, the capacity 
 is 2 farads; or if 1-volt pressure produces a charge of one-half 
 coulomb, the capacity is one-half farad. If the capacity of a 
 condenser is constant, the quantity of charge is directly pro- 
 portional to the impressed voltage; or if the impressed voltage 
 is constant, the quantity of charge is directly proportional 
 to the capacity. These two statements may be combined in 
 an equation which states that the quantity varies directly as 
 the capacity and the impressed voltage, or 
 
 Q = CE (94) 
 
 The above equation gives the value of the quantity in cou- 
 lombs stored in a condenser whose capacity is (C) farads, 
 when it is subjected to a pressure of (E) volts. Since the 
 microfarad is the more common unit of capacity, it being 
 equal to the one-millionth part of a farad, the above equa- 
 
ELECTEICAL INSTRUMENTS 149 
 
 tion may be rewritten with the value of (C) m microfarads, 
 which gives 
 
 C n,f. 
 Q = E (95) 
 
 106 
 
 It is often desirable to measure the quantity in a unit smaller 
 than the coulomb, in which case the microcoulomb is used, 
 it being the one-millionth part of a coulomb. 
 
 PROBLEMS OF CONDENSERS 
 
 (1) Calculate the capacity of a telephone condenser com- 
 posed of 1001 sheets of tinfoil 3X6 inches, separated by 
 paramne paper .007 of an inch thick, and having a dielectric 
 constant of 2. 
 
 Ans. 1.15 -f microfarads. 
 
 (2) Two condensers of 4 and 6 microfarads, respectively, 
 are connected in series. Calculate their combined capacity. 
 
 Ans. 2.4 microfarads. 
 
 (3) What quantity of electricity will be stored in the two 
 condensers in problem 2 when they are connected in series 
 and there is an electrical pressure of 100 volts applied to 
 the terminals? 
 
 Ans. .000 24 coulomb, or 240 microcoulombs. 
 
 (4) Two condensers of 4 and 6 microfarads, respectively, 
 are connected in parallel. Calculate their combined capacity. 
 
 Ans. 10 microfarads. 
 
 (5) What quantity in microcoulombs will be stored in 
 each condenser when there is a pressure of 100 volts ap- 
 plied to the terminals of the combination in problem 4? 
 
 Ans. 400 microcoulombs in 4 m.f. condenser; 600 micro- 
 coulombs in 6 m.f. condenser. 
 
 (6) What pressure is required to charge a 2-microfarad 
 condenser with a charge of .0002 coulomb? 
 
 Ans. 100 volts. 
 
 (7) What is the capacity of a condenser when 100 volts 
 will give it a charge of .00015 coulomb? 
 
 Ans. 1.5 microfarads. 
 
150 
 
 PEACTJCAL APPLIED ELECTKICITY 
 
 158. Electrostatic Voltmeter. The electrostatic voltmeter 
 is really nothing more than a condenser constructed so that 
 one plate may move with respect to the other. When a 
 condenser is charged, there is a force tending to draw the 
 plates together, due to the charges of opposite kind on the 
 two sets of plates, and it is this force that produces the 
 deflection in the case of an electrostatic voltmeter. In some 
 instruments only two plates are used, while in others a 
 number of plates are used to form each terminal, the con- 
 struction being such that the movable plates move between 
 the stationary plates. 
 
 Fig. Ill 
 
 An electrostatic voltmeter suitable for measuring extremely 
 high voltages is shown diagrammatically in Fig. 110. The 
 principal parts are the moving elements (Mj) and (M 2 ), the 
 curved plates (Bj) and (B 2 ), the condensers (C^) and (C 2 ), 
 scale (S), pointer (P), and terminals (T x ) and (T 2 ). The 
 plate (Bj) is connected to the inner plate of (Cj) and (B 2 ) 
 to the inner plate of (C 2 ). The plates (B x ) and (B 2 ) are 
 so arranged with respect to (M^ and (M 2 ), which are elec- 
 trically connected, that an angular deflection of the pointer 
 over the scale in the positive direction (above zero) short- 
 ens the gap between the moving elements and the fixed 
 plates. The charges on the plates (B^ and (B 2 ) are of op- 
 posite sign and they induce opposite charges on (M.^) and 
 
ELECTRICAL INSTRUMENTS 151 
 
 (M 2 ), which results in a force that tends to cause the mov- 
 ing system to turn about its own axis, or into such a posi- 
 tion that (Mj) and (M 2 ) are nearer (Bj.) iind (B 2 ). The 
 movement, however, is restrained by means of a spiral spring 
 and the deflection is indicated by the pointer (P) on the 
 scale (S). The form of the plates (E^) and (B 2 ) is such 
 that the deflection increases almost directly as the impressed 
 voltage. The condensers (Cx) and (C 2 ) are so constructed 
 that either or both of them may be short-circuited, which 
 results in the pressure required to produce a full scale de- 
 flection being less than when they are in circuit, thus giving 
 a wide range to the instrument. The moving system is im- 
 mersed in a tank of oil, which affords a good insulation and 
 buoys up the moving system, practically removing all the 
 weight from the bearings. Instruments of this type are con- 
 structed to measure voltages up to 200 000 volts. An in- 
 terior view of the various parts is shown in Fig. 111. There 
 are many other forms of electrostatic voltmeters on the mar- 
 ket, but their operation is based on the same fundamental 
 principle as the one just described,, 
 
 159. Adaptability of Electrostatic Instruments. Electro- 
 static instruments may be used in measuring either direct 
 or alternating pressures. Their operation is more satisfac- 
 tory, however, on an alternating-current circuit, because a.c. 
 pressures are, as a rule, larger in value than d.c. pressures. 
 Their operation is not at all satisfactory when the pres- 
 sure to be measured is below 50 volts, and for this reason 
 they cannot be used in combination with a shunt in the 
 measurement of currents, as the resistance of the shunt 
 would have to be large in order that there be the proper 
 difference in pressure between its terminals to operate the 
 meter. A high-resistance shunt of this kind in any circuit 
 would mean a large loss in comparison to that which would 
 occur if a low-resistance shunt could be used. 
 
 Measurement of Electric Power and Construction of Watt- 
 meters 
 
 160. Measurement of Power. The power that is used in 
 any part of a direct-current circuit may be determined by 
 measuring the current with an ammeter, and the difference 
 in pressure, by means of a voltmeter, between the terminals 
 
152 
 
 PEACTICAL APPLIED ELECTRICITY 
 
 of the portion of the circuit in which it is desired to ascer- 
 tain the power. The power can then be calculated by multi- 
 plying the ammeter reading, in amperes, by the voltmeter 
 reading, in volts, or 
 
 W = IE (96) 
 
 Thus the power taken by the ten incandescent lamps shown 
 in Fig. 112 can be determined by connecting the ammeter 
 (A) and the voltmeter (V), as shown in the figure, and noting 
 their indication when the lamps are turned on. (All of the 
 lamps are not shown). The product of these instrument 
 readings, in volts and amperes, will give the power in watts. 
 When the connections are made, as shown in Fig. 112, the 
 
 Load I L I C 
 
 Ten Lamps 
 
 Fig. 112 
 
 ammeter indicates the current through the lamps and volt- 
 meter combined. This results in a small error in the cal- 
 culation of the power taken by the lamps, provided the 
 current through the voltmeter is small in comparison to 
 the current through the lamps. For very accurate measure- 
 ments, the current through the voltmeter should always be 
 subtracted from the total current indicated by the ammeter. 
 If the voltmeter be connected across the line before the 
 ammeter that is, the ammeter would be between the volt- 
 meter connection and the lamps the indication of the volt- 
 meter would not be the true value of the pressure between 
 the terminals of the lamps, as there would be a certain drop 
 in pressure across the ammeter. The drop across the am r 
 meter should be subtracted from the voltmeter indication 
 in order to obtain the true pressure across the lamps. With 
 
ELECTRICAL INSTRUMENTS 
 
 153 
 
 a low-resistance ammeter, this drop is very small and may 
 be neglected except when very accurate results are desired. 
 
 161. Principle of the Wattmeter. Wattmeters are so con- 
 structed that their indication is proportional to the product 
 of a current and an electrical pressure; hence, they indicate 
 the power direct. Instruments of this kind are called watt- 
 meters, because they measure watts. 
 
 The principle of the wattmeter can be illustrated by ref- 
 erence to Fig. 113, which shows an electrodynamometer 
 with one coil connected in series with the line and the other 
 coil connected across the line. The coil connected in series 
 with the line is wound as though it were to be used as an 
 ammeter, and consists of a few turns of large wire, while 
 the coil connected across the line is wound as though it were 
 to be used as a voltmeter and consists of many turns of 
 fine wire. These two coils will be called the pressure coil and 
 the series coil, respectively. 
 
 The actual operation of such a meter can best be explained 
 by taking a practical example sim- 
 ilar to that shown in Fig. 113. The 
 current through the lamps passes 
 through the current coil of the 
 meter and produces a certain mag- 
 netic effect, which changes in value 
 as the current changes in value. 
 There will also be a magnetic effect 
 produced by the current that exists 
 in the pressure coil. The current in 
 the pressure coil, or circuit, will 
 vary with the difference in pressure 
 between the terminals of the circuit, 
 since the resistance of the circuit 
 remains constant and, as a result, 
 the magnetic field about the pres- 
 sure coil will vary with the voltage of the line. The deflection 
 of the moving coil of the electrodynamometer is proportional 
 to the product of the magnetic effects of the two coils, and since 
 the magnetic effects of the two coils are proportional to the 
 current and the voltage, respectively, the indication of the 
 instrument must be proportional to the product of (E) and (I), 
 or it irdicates watts. 
 
 Pressure 
 i/Cci, 
 
 Fig. 113 
 
154 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 When an instrument of this kind is connected in a cir- 
 cuit in which a fluctuating current, due to a varying load, 
 exists, the pressure between lines remaining constant, the 
 indications will vary directly with the load current. The 
 magnetic effect due to the current in the pressure circuit re- 
 mains constant, since the voltage or pressure impressed upon 
 this circuit remains constant. When the load current re- 
 mains constant and the voltage varies, the magnetic effect 
 of the current in the series coil remains constant and the 
 magnetic field about the pressure coil changes and the de- 
 flection varies with the voltage. 
 
 162. Whitney Wattmeter. The principle of this wattmeter 
 is the same as that of the dynamometer wattmeter just de- 
 scribed, except that the construction is modified to make 
 
 the instrument portable and 
 more suitable for commer- 
 cial work. In this wattmeter 
 the heavy current winding 
 is composed of two coils, 
 which are supported in 
 suitable frames and enclose 
 a coil composed of fine wire. 
 This coil is mounted on a 
 shaft with pointed ends rest- 
 ing in jeweled bearings. 
 Two volute springs serve to 
 hold the coil in its zero posi- 
 tion and balance the turning 
 effort of the coil when there 
 is a current in it. These two 
 springs also serve to con- 
 duct the electricity into and 
 
 from the movable coil, instead of the mercury cups, as in the 
 previous case. A balance is obtained by turning the torsion 
 head until the needle that is attached to the movable coil is 
 indicating no deflection, the reading of the pointer attached to 
 the torsion head is then noted and represents the indication of 
 the instrument. The scale of the instrument may be divided 
 into degrees, and the deflection read on this scale must be 
 multiplied by some constant to obtain the power indicated by 
 the instrument, or the scale may be so drawn that the power 
 
 Fig. 114 
 
ELECTRICAL INSTRUMENTS 155 
 
 in watts can be read directly from it. The general appearance 
 of the instrument is shown in Fig. 114. 
 
 163. Weston Wattmeter. The principle of this instrument 
 is practically the same as the one described in the previous 
 section. No torsion head, however, is used and the pressure 
 coil, instead of being maintained at practically the same 
 position for all indications of the instrument, rotates about 
 its axis through an angle of approximately eighty degrees. 
 Two volute springs serve to conduct the electricity into 
 and from the movable coil. They also offer the opposing 
 force to that produced by the 
 
 magnetic effect of the cur- 
 rents in the two coils. This 
 form of instrument has an ad- 
 vantage over the other forms 
 described in that no manipu- 
 lation is necessary and the 
 needle points at once to the 
 scale mark showing the watts. 
 A Weston instrument is 
 shown in perspective in Fig. 
 115 and diagrammatically in 
 Fig. 116. In Fig. 116 (C^ and 
 
 (2) represent the two current coils, which are connected in 
 series between the two posts numbered (1) and (2). The 
 pressure connections can be made to (3) and (5), or (3) and 
 (6). The resistance between (3) and (6) is usually just half 
 the value of the resistance between (3) and (5). 
 
 164. Compensated Wattmeter. The power indicated by 
 a wattmeter will be in error just the same as the value of 
 the power determined by the voltmeter and ammeter read- 
 ings is in error, due to the current taken by the voltmeter, 
 or the drop across the ammeter, unless some means be pro- 
 vided that will counteract or compensate for this error. This 
 compensation is provided in the Weston wattmeter in the 
 following way: The pressure circuit is always to be con- 
 nected across the line after the current coil, which results 
 in the current coil carrying the current that passes through 
 the pressure circuit. This current in itself would produce 
 a deflection, even though there be no load on the circuit, 
 and, as a result, the meter would always indicate a higher 
 
156 
 
 PEACTICAL APPLIED ELECTKICITY 
 
 -J / <A/WAAVWV ' 
 
 value of power than that actually taken by the load. If, 
 however, the pressure circuit be wound around the series 
 coil the same number of times there are turns in the series 
 coil, and this winding be so connected that the magnetic 
 effect of the current in it is opposite to that of the cur- 
 rent in the series coil, the magnetic field produced by the 
 pressure current passing through the series coil will be 
 completely annulled and there will be no deflection of the 
 moving system until there is a load current through the 
 series coil. The turns of wire that are wound around the 
 series coil are called compensating turns and they are shown 
 
 in Fig. 116. When a sepa- 
 rate source of current and 
 potential is used in cali- 
 brating wattmeters, there 
 should be no compensating 
 turns in the circuit, and 
 terminal (4) should be 
 used instead of terminal 
 (3). The resistance of the 
 pressure circuit should be 
 the same in both cases, 
 and a small coil (R), whose 
 resistance is equal to that 
 of the compensating turns, 
 is connected in the pres- 
 sure circuit instead of the 
 compensating turns. 
 
 165. Adaptability 
 
 of Wattmeters. All wattmeters that have been described will 
 operate on either direct- or alternating-current circuits. Their 
 indications on direct-current circuits will, however, be in- 
 fluenced by stray magnetic fields, and, in the majority of cases, 
 a reversal of current through the coils, although the current 
 remains constant in value, will result in a different indication. 
 When the instruments are used in an alternating-current cir- 
 cuit, these errors are very much reduced provided the dis- 
 turbing field is not alternating since the current passes 
 through the circuit in one direction for the same time it passes 
 in the opposite direction. 
 
 166. Watt-Hour Meters. The Weston wattmeter, described 
 
 Fig. 116 
 
ELECTEICAL INSTRUMENTS 
 
 157 
 
 in section (163), is called an indicating wattmeter, since 
 it gives the instantaneous value of the watts expended in a 
 circuit, just as a voltmeter and ammeter indicate the fluctua- 
 tion in voltage and current. The watt-hour consumption in 
 any circuit could be determined by means of such a meter 
 by multiplying the average indication of the meter for a 
 
 Fig. 117 
 
 given time by the time expressed in hours. An integrating 
 wattmeter automatically multiplies the average of the in- 
 stantaneous readings by the time. The Thomson integrating 
 wattmeter, shown in Fig. 117, is similar to the dynamometer 
 wattmeter, but the movable coil rotates. It is really a small 
 electric motor without any iron in its working parts. The 
 revolving part, or armature, is the pressure coil and the 
 field in which this coil rotates is produced by the load cur- 
 rent in stationary coils mounted outside of the armature. 
 The force tending to produce rotation is proportional to the 
 product of the two magnetizing effects and this is proper- 
 
158 PKACTICAL APPLIED ELECTRICITY 
 
 tional to the watts in the circuit, just as in the case of 
 the electrodynamometer. The magnetizing effect of the cur- 
 rent in the armature is made continuous by winding the 
 armature with a number of coils, which are symmetrically 
 placed on the armature frame and connected to the external 
 circuit through a small commutator and two brushes. The 
 current through the armature coils is reversed at such a 
 time that the turning effort is always in the same direction. 
 
 The speed of the armature is made proportional to the 
 driving force by mounting, on the same shaft that carries 
 the armature, a copper disk which is arranged to revolve be- 
 tween permanent magnets and constitutes a small generator. 
 The torque required to drive this disk is directly propor- 
 tional to the speed, and hence, if the torque produced by 
 the action of the two magnetizing effects be doubled, the 
 speed of the meter will be doubled. The speed of the meter 
 at any instant is proportional to the product of (E) and (I), 
 or the power. The average speed for a unit of time, say one 
 hour, would be proportional to the average power times the 
 time it acts (average E X I X time in hours), which gives 
 the value of the energy in watt-hours. 
 
 An indicating device is usually attached to the meter, the 
 pointers of which are driven by a worm that is rigidly fastened 
 to the shaft upon which the armature is mounted. The rela- 
 tion between the movement of the pointers on the dials is 
 usually such that the dial readings give the energy direct in 
 watt-hours, or kilowatt-hours. In some cases, however, the 
 dial readings must be multiplied by a constant in order to 
 obtain the true watt-hour or kilowatt-hour consumption. 
 
 A diagram of the connections of a Thomson watt-hour 
 meter is shown in Fig. 118. The coils (Cj) and (C 2 ) rep- 
 resent the series coils connected in series with the line and 
 carrying the load current. The pressure circuit, which is 
 connected across the line, consists of the resistance coil 
 (S) and the winding on the armature (A). The coil (S) 
 serves a double purpose: it prevents an excessive current 
 passing through the pressure circuit and it creates a mag- 
 netic field which is just sufficient to produce the required 
 turning effort to overcome the static friction of the meter. 
 If this magnetic field were not produced by the coil (S) 
 or a similar coil, the armature of the meter would not start 
 
ELECTEICAL INSTRUMENTS 
 
 159 
 
 to rotate with a small load current in the coils (Cj) and 
 (2), and its indications, as a result, would always be lower 
 than the true value of the energy. The magnetic field pro- 
 duced by the coil (S) is in Lhe same direction as that pro- 
 duced by the current in the coils (C^) and (C 2 ). The ef- 
 fect of this field on the armature can be varied by changing 
 the position of the coil (S) with respect to the armature. 
 With this adjustment, the friction of the meter may be prop- 
 erly compensated for and it will start to rotate with an 
 extremely small current in the series coils. Meters of this 
 kind are called integrating wattmeters, since their dials in- 
 dicate the average of the product of the instantaneous power 
 times the time that power 
 acts; or their indication is 
 proportional to the energy. 
 The watt-hour meter just 
 described will operate in 
 an alternating-current cir- 
 cuit, but not very satis- 
 factorily on account of the 
 inductance of the w i n d- 
 
 Source of 
 Energy 
 
 LoadQ 000 
 
 Fig. 118 
 
 ings. 
 
 167. Coulomb, or Ampere- 
 Hour Meters. There are 
 several recording meters 
 
 on the market whose indications are proportional to the aver- 
 age current through them times the time the current exists 
 in the circuit, and entirely independent of the voltage produc- 
 ing the current. Such instruments are often called coulomb, 
 or ampere-hour meters. Meters of this kind can be used in 
 measuring energy, when properly calibrated, provided the 
 pressure producing the current remains constant. The voltage 
 of a line, as a rule, is not always the same, but will fluctuate 
 quite a number of volts and, as a result, a coulomb meter will 
 not indicate the true energy. 
 
 The old Edison chemical meter was nothing more than a 
 coulomb, or ampere-hour meter. It consisted of two zinc 
 plates immersed in a solution of zinc sulphate. The quan- 
 tity of electricity that had passed through the meter was 
 determined by weighing the plates and, from their change in 
 weight, the quantity was calculated by means of the elec- 
 
160 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 trochemical equivalent. Fluctuations in line voltage pro- 
 duced no effect upon the indications of the meter directly; 
 voltage changes, however, produce a change in the value of 
 the current and this changed the meter's indication. The 
 customer's bill was calculated on the assumption that the 
 voltage remained constant. 
 
 168. Maximum Demand Meters. In order to charge the 
 purchaser of electrical energy a fair amount for the energy 
 consumed in a given time, it is often 
 desirable to know the maximum 
 amount called for during any time, in 
 order that he may be properly taxed 
 or that part of the supply equipment 
 that must be held in reserve for him 
 so that he may take that maximum de- 
 mand at any time. An instrument 
 used in measuring the value of this 
 maximum demand is called a max- 
 imum demand, or demand, rneter. 
 
 The Wright demand meter is shown 
 in Fig. 119. It consists of a U-shaped 
 tube with enlarged ends and a side 
 tube (S) opening out of one of them. 
 A few turns of wire are wound around 
 the enlarged end of the tube (A), that 
 has not the side outlet, so that the heat 
 
 generated in the wire due to the passage of a current through 
 it will warm the air in the chamber. The U-shaped tube is 
 filled with liquid to about the height shown in the figure. The 
 expansion of the air in the chamber (A), due to the heat, 
 forces the surface of the liquid in the left-hand leg of the tube 
 downward and the surface of the liquid in the right-hand 
 one upward. If the current strength is sufficiently high to 
 cause the liquid in the right-hand tube to rise to the point 
 where the outlet tube is connected, the liquid will over- 
 flow into the tube (S). The greater the current in the wind- 
 ing about (A), the greater the overflow from the tube (R) 
 into (S), and a scale properly graduated placed alongside 
 the tube (S) will show the maximum amperage that has 
 passed through the winding about (A). The indication of 
 the instrument is rather slow; that is, it takes some time 
 
 Fig. 119 
 
ELECTRICAL INSTRUMENTS 
 
 161 
 
 for the liquid in (R) to rise to the point where it will over- 
 flow into (S), even though the proper current is passing 
 through the winding about (A). This prevents the customer 
 being penalized due to a momentary short- 
 circuit on his line or the large current 
 taken for a short time in starting motors. 
 The meter is reset, usually when the con- 
 sumer's integrating meter is read, by sim- 
 ply inverting the tube and draining all of 
 the liquid out of the tube (S) back into 
 the U-shaped tube. Changes in the 
 temperature of the atmosphere do not in- 
 terfere to any great extent with the correct 
 registration of the meter, and it will work 
 equally well in either a direct- or an 
 alternating-current circuit. The whole 
 instrument is placed in a case that can 
 be locked or sealed, as shown in Fig. 120, 
 so that it cannot be reset by a party not 
 authorized to do so. 
 
 CALIBRATION OF INSTRUMENTS . 
 
 169. Calibration of Voltmeters by 
 Means of a Standard Instrument. The 
 accuracy of a voltmeter's indications may 
 be determined by connecting it in parallel 
 with another voltmeter whose calibration 
 is known (called a standard), and compar- 
 ing their indications for various impressed 
 voltages. The connections of the instru- 
 ments are shown in Fig. 121, where (S) represents the 
 standard instrument, (X) the instrument to be calibrated, 
 and (R) a suitable rheostat for varying the pressure over 
 the voltmeter terminals. 
 
 170. Calibration of Voltmeters by Means of a Potentiome- 
 ter. The potentiator is a special arrangement for meas- 
 uring an electrical pressure by comparison. It is shown 
 diagrammatically in Fig. 122. The pressure to be meas- 
 ured is connected between the terminals (A ) and (A+). 
 There is a variable known resistance connected between 
 
 Fig. 120 
 
162 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 Fig. 121 
 
 these two points. Across a portion of this resistance, such as 
 that between the points (1) and (2), there is connected a 
 shunt circuit which consists of a sensitive galvanometei 
 (G), a standard cell (SC), a contact key (K), and a high 
 resistance (H) that may be easily cut in or out of the circuit. 
 
 The operation of the po- 
 tentiometer is as follows: 
 
 ? L^ ==a =* % | First, assume it is desired 
 
 v55>y to know the value of some 
 
 \ Ck-xO // 
 
 o 1 ^) f pressure that is connected 
 
 ^ to the points (A) and 
 
 (A-f). The resistance (R) 
 between the points (1) and 
 (2) should be adjusted to 
 1000 (this need not always 
 be 1000) times the voltage 
 of the standard cell, which 
 is 1.434 for a Clark cell 
 at 15 Centrigrade, and 
 1.018 30 for a Weston nor- 
 mal cell. Assuming a Weston cell is used, then the value of 
 the resistance in (R) will be 1018.30 ohms. Now, there will be 
 a difference in pressure between the points (1) and (2), 
 due to the current in the 
 resistance (R) produced by 
 the pressure impressed 
 upon the terminals (A ) 
 and (A+). The current 
 through the resistance (R) 
 is in such a direction that 
 the point (1) is at a higher 
 potential than the point 
 (2). This difference in 
 pressure between the 
 points (1) and (2) would 
 
 tend to produce a current in the shunt circuit when the key 
 (K) was closed. The standard cell, however, is connected in 
 the circuit in such a way that its electromotive force tends to 
 counteract the difference in pressure between the points (1) 
 and (2) and there will be no current in the shunt circuit when 
 the drop in potential over (R) is exactly equal to the e.m.f. of 
 
 Fig. 122 
 
ELECTKICAL INSTRUMENTS 
 
 163 
 
 the standard cell. The drop over the resistance (R) can be 
 varied by changing the value of the total resistance between 
 (A) and (A-f). There will be no deflection of the galvan- 
 ometer when a balance is obtained. The high resistance (H) 
 should be cut out of circuit for a final adjustment. The pur- 
 pose of this resistance is to protect the standard cell from 
 supplying too large a current while adjusting the drop over 
 (R), which is likely to change the value of its e.m.f. and per- 
 haps ruin the cell. When this balance is secured, there will be 
 1.018 30 volts drop in pressure over 1018.30 ohms in the main 
 part of the circuit, or 1 volt over every 1000 ohms. The total 
 difference in pressure between (A ) and (A+) will then 
 be equal to the resistance between (A ) and (A+) divided 
 by 1000. 
 
 Ordinary resistance boxes may be used for the resistances 
 shown in the scheme, but commercial forms of the poten- 
 tiometer are constructed with all the keys, resistances, etc., 
 contained in a single case. 
 
 171. Calibration of Ammeters by Means of a Standard In- 
 strument. An ammeter may be calibrated by connecting it 
 in series with a standard 
 
 instrument and comparing 
 their indications for differ- 
 ent values of current. The 
 scheme of connections is 
 shown in Pig. 123, in which 
 (S) represents the stand- 
 ard instrument, (X) the in- 
 strument to be calibrated, 
 (B) a storage battery or 
 some source of electrical 
 energy, and (R) a rheostat 
 
 suitable for changing the value of the current in the circuit by 
 a change in its resistance. 
 
 A standard resistance may be connected in series with an 
 ammeter and the current in the circuit determined by divid- 
 ing the drop over the resistance which may be determined 
 by means of a voltmeter or a potentiometer by the resist- 
 ance of the standard resistance. 
 
 172. Calibration of a Wattmeter by Means of a Voltmeter 
 and an Ammeter. The connections for calibrating a watt- 
 
 r | h| \] K^WVWVWW 
 
 Fig. 123 
 
164 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 meter or a watt-hour meter by means of a voltmeter and 
 an ammeter are shown in Fig. 124. The current in the 
 series coil of the wattmeter exceeds that in the ammeter by 
 an amount equal to the current in the voltmeter. The true 
 power, then, should be calculated by adding to the ammeter 
 reading (I a ) the voltmeter current (Iv) and multiplying the 
 sum by the voltmeter reading (E), or 
 
 W = (la + 
 
 E 
 
 (97) 
 
 The per cent error introduced by not taking the voltmeter 
 
 Pressure Coil 
 Series Coils 
 
 Load 
 
 66000 
 
 Fig. 124 
 
 current into account is very small, except in the calibra- 
 tion of low reading wattmeters. 
 
 When a separate source of current and pressure are used, 
 the current taken by the voltmeter produces no error and 
 the true power is given by the equation 
 
 W = EXI (98) 
 
 The indication of the dial on a watt-hour meter can be 
 checked by maintaining the e.m.f. and current constant for 
 a given time and noting the difference in the dial read- 
 ings before and after the test. The energy indicated on 
 the dial should equal the product of (E), (I), and (t), or 
 
 k.w. hours = E X I X t (99) 
 
 The time (t) in the above equation should be in hours. The 
 dial indication can be accurately determined from the num- 
 
ELECTKICAL INSTEUMENTS 
 
 165 
 
 ber of revolutions of the armature, if the number of revolu- 
 tions of the armature per unit indication on the dial is known. 
 This relation is called the gear ratio, and once determined 
 it can be used in succeeding tests. 
 
 173. Calibration of Wattmeters by Means of Standard 
 Wattmeter. Two wattmeters are shown connected in the 
 same circuit in Fig. 125. The instrument (S) is a standard, 
 
 JLL 
 
 X 
 
 
 j 
 
 5 
 
 I 
 
 Load 
 
 00 
 
 <y 
 
 00 
 
 PV 
 
 00 00 
 
 rt 
 
 
 I 
 
 L k k 
 
 I 
 
 f ( ( 000 
 
 Fig. 125 
 
 or one whose calibration is known, while (X) is an instru- 
 ment to be calibrated. If the series coils of the two instru- 
 ments have the same resistance, the pressure impressed upon 
 the pressure circuits of the two meters is the same, when the 
 connections are made, as shown in the figure. The same load 
 current exists in the series coils of both instruments and the 
 indication of (X) can, therefore, be determined in terms of 
 the indication of (S). 
 
CHAPTEE IX 
 
 THE DIRECT-CURRENT GENERATOR 
 
 174. The Dynamo. The dynamo is a machine for convert- 
 ing mechanical energy into electrical energy, or electrical en- 
 ergy into mechanical energy by means of electromagnetic in- 
 duction, the principles of which were discovered by Faraday 
 about 1831. The dynamo, when used to transform mechan- 
 ical energy into electrical energy, is called a generator, and 
 when used to transform electrical energy into mechanical, it 
 is called a motor. The generator does not create electricity, 
 but simply imparts energy to it, just as energy is imparted 
 to the electricity as it passes through the primary cell. The 
 e.m.f. which is generated in the dynamo produces a current 
 in a closed circuit connected to the machine and this cur- 
 rent will pass from a higher to a lower potential in the ex- 
 ternal circuit and from a lower to a higher potential in the 
 internal circuit of the machine itself. This corresponds 
 to the flow of water through a pipe connected to a pump. 
 In the external circuit, the water flows from a higher to a 
 lower pressure, while the action of the pump causes it to 
 flow from a lower to a higher pressure through the pump 
 itself. 
 
 The dynamo consists fundamentally of two parts a mag- 
 netic field, which may be produced by permanent magnets or 
 electromagnets, and an armature, which consists of a coil or 
 number of coils usually wound or mounted on an iron core 
 and so arranged that they may be revolved or moved in the 
 magnetic field of the machine. The movement of the coils 
 in the magnetic field results in the conductor forming the 
 ceils cutting the magnetic lines of the field and an e.m.f. is 
 induced in the winding. 
 
 175. Kinds of Generators. Generators may be grouped into 
 two main classes, depending upon the nature of their output; 
 viz., direct-current and alternating-current. 
 
 166 
 
THE DIRECT-CURRENT GENERATOR 167 
 
 The current in a circuit connected to a direct-current gen- 
 erator is in the same direction all the time, while in the case 
 of the alternating-current generator it is continuously revers- 
 ing in direction. This chapter will deal with the direct- 
 current machine,, the discussion of the alternator being de- 
 ferred to a later chapter. 
 
 The mechanical construction of dynamos permits their be- 
 ing divided into three classes, the fundamental electrical prin- 
 ciple being the same in. each case. 
 
 (a) Revolving armature and stationary field magnet. 
 
 (b) Revolving field and stationary armature. 
 
 (c) Armature and field winding both stationary, but con- 
 structed so that an iron core may be revolved near them. 
 
 The external circuit is connected to the armature winding 
 in the first class by means of collector rings, see section (177), 
 or by means of a commutator, see section (178), while the con- 
 nection to the field winding is permanent since it is stationary. 
 In the second class the armature is permanently connected 
 to the external circuit, and the connection is made to the 
 field winding by means of slip rings. There are no moving 
 conductors in the third class, but the magnetic flux through 
 the armature winding that is produced by the current in the 
 field winding is caused to change in value by changing the 
 position of a part of the magnetic circuit. This part of the 
 magnetic circuit is called the inductor and it is arranged so 
 that it may be rotated near the armature and field windings. 
 
 Direct-current generators may also be divided according to 
 their output, viz., 
 
 (a) Constant-Current Generators. 
 
 (b) Constant-Potential Generators. 
 
 The output of the constant-current generator is at a con- 
 stant current and variable pressure, while the output of the 
 constant-potential generator is at a constant potential and 
 variable current. 
 
 176. Simple Dynamo. If a single loop of wire, such as 
 (ABCD), Fig. 126, be revolved about an axis, such as (EF), 
 in the magnetic field of a permanent magnet, or an electro- 
 magnet, as shown in the figure, there will be an electromotive 
 force induced in the two sides of the loop (AB) and (CD). 
 This induced electromotive force will produce a current in 
 the loop if the conductor forming the loop be closed. The 
 
168 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 direction of the induced e.m.f. in the two sides of the loop 
 may be determined by a simple application of Fleming's dy- 
 namo rule, as given in section (118). The motion of one side 
 of the loop, such as (AB), with respect to the field is just the 
 reverse of the motion of the other side (CD). As a result 
 of this difference in motion of the two sides of the loop with 
 respect to the magnetic field, the e.m.f. induced in one side 
 of the loop will be from the observer, while that induced in 
 
 Fig. 126 
 
 the other side will be toward the observer. These two e.m.f.'s 
 are acting in series and, since their directions are opposite 
 with respect to the position of the observer, they both tend to 
 produce a current in the same direction around the loop. The 
 value of the current in the loop will depend upon the induced 
 e.m.f. and the ohmic resistance of the loop. There will be 
 no induced e.m.f. in the ends of the loop since they do not 
 cut any of the magnetic lines. 
 
 177. Simple Alternator. If the loop, shown in Fig. 126, be 
 cut at one end and the two ends thus formed be connected 
 to two metallic rings (Rj) and (R 2 ) mounted on the shaft 
 and insulated from each other, as shown in Fig. 127, the com- 
 bination will constitute what is called a simple alternator- 
 An external circuit can be connected to the coil or armature 
 by means of two brushes (B^ and (B 2 ) that rub on the two 
 metallic rings. The e.m.f. induced in the armature will now 
 produce a current through the external circuit and the armature 
 in series. The value of this current will, as in the previous 
 case, depend upon the value of the induced e.m.f. and the 
 ohmic resistance of the entire circuit. 
 
 The e.m.f. induced in the two sides of the loop at any time 
 
THE DIEECT-CUBEENT GENEEATOE 
 
 169 
 
 will depend upon the number of magnetic lines cut in one 
 second, or the rate at which the lines are being cut. This 
 rate of cutting of magnetic lines will depend upon the length 
 of the two sides of the loop, the strength of the magnetic 
 field, and the direction in which the conductor is moving with 
 respect to the magnetic field. Assuming the strength of the 
 magnetic field is uniform and it remains constant, and the 
 loop revolves about its axis at a constant rate, then the e.m.f. 
 induced in the loop will change in value, due only to a change 
 in the direction of motion of the two sides of the loop with 
 respect to the magnetic field. Thus, when the loop is in the 
 
 
 
 90 
 
 Fig. 128 
 
 Fig. 129 
 
 horizontal position, the direction of the field also being 
 horizontal, the two sides of the loop will be moving in a 
 path, just for an instant, perpendicular to the direction of 
 the field, and the number of lines of force that the two sides 
 of the loop will cut, due to a given motion of the coil, will 
 be a maximum. When the loop is in a vertical position, or 
 perpendicular to the direction of the magnetic field, any small 
 movement of the loop will result in no lines of force being 
 cut by the two sides and, hence, no e.m.f. will be induced. The 
 value of the e.m.f. induced in the two sides of the loop for 
 positions between those just given, will depend upon the part, 
 or component, of the motion that is perpendicular to the 
 direction of the magnetic field. This component is propor- 
 tional to the sine of the angle between the position of the 
 coil and the plane perpendicular to the magnetic field. The 
 sine of an angle (9), see Fig. 128, is equal to the length of the 
 
170 PRACTICAL APPLIED ELECTEICITY 
 
 line (a) divided by the length of the line (b). This relation 
 remains the same regardless of the size of the triangle so 
 long as the angle (0) does not change in value. From the 
 table of "Trigonometrical Functions" in Chapter 20, may be 
 found the values of the sines of different angles from 
 to 90. 
 
 A curve can be drawn which will show graphically the rela- 
 tion between the induced e.m.f. in the coil and its angular 
 position with respect to some reference plane, say the 
 plane parallel to the magnetic field. Draw a line (AB), 
 Fig. 129, and divide this line into, say, 90 equal parts, each 
 part will then correspond to four-degrees movement of the 
 coil about its axis. Starting with the coil in a plane per- 
 pendicular to the magnetic field, and let this correspond to the 
 point (A) in the figure, the e.m.f. induced in the coil for any 
 angular displacement from this position should be measured 
 off to a convenient scale on a line drawn through the point 
 on (AB), corresponding to the displacement of the coil. Thus, 
 the e.m.f. will be a maximum when the coil has rotated 
 through an angle of 90, since the value of the sine of the 
 angular displacement is increasing up to this point. It then 
 decreases as the angle increases from 90 to 180 and becomes 
 equal to zero when the coil has rotated through 180. The 
 direction of the movement of the two sides of the loop with 
 respect to the magnetic field changes just as the coil passes 
 through its 180 position and, as a result, the direction of the 
 induced e.m.f. changes. The numerical values of the e.m.f. 
 for the second 180 are identical to those for the first 180, 
 but they are opposite in sign. The difference in sign is 
 represented in the curve by drawing the second part of the 
 curve below the horizontal line. 
 
 178. Simple Direct-Current Dynamo. Purpose of the Com- 
 mutator. The e.m.f. induced in the loop of wire described 
 in the previous section can be made to produce a direct cur- 
 rent one that is constant in direction in the external circuit 
 in the following way: Suppose the two continuous metallic 
 rings be replaced by a single ring composed of two parts that 
 are insulated from each other, the distance between the ends 
 of the two parts composing the rings being small in compari- 
 son to the total circumference of the combined ring. If the 
 two ends of the loop be connected to these two parts of the 
 
THE DIEEOT-CUEEENT GENEEATOE 
 
 171 
 
 ring, which we shall call segments, and two brushes that 
 are insulated from each other be so mounted with respect to 
 each other and the ring that they rest upon the insulation 
 between the segments when the e. m. f. induced in the coil is 
 zero, the connection of the external circuit with respect to 
 the loop will be reversed at the same instant the direction of 
 the induced e.m.f. in the loop changes. This results in the 
 induced e.m.f. in the coil always tending to send a current 
 through the external circuit in the same direction. The proper 
 arrangement of the loop, segments, and the brushes is shown 
 in Fig. 130. Such a machine is called a simple direct-current 
 dynamo, because it delivers a direct current to the external 
 circuit. The two-part ring constitutes a simple commutator 
 of two segments, and its purpose, as pointed out, is to reverse 
 the connection of the external circuit with respect to the 
 
 90 180 270 360" 
 
 Fig. 131 
 
 armature winding, or vice versa, so that the induced e.m.f.' 
 in the winding will send a direct current through the external 
 circuit. A curve representing the value of the e.m.f. impressed 
 upon the external circuit when the two-part commutator is 
 used is shown in Fig. 131. An e.m.f. such as that represented 
 in Fig. 131 is called a pulsating e.m.f., because it pulsates or 
 changes from zero to a maximum and back to zero at regular 
 intervals. 
 
 179. Multiple-Coil Armatures. If the armature of a direct- 
 current generator were constructed with a single coil com- 
 posed of one or more turns, the current delivered by such a 
 machine would pulsate in value the same as the e.m.f., as 
 
172 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 18 
 
 Fig. 132 
 
 shown in Fig. 131. The operation of such a machine would 
 be very unsatisfactory in a great many cases. Fortunately the 
 e.m.f. between the brushes of the machine can be made more 
 nearly constant in value in the following way: 
 
 Suppose two closed coils 
 
 A D (A) and (B) be placed on 
 
 the armature at right an- 
 gles to each other, then 
 the induced e.m.f. in one 
 of them will be a maxi- 
 mum when the induced 
 e.m.f. in the other one is 
 zero. Now as the arma- 
 ture rotates from such a 
 position that the plane of 
 coil (A) is perpendicular 
 to the magnetic field zero 
 e.m.f. induced in it and 
 the plane of coil (B) is 
 
 parallel to the magnetic field maximum induced e.m.f. in 
 it the induced e.m.f. in coil (A) will increase and the 
 induced e.m.f. in coil (B) will decrease, and this action will 
 continue until the armature has turned through an angle 
 of 90. After the armature has turned through an angle of 
 90, the e.m.f. in coil (A) is a maximum and that in coil (B) 
 is zero. For the next 90, the e.m.f. in coil (A) is decreasing 
 and the e.m.f. in coil (B) is increasing, but in the opposite di- 
 rection. The corresponding values of induced e.m.f. will occur 
 in the two coils at inter- 
 vals which differ in value 
 by one-fourth revolution, 
 or 90. The two curves (A) 
 and (B) in Fig. 132 show 
 the relation of the e.m.f.'s 
 in the two coils. 
 If now a four-segment 
 
 180 
 Fig. 133 
 
 no" 
 
 360 
 
 o 9(r 
 
 commutator be used and 
 two coils be symmetrically 
 
 placed on the armature, the terminals of each coil being con- 
 nected to opposite commutator segments, the e.m.f. between 
 the brushes of the machine will never fall to zero value but 
 
THE DIRECT-CURRENT GENERATOR 173 
 
 will be of the form shown by the full line in Fig. 133, when 
 the brushes are properly placed with respect to the commu- 
 tator. The e.m.f. can be made more nearly constant by 
 placing more coils on the armature in such a position with 
 respect to the first ones that the induced e.m.f. in them does 
 not reach a maximum or zero value at the same time it does 
 in the others, and connecting them in such a way that the 
 induced e.m.f. in all of the coils acts in series and in the 
 same direction as far as the external- circuit is concerned. 
 
 180. The Armature of a Dynamo. The loops of wire, or 
 coils, in which the e.m.f. is induced by a movement of them 
 with respect to the magnetic field, together with the iron parts 
 upon which they are mounted, insulating material, and slip 
 rings or commutator in the cases where the coils move 
 constitute what is called the armature of a dynamo. The classi- 
 fication of armatures, their construction, and methods of wind- 
 ing will be taken up in detail in the chapter on "Armatures 
 for Direct-Current Dynamos." 
 
 181. Magnetic Field of a 
 Dynamo. In the majority of 
 cases the magnetic field of 
 a dynamo is produced by 
 electromagnets. In the case 
 of magnetos, however, the 
 magnetic field is created by 
 several powerful permanent 
 horseshoe magnets. Such a 
 machine is shown in Fig. 
 134. Small machines are 
 
 usually bipolar, that is, they Fig. 134 
 
 have one N-pole and one 
 
 S-pole which create the magnetic field in which the armature 
 
 rotates. These magnetic fields assume a number of different 
 
 forms, a few of which are shown in Fig. 135. 
 
 In large machines it is customary to use multipolar field 
 magnets in which any even number of poles are arranged 
 alternately around the armature. The magnetic circuit of a 
 machine whose field is created by an electromagnet usually 
 consists of. five parts, as shown in Fig. 136. (1) The field 
 cores (C) are the centers of the coils carrying the magnetiz- 
 ing current. (2) The yoke (Y) connects the field cores 
 
174 
 
 PKACT1CAL APPLIED ELECTKICITY 
 
 together at one end, as shown in the figure. (In some 
 machines there is no yoke in the magnetic circuit, see Fig. 
 135 A.) (3) The pole pieces (P) are the metallic parts of the 
 magnetic circuit next to the armature. They are usually cut 
 to conform to the curvature of the armature and in some 
 cases are an entirely different piece of metal than the field 
 cores, being fastened to the end of the field cores by means 
 of bolts. The surface of the pole pieces next to the armature 
 
 D 
 
 Fig. 135 
 
 Is called the pole face; and the projecting edges, when so 
 constructed, are called the horns. (4) The air gap (G) is the 
 space between the pole face and the armature core. (5) The 
 armature core conducts the magnetic lines from one air gap 
 to another. 
 
 The coils carrying the magnetizing current may be placed 
 on the magnetic circuit as shown in Fig. 135 D or they may 
 be placed on the magnetic circuit as shown in Fig. 135 C. 
 When the field windings are placed, as shown in Fig. 135 D, 
 the magnetomotive force created by the current in one wind- 
 
THE DIRECT-CURRENT GENERATOR 
 
 175 
 
 ing is in series with that created in the other winding, or the 
 magnetomotive force on any magnetic circuit is that produced 
 by two windings in series. If the windings be placed upon 
 the magnetic circuit, as shown in Fig. 135 C, the magneto- 
 i motive force acting on each magnetic circuit would be that 
 of a single coil. This results in only half the ampere-turns 
 per coil being required when they are placed as shown in 
 Fig. 135 D, as would be required if the coils were placed as 
 shown in Fig. 135 C. 
 
 182. Materials Used in the Construction of the Magnetic 
 Circuit. There are three materials that are commonly used 
 
 in the construction of the 
 magnetic circuit of a dyna- 
 mo cast iron, wrought 
 iron, and cast steel. There 
 are a number of factors 
 which govern the selection 
 of the materials to be used 
 in a particular machine, 
 such as initial cost, weight, 
 efficiency demanded b y 
 purchaser, regulation, etc. 
 The cheapest of the 
 above materials is cast 
 iron and it is the poorest 
 of them all magnetically. 
 
 So the saving in the initial cost of the iron per pound would 
 more than likely be offset by the fact that a larger bulk of cast 
 iron would be required to form a certain magnetic circuit than 
 would be required if wrought iron, for example, were used. 
 There would also be an increase in the cost of copper required 
 to magnetize the large cast-iron core, since the length of each 
 turn would be more than when some better magnetic material 
 was used. 
 
 Wrought iron, on the other hand, is the best magnetic 
 material and at the same time the most expensive. It is used 
 where economy in weight and reduction of cross-section are 
 desired. Machines used aboard ships or electric automobiles, 
 etc., are usually made of wrought iron on account of the large 
 reduction in weight, which is a more important factor than 
 the initial cost. 
 
 Fig. 136 
 
176 PBACT1CAL APPLIED ELECTEICITY 
 
 Cast steel occupies a place intermediate between cast iron 
 and wrought iron both in cost and magnetic properties. 
 Machines are, as a rule, constructed of more than one mate- 
 rial. Thus the field cores will be of wrought iron, as that 
 would mean a saving in copper since the length of wire per 
 turn would be less than if cast iron were used; the yoke may 
 be of cast iron as its area can be made much larger than that 
 of the field cores and this increase in area will add strength 
 to the machine. The armature core is usually constructed of 
 wrought-iron sheets, so as to reduce the eddy-current loss to 
 a minimum; the pole shoes may be cast or they are sometimes 
 laminated in order to reduce the eddy-current loss in them. 
 
 183. Magnetic Leakage, Shape of Magnetic Circuit. The 
 total number of magnetic lines created by the current in the 
 field winding do not pass through the armature core, and 
 therefore, they are not all useful in inducing an e.m.f. in the 
 armature winding. The ratio of the total number of magnetic 
 lines created to the number that are actually useful in gen- 
 erating an e.m.f. is called the leakage coefficient. The value 
 of this coefficient can never be less than unity and in the 
 case of poorly designed machines, it will reach a value as 
 high as 1.4. 
 
 The value of this coefficient can be reduced by constructing 
 the magnetic circuit so it will be as short as possible, or of 
 low reluctance, and without abrupt turns. Placing the field 
 winding upon or near that part of the magnetic circuit offer- 
 ing the greatest reluctance will also reduce the value of the 
 leakage coefficient. 
 
 184. Value of Induced E.M.F. in Armature Winding. The 
 induced e.m.f. in an armature winding depends upon the 
 following factors: 
 
 (a) The useful flux (<i>) per pole of the machine. 
 
 (b) The number of poles (p) composing the magnetic 
 
 circuit. 
 
 (c) The total number of inductors (Z) on the armature. 
 
 (d) The number of paths (b) in parallel through the arma- 
 
 ture. 
 
 (e) The speed (s) in revolutions per second. 
 
 (f) The number of magnetic lines (108) that must be cut 
 
 per second in order that there be an e.m.f. of one 
 volt induced. 
 
THE DIEECT-CUBEENT GENEEATOE 177 
 
 These factors can all be combined in a simple equation which 
 will give the value of (E) in volts between the brushes of 
 the machine when it is operating without load, or when it is 
 delivering no current. 
 
 $ X P X Z X s 
 E = - (100) 
 
 108 x b 
 
 The value of (b) in the above equation will depend upon the 
 type of winding on the armature. For a simple lap winding 
 (singly re-entrant) it is equal to the number of poles and for 
 a simple wave winding (singly re-entrant) it is always two 
 regardless of the number of poles. This will be taken up 
 again in the chapter on "Armature Winding." 
 
 Example. A six-pole generator is operating at 900 revolu- 
 tions per minute. The useful flux per pole is 4 000 000 lines. 
 The armature has a simple lap winding (singly re-entrant) 
 of 198 inductors. What e.m.f. will be generated? 
 
 Solution. First obtain the value of the speed in revolutions 
 per second by dividing 900 by 60, or 
 
 900 -f- 60 = 15 
 
 The machine is then running at 15 revolutions per second. 
 Since the winding on the armature is a simple lap winding, 
 the value to substitute for (b) in equation (100) is equal to 
 the number of poles, or 6. Substituting the values of the 
 various quantities in equation (100) gives 
 
 4 000 000 X 6 X 198 X 15 
 E= - = 118.8 
 
 100 000 000 X 6 
 
 Ans. 118.8 volts. 
 
 185. Separate Excitation and Self-Excitation of a Genera- 
 tor. There are two methods by which the electromagnets of 
 the generator may be energized, and they are 
 
 (a) Separate excitation. 
 
 (b) Self-excitation. 
 
 In the case of separate excitation, the field windings of the 
 machine are connected to some source of energy, other than 
 the dynamo under consideration, such as a storage battery 
 or another dynamo, and the current in the field winding is 
 independent of the e.m.f. generated by the machine that is 
 
178 
 
 PEACTICAL APPLIED ELECTK1CITY 
 
 being excited. The field current is adjusted in value by 
 changing the value of the resistance in the field circuit, which 
 is accomplished by what is known as a field rheostat, or by 
 changing the e.m.f. of the generator that is supplying the 
 current to the field. The connections for separate excitation 
 are shown diagrammatically in Fig. 137. The rheostat (Rj) 
 is connected in series with the field of the main generator 
 
 (G). The field of the main generator may be connected to 
 either the storage battery (B) or the small generator (E), 
 which is called the exciter. A rheostat (R 2 ) is connected in 
 series with the field of the generator (E) and by means of this 
 rheostat the voltage generated in the armature of the exciter 
 can be changed, and hence the current in the field of the 
 generator (G), if (E) is supplying current to the field. 
 
 There are three different methods of self-excitation and 
 they will each be taken up in turn in the following three 
 sections. 
 
 186. Shunt -Wound Generator. 
 
 A/WWW ^ e field winding in the case of a 
 
 ~T \ p shunt-wound generator consists of a 
 
 (G) jo Shunt large number of turns of relatively 
 
 ] Sr 1 field small wire that may be connected 
 
 l__/ JWinding directly across the terminals of the 
 
 Fig. 138 machine. The potential difference 
 
 between the two terminals of the 
 
 machines produces a current in the field windings, which is 
 regulated in value by a resistance or rheostat. A diagram of 
 the connections of a self-excited shunt machine is given in 
 Fig. 138. 
 
 187. Series-Wound Generator. The field winding in the 
 case of a series-wound generator consists of a few turns of 
 large wire connected directly in series with the armature and 
 
THE DIRECT-CURRENT GENERATOR 
 
 179 
 
 load. The current in the field windings of a machine of this 
 kind is of the same value as the current through the load. A 
 diagram of the connections of a series-wound machine is 
 given in Fig. 139. 
 
 ~\ 
 
 Fig. 139 
 
 Fig. 140 
 
 188. Compound-Wound Generator. In the case of a com- 
 pound-wound generator, the field windings consist of two sets 
 of coils. The coils of one set consist of a few turns of large 
 wire connected in series with the armature and the load; the 
 coils of the other set consist of a large number of turns of 
 
 j 
 
 Fig. 141 
 
 small wire, all connected in series across the terminals of (he 
 machine. The compound generator is nothing more than a 
 combination of a shunt and series generator. 
 
 When the shunt winding is connected directly across the 
 armature, as shown in Fig. 140, the machine is called a short 
 shunt; when it is connected across the armature and the 
 series field, as shown in Fig. 141, the machine is called a long 
 
PRACTICAL APPLIED ELECTEICITY 
 
 shunt. In the case of a long shunt the current in the shunt 
 field passes through the series field in completing its circuit 
 through the armature; while in the case of a short shunt, the 
 current in the shunt field passes directly through the arma- 
 ture without passing through the series field. The current in 
 the shunt field can be regulated by a rheostat (R), while the 
 current in the series field depends upon the current in the 
 load to which the machine is connected. 
 
 189. Armature Reaction. When a dynamo is operating 
 under a load, the current in the armature will produce a 
 magnetizing effect upon the field of the machine and this 
 effect is called armature reaction. The direction of this mag- 
 netizing effect due to the armature current can be determined 
 as follows: Take a simple drum armature with twelve coils 
 equally spaced around the core and revolving in a bipolar 
 magnetic field. (A cross-section through such an armature 
 and field is given in Fig. 142.) The induced e.m.f. in the 
 armature inductors on the right of a plane (AC), drawn 
 perpendicular to the direction of the magnetic field, will be 
 just the reverse of the direction of the induced e.m.f. in the 
 conductors to the left of the plane (AC). The induced e.m.f. 
 in the conductors is zero when they are in the plane (AC), and 
 it changes in direction as the conductors pass from one side 
 of the plane to the other. The plane (AC) is called the 
 normal neutral plane, it being perpendicular to the magnetic 
 flux when there is no current in the armature and, as a result, 
 the field is not distorted. The brushes (Bj) and (B 2 ) should 
 be placed in this plane, and when they are connected through 
 an external circuit there will be a current in the armature 
 conductors the value of which will depend upon the value of 
 the induced e.m.f. and the total resistance of the circuit. The 
 direction of this current in the inductors will be the same as 
 that of the induced e.m.f. shown in Fig. 142, and it will 
 produce a certain magnetizing effect upon the armature core. 
 This magnetizing effect can best be shown by connecting the 
 terminals of the machine to some source of e.m.f. in such a 
 way that the current in the armature will be in the same 
 direction as though it was produced by the induced e.m.f. 
 (When the machine is connected to the external source of 
 e.m.f., there should be no current in the field windings and 
 the armature should be stationary.) The magnetic field due 
 
THE DIRECT-CUEEENT GENEEATOR 
 
 181 
 
 to the armature current alone is shown in Fig. 143. It is 
 seen that this field is at right angles to the field of the 
 machine. In actual operation the magnetizing effect of the 
 armature current and the 
 field current are both 
 present at the same time 
 and the resultant field is 
 a combination of the two 
 as shown in Fig. 144. 
 This results in a non- 
 uniform distribution of 
 the magnetic flux through 
 the generator pole pieces, 
 air gaps, and armature 
 core. The distortion 
 takes place in the direc- 
 tion of rotation which re- 
 sults in a crowding of 
 the flux in the trailing 
 horns of the pole pieces. 
 
 The neutral plane of the resultant magnetic field will make 
 an angle with the normal neutral plane, and the value of this 
 angle will depend upon the amount of armature reaction. As 
 a result of the neutral plane changing its position, the posi- 
 tion of the brushes must also be changed so that it 
 will correspond more nearly to the position of the 
 neutral plane. With a change in the position of the brushes, 
 there wilj be a change in the direction of the current in some 
 of the armature conductors. Thus, if the brushes be shifted 
 in the direction of rotation, as shown in Fig. 145, the direction 
 of the current in the inductors in the angle (0) will change 
 and the magnetic effect of a current in the armature will no 
 longer be in a direction perpendicular to the magnetic field 
 of the machine, but in a direction such as that shown in 
 Fig. 145. This magnetizing effect can be thought of as made 
 up of two parts, one acting parallel to the magnetic field of 
 the machine and another acting perpendicular to the magnetic 
 field of the machine. The magnetizing effect of the armature 
 current perpendicular to the field of the machine is called the 
 cross-magnetizing effect, and the effect parallel to the field of 
 the machine is called the demagnetizing effect. One of the 
 
182 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 above effects tends to weaken the magnetic field of the 
 
 machine, while the other tends to distort the magnetic field. 
 
 190. Cross-Turns and Back Turns. In the previous section 
 
 it was pointed out that 
 
 A 
 
 B, 
 
 ii 
 
 .V.j0r:::rx---/&^--" 
 
 Fig. 144 
 
 the plane of the brushes, 
 known as the com mutat- 
 ing plane, should be moved 
 in the direction of rota- 
 tion in order that the 
 brushes be nearer the neu- 
 tral plane. The position 
 of this commutating plane 
 will always be in advance 
 of the normal neutral 
 plane in the case of a 
 generator, and behind the 
 normal neutral plane in 
 the case of a motor. 
 
 The angle between the 
 commutating plane and 
 
 the normal neutral plane is called the angle of lead in the case 
 of a generator, and the angle of lag in the case of a motor. 
 The position of the two commutating planes is shown in 
 Fig. 146, the full line (DB) 
 representing the commu- 
 tating plane of the gener- 
 ator and the dotted line 
 (FG) representing the 
 commutating plane of the 
 motor. The conductors in 
 the double angle (26) on 
 one side of the armature 
 can be thought of as being 
 in series with the con- 
 ductors in the angle (29) 
 on the other side of the 
 armature, and forming a 
 number of complete turns 
 about the core. The re- 
 maining conductors can be thought of as forming a second set 
 of turns. The product of the turns in the double angle (26) 
 
THE DIEECT-CUEEENT GENEEATOE 
 
 183 
 
 D 
 
 and the current in them gives what is called the demagnetizing 
 ampere-turns because their effect is to produce a weakening of 
 the magnetic field of the machine. The remaining turns times 
 the current in them are called the cross-magnetizing ampere- 
 turns because they act at 
 right angles to the mag- 
 netic field of the machines. 
 The turns in the angle 
 (29) are called back 
 turns and the remaining 
 ones are called cross-turns. 
 191. Means of Reduc- 
 ing Armature Reaction. 
 Armature reaction inter- 
 feres with the satisfactory 
 operation of the dynamo 
 and should be reduced to a 
 minimum where possible. 
 There are a number of 
 ways of bringing about a 
 
 reduction in the effect of armature reaction, some of the more 
 important ones being: 
 
 (a) By increasing the length of the air gap of the machine. 
 
 (b) By slotting the poles parallel to the axis of the arma- 
 
 ture. 
 
 (c) By properly shaping the pole pieces. 
 
 (d) By using auxiliary poles. 
 
 (e) By placing a winding in perforations in the pole faces. 
 
 (Invented by Mr. Ryan.) 
 
 (a) Increasing the length of the air gap increases the 
 reluctance in the magnetic circuit that is acted upon by the 
 cross-magnetizing ampere-turns, but at the same time increases 
 the number of ampere-turns required in the field winding of 
 the machines. Thus the effect of the distorting, or cross-turns, 
 will not be so great as it would be if the magnetic field of the 
 machine were weaker. 
 
 (b) Cutting slots in the pole faces parallel to the axis of 
 the armature introduces a large reluctance in the path of the 
 cross flux, produced by the cross-magnetizing ampere-turns, 
 but does not introduce anything like as great a reluctance in 
 the main magnetic circuit. Fig. 147 shows a stamping used in 
 
184 
 
 PKACTICAL APPLIED ELECTRICITY 
 
 the construction of a field core, there being a small slot 
 punched in each piece. When these stampings are all 
 assembled there will be one long slot through the pole piece 
 parallel to the axis of the armature. 
 
 (c) The shifting of the magnetic flux across the pole shoe 
 of the machine can be greatly reduced by properly shaping 
 
 Fig. 147 Fig. 148 
 
 them so that the parts of the air gap where the flux tends to 
 become most dense will have the greater reluctance. Thus the 
 pole faces may be cut so that the trailing horn, in the case of 
 a generator, will be farther from the surface of the armature. 
 The trailing horn of the pole piece may also be made longer 
 
 than the advancing side, 
 which also results in a 
 more uniform distribu- 
 tion of the magnetic flux 
 and the armature in- 
 ductors will enter and 
 leave the magnetic field 
 more gradually than they 
 would if an ordinary pole 
 piece were used. Such a 
 pole piece is shown in 
 Fig. 148. 
 
 (d) Auxiliary poles 
 may be placed between 
 the main poles of the ma- 
 chines and so connected 
 149 that their magnetizing 
 
 effect is just the reverse of that of the cross-magnetizing am- 
 pere-turns. The windings on these poles are connected so that 
 they carry all or a definite portion of the full load current. 
 This results in their effect varying directly as the load cur- 
 rent, just as the effect of the cross ampere-turns varies with 
 
THE DIRECT-CURRENT GENERATOR 
 
 185 
 
 the load current, and if the effects balance for one particular 
 load, they will practically balance for all other loads and the 
 position of the neutral plane of the magnetic field will remain 
 almost constant. The auxiliary poles of a machine are shown 
 in Fig. 149. 
 
 192. Commutation. The process of commutation can best 
 be explained by reference to Fig. 150. The commutator seg- 
 ments are shown shaded while the various elements of the 
 armature winding are 
 shown connected in series, 
 the junctions of these ele- 
 ments being connected to 
 the commutator segments 
 in regular order. The direc- 
 tion of rotation of the arma- 
 
 ture is indicated by the 
 arrow (A), and the position 
 of the neutral plane by the 
 line (DE). The direction 
 of current in the various 
 elements is indicated by the Fig. 150 
 
 small arrows. With a direc- 
 tion of current corresponding to that shown in the figure, the 
 brush (B}) must be positive. 
 
 Now as the armature rotates, the commutator segments in 
 turn pass under the brush (Bj). If the contact surface of the 
 brush is greater than the width of the insulation between the 
 segments, which should always be the case, then an element 
 ot the winding will be short-circuited when the brush is in 
 contact with the two segments to which the element is con- 
 nected. The current in the short-circuited coil drops to zero 
 when it is shorted, but it does not do so instantly on account 
 of the inductance of the coil. As the armature rotates, the 
 brush moves from commutator segment (C 4 ), Fig. 150, and 
 the element of winding (4) is connected in series with 
 the other elements in the left-hand path. When the element 
 becomes a part of the left-hand path, it carries the same 
 current the other elements in that path carry. Now if there 
 is zero current in the coil that is finishing commutation, 
 just as it moves from the short-circuited position, the current 
 in it must increase almost instantly to a value equal to that 
 
186 PRACTICAL APPLIED ELECTRICITY 
 
 in the other elements. The inductance of the element op- 
 poses this sudden increase in current and, as a 'result, there 
 is a tendency for an arc to form between the brush and the 
 commutator segment (C 4 ) until the current in the coil (4) has 
 reached its proper value, or the inductance of the coil has been 
 overcome. This condition of affairs would result in a con- 
 tinuous sparking at the brushes, which would not only repre- 
 sent a loss but would be injurious to both the commutator and 
 the brushes. Sparking due to the cause just mentioned can 
 be reduced and practically overcome by advancing the brushes 
 beyond the neutral plane. When the brushes are thus ad- 
 vanced, there will be an e.m.f. induced in the coil undergoing 
 commutation while it is short-circuited and this induced e.m.f. 
 will be in such a direction as to produce a current in the same 
 direction as the current in the elements to the left of the 
 brush, as shown in Fig. 150. This results in the inductance 
 of the coil being overcome while the coil is still short-cir- 
 cuited, and the current will meet with no opposition other 
 than the ohmic resistance when the coil becomes a part of 
 the left-hand circuit. Advancing the brushes beyond the 
 neutral plane results in a slight lowering of the terminal e.m.f. 
 of the machine, but this is more than offset by the advantage 
 in the reduction in sparking. 
 
 193. Capacity of a Generator. The output of a generator is 
 limited by one of the three following factors, when sufficient 
 power is applied to drive it. These factors are: 
 
 (a) Excessive drop In the armature of the machine. 
 
 (b) Excessive heating. 
 
 (c) Excessive sparking. 
 
 (a) As the load on a generator is increased, there is an 
 increase in drop in the armature due to the (IR) drop and 
 armature reaction. These two effects combined decrease the 
 terminal voltage of the machine and this decrease is usually 
 excessive when the machine is overloaded. 
 
 (b) The allowable temperature rise as prescribed by the 
 American Institute of Electrical Engineers is as follows: 
 "Under normal conditions of operating and ventilation, the 
 maximum temperature rise referred to a standard room tem- 
 perature of 25 C. should not exceed 50 C. for field coils and 
 armature as measured by the increase in resistance; and 
 55 C. for commutator and brushes, and 40 C. for all other 
 
THE DIKECT-CUEEENT GENEEATOE 
 
 187 
 
 Field Current 
 
 Ffe. 151 
 
 parts, bearings, etc., as determined by a thermometer." It Is 
 usually safe to operate a machine above these temperatures 
 for a few hours, but an excessive heating of commutator, 
 armature, or field coils, is 
 likely to injure and in 
 some cases destroy the in- 
 sulation. 
 
 (c) The heat generated 
 as a result of sparking 
 usually limits the allow- 
 able sparking, as it causes : 
 a rise in temperature of 
 the commutator and 
 the brushes. 
 
 194. Building Up of a 
 Self-Excited Shunt Gener- 
 ator. The iron composing 
 the magnetic circuit of a generator usually retains some of its 
 magnetism and when the armature is revolved in this weak 
 magnetic field, there is a small e.m.f. induced which produces 
 a current in the field windings. This current, if the windings 
 
 are properly connected, 
 will increase the magnetic 
 flux through the arma- 
 ture, which in turn will 
 increase the e.m.f. and 
 field current, etc. A curve 
 showing the relation be- 
 tween terminal voltage 
 and field current is given 
 in Fig. 151. Such a curve 
 is called a magnetization 
 curve. The abrupt bend 
 in the curve near the top 
 indicates that the mag- 
 
 Load Current 
 
 Fig. 152 
 
 netic circuit is practically saturated. 
 
 195. External Characteristics of Shunt, Series, and Com- 
 pound Generators. The external characteristic curve of a gen- 
 erator is a curve that shows the relation between the current 
 output of the generator and the terminal voltage. 
 
 In the case of the shunt generator, assuming the speed 
 
188 
 
 PEACTICAL APPLIED ELECTRICITY 
 
 remains constant and the field resistance is not changed after 
 it is adjusted to give normal terminal voltage at no load, the 
 voltage at the terminals of the machine will decrease with an 
 increase in load on account of armature reaction and copper 
 
 drop. The curve in Fig. 152 
 shows the relation between 
 the terminal voltage and 
 the load current for a shunt 
 generator. The drop in 
 voltage will be different 
 for different machines, de- 
 pending upon the resist- 
 
 ru 
 
 -dr 
 loE 
 
 Load Current 
 
 Fig. 153 
 
 ance of the armature and 
 the amount of armature 
 reaction. 
 
 In the case of a series 
 generator, the terminal 
 voltage is zero with zero 
 
 load, but it increases as the load current increases because 
 the field excitation is increasing. The field strength of the ma- 
 chine will continue to increase very rapidly with an increase 
 in load until the iron becomes saturated, when the effects of 
 armature reaction and cop- 
 per drop produce a de- 
 crease in terminal voltage 
 with a further increase in 
 load, as shown in Fig. 153. 
 In the case of a com- 
 pound generator, the series 
 winding may be so con- 
 nected as to produce a 
 magnetizing effect that 
 aids the shunt field, and 
 with an increase in load 
 there is an increase m 
 total field excitation. If 
 
 this increase in field excitation is just sufficient to main- 
 tain the terminal voltage practically constant, the ma- 
 chine is said to be flat-compounded. If there is a rise in 
 terminal voltage with an increase in load, the machine is 
 said to be over-compounded, and if the voltage drops with an 
 
 Load Current 
 
 Fig. 154 
 
THE DIRECT-CURRENT GENERATOR 
 
 189 
 
 increase in load the machine is said to be under-compounded. 
 The external characteristic curve of an over-compounded gen- 
 erator is shown by curve (A) it, Fig. 154, and the external 
 characteristic curve of a flat-compounded generator, by 
 curve (B). 
 
 196. Adaptability of Shunt, Series, and Compound Gen- 
 erators. The shunt generator is usually used where it is 
 desired to have a practically constant voltage, and the dis- 
 tance from the machine to the load is not very great, resulting 
 in a small voltage loss in the line. 
 
 The series generator is usually used in supplying a constant 
 current to a load at a varying potential, such as a number of 
 arc lamps connected in series. 
 
 The compound machine 
 can be constructed so that 
 the voltage at its ter- 
 minals, or at the load, can 
 be maintained constant or 
 allowed to increase or de- 
 crease with a change in 
 load. Thus it can operate 
 a number of lamps at a 
 constant pressure even 
 though they be located 
 some distance from the 
 generator, or the voltage 
 at the end of the line can 
 be made to increase with 
 an increase of load, as is 
 quite often the case in 
 railway work. A modern compound generator is shown in 
 Fig. 155. 
 
 197. Losses in Generators. The losses in generators may 
 be divided into two main groups: 
 
 (A) I2R, or electrical losses. 
 
 (B) Stray-power losses. 
 
 (A) The I2R losses occur in the field windings and the 
 armature. If (I c ), (Is), and (I a ) represent the currents in the 
 shunt-field winding, series-field winding, and armature, re- 
 spectively, and (R c ), (Rs), and (R a ) represent the resistance 
 of the shunt-field winding, series-field winding, and armature, 
 
 Fig. 155 
 
190 PRACTICAL APPLIED ELECTRICITY 
 
 respectively, then the loss in the shunt-field winding (W c ), 
 series-field winding (W s ), and armature (W a ) can be deter- 
 mined by the following equations: 
 
 We = I2 c R c (101) 
 
 W s = I2 S R S (102) 
 
 W a = I2 a R a (103) 
 
 (B) The stray-power losses consist of 
 
 (a) Hysteresis and eddy-current losses chiefly in the arma- 
 
 ture core. 
 
 (b) Friction losses at bearings and brushes, and air fric- 
 
 tion, or windage, as it is called, due to the fan-like 
 
 action of the moving parts. 
 
 The stray-power losses cannot be calculated with the same 
 degree of accuracy that the (I2R) losses can; but they can, 
 however, be quite accurately determined for a given machine 
 by experiment. 
 
 198. Efficiency of Generators. There are three efficiencies 
 for a generator: 
 
 (a) Efficiency of conversion. 
 
 (b) Electrical efficiency. 
 
 (c) Commercial efficiency. 
 
 (a) The efficiency of conversion is the ratio of the total 
 electrical power generated to the total mechanical power 
 supplied. Let (P) represent the mechanical power supplied, 
 then 
 
 El + (electrical losses) 
 
 Efficiency of conversion = X 100 
 
 P (104) 
 
 Where (El) represents the output in watt. 
 
 (b) The electrical efficiency is the ratio of the total elec- 
 trical power delivered to the total electrical power developed. 
 
 El 
 
 Electrical efficiency = X 100 
 
 El -f (electrical losses) (105) 
 
 (c) The commercial efficiency of a generator is the ratio 
 of the electrical output to the mechanical input, or 
 
 El 
 
 Commercial efficiency = X 100 (106) 
 
 P 
 
THE DIRECT-CURRENT GENERATOR 191 
 
 The commercial efficiency is the most important of the three, 
 as it includes all the losses in the machine. 
 
 199. Commercial Rating of Generators. Generators are 
 rated according to their k.w. output. Thus a 100-k.w. 100-volt 
 generator means the machine will deliver 100 k.w. to an 
 external circuit connected to its terminals, and that the 
 voltage will be 100 volts. If the output is 100 k.w. at 100 
 volts, then the current will be 10 000 -=- 100 = 1000 amperes. 
 
 PROBLEMS ON DIRECT-CURRENT GENERATORS 
 
 1. Calculate the e.m.f. generated in the armature of a 10- 
 pole direct-current generator wound with 1000 inductors, lap 
 winding (simplex singly re-entrant), and revolving at 300 revo- 
 lutions per minute. The magnetic flux per pole is 5 000 000 
 maxwells. Ans. 250 volts. 
 
 2. If the winding in the above problem was changed to a 
 wave winding (simplex singly re-entrant), what e.m.f. would 
 be generated? Ans. 1250 volts. 
 
 Note: See section (184). 
 
 3. If the speed in problem (1) is decreased to 250 revolu- 
 tions per minute and the flux (<) per pole is raised to 
 6 000 000 maxwells, what would be the change in the e.m.f. 
 generated? Ans. No change. 
 
 4. The armature of the machine in problem (1) has a 
 resistance of .006 ohm, what will be the value of the terminal 
 voltage when the machine is delivering a current of 750 
 amperes? (Assume the internal voltage remains constant.) 
 
 Ans. 245.5 volts. 
 
 5. How much should the flux per pole be increased in order 
 that the terminal voltage in problem (4) remain constant? 
 
 Ans. Increase 90 000 maxwells. 
 
 6. There are 180 inductors on the surface of a bipolar drum- 
 wound armature and in each of these inductors there is a 
 current of 50 amperes. Calculate the demagnetizing and cross- 
 magnetizing ampere-turns when the commutating plane makes 
 an angle (9) of 10 degrees with the normal neutral plane. 
 
 Ans. 500 demagnetizing ampere-turns. 
 4000 cross-magnetizing ampere-turns. 
 
192 PRACTICAL APPLIED ELECTRICITY 
 
 7. The total flux produced by a field winding is 5 800 000 
 maxwells and the useful flux is 5 000 000 maxwells, calculate 
 the coefficient of magnetic leakage. 
 
 Ans. Leakage coefficient = 1.16. 
 
 8. The output of a 110-volt generator is 300 amperes, what 
 is the horse-power input if the efficiency of the machine is 
 90 per cent? Ans. 49.2 horse-power. 
 
 9. If the electrical loss in problem (8) is 1375 watts, what 
 is the electrical efficiency of the machine? The efficiency of 
 conversion? 
 
 Ans. Electrical efficiency, 96 per cent. 
 
 Efficiency of conversion, 93.8 per cent. 
 
 10. What is the commercial efficiency of a machine that 
 will deliver 500 amperes at 550 volts when the input is 400 
 horse-power? Ans. 92.1 + per cent. 
 
CHAPTER X 
 
 DIRECT-CURRENT MOTORS 
 
 200. Fundamental Principle of the Direct-Current Motor. 
 If a conductor in which there is a direct current be placed in 
 a magnetic field in such a position that it makes an angle with 
 the direction of the field, there will be a force tending to move 
 the conductor. This same force is present in the case of a 
 generator, but it is overcome by the mechanical force that 
 drives the machine. With an increase in current in the con- 
 ductor or an increase in the strength of the magnetic field, 
 there will be an increase in the force which tends to move the 
 conductor. 
 
 201. Fleming's Left-Hand or Motor Rule. There is a 
 definite relation between the direction of current in a con- 
 ductor, the direction of motion, and the direction of the mag- 
 netic field for a motor; just as there is a definite relation 
 between these three quantities in the case of a generator. If 
 the thumb and first and second fingers of the left hand be 
 placed at right angles to each other, the second finger pointing 
 in the direction of the current in the conductor, the first finger 
 in the direction of the magnetic field, then the thumb will 
 point in the direction in which the conductor will tend to 
 move. This simple rule is known as Fleming's left-hand or 
 motor rule. If the direction of the current in the conductor 
 be reversed, the direction of the magnetic field remaining 
 constant, the direction of motion will be reversed; or, if the 
 direction of the magnetic field be reversed, the direction of 
 the current remaining the same, the direction of motion will 
 be reversed. If, however, the direction of the current and 
 the direction of the magnetic field are both reversed, the 
 direction of motion of the conductor will remain the same. 
 Fig. 156 illustrates Fleming's left-hand rule. 
 
 202. Generator and Motor Interchangeable. The essential 
 parts of a direct-current motor are identical with those of a 
 
 193 
 
194 PEACTICAL APPLIED ELECTRICITY 
 
 generator, namely, an armature and magnetic field. The con- 
 nection of the armature conductors to the external circuit is 
 made by means of a commutator which serves to reverse the 
 direction of current in the armature 
 winding at the proper time so that the 
 forces tending to move the various con- 
 ductors in the magnetic field all act to- 
 gether and a continuous rotation of the 
 armature is produced. Any direct-current 
 etic generator may be used as a direct-cur- 
 
 rent mOtOI> Or vice Versd > their COnstrUC- 
 
 tion being practically the same. 
 Fig. 156 203. Classes of Motors. Direct-cur- 
 
 rent motors may be divided into three 
 
 main groups according to the method employed in exciting 
 
 the field magnets. These are: 
 
 (a) Shunt motors. 
 
 (b) Series motors. 
 
 (c) Compound motors. 
 
 (a) The field windings of a shunt motor consist of a large 
 number of turns of small wire connected directly across the 
 terminals of the machine, or the line to which the machine is 
 connected. The current in the field winding of a shunt 
 machine is independent of the current in the armature so 
 long as an increase in armature current produces no change 
 in the voltage impressed upon the shunt field winding. The 
 field strength of the shunt machine is regulated by changing 
 the current in the field winding, which may be done by either 
 changing the impressed voltage or the total resistance of the 
 circuit. 
 
 (b) In the case of the series motor, the field winding con- 
 sists of a few turns of large wire connected directly in series 
 with the armature and the line. The current in the field 
 windings is the same as the current in the armature, and the 
 ^eld strength varies with the load on the machine, the field 
 current increasing with the load. 
 
 (c) The field windings of a compound motor are a combi- 
 nation of the shunt and the series windings. The magnetic 
 effect of these two windings may aid or oppose each other, de- 
 pending upon the way they are connected. When the two 
 magnetizing effects act together, the machine is called a cumu- 
 
DIRECT-CURRENT MOTORS 
 
 195 
 
 lative compound motor; and when their magnetizing effects 
 oppose each other, the machine is called a differential com- 
 pound motor. In the case of the cumulative compound 
 machine, the field strength increases with an increase in load 
 I since the two magnetizing effects act together; and in the 
 case of the differential compound motor, the field strength 
 decreases with an increase in load since the two magnetizing 
 effects act opposite to each other. 
 
 204. Direction of Rotation of Machines when Changed from 
 a Generator to a Motor. The direction of current in the 
 armature, field winding, and line for a self-excited shunt 
 generator, and the polarity of the machine and direction 
 
 To Line 
 
 Fig-. 157 
 
 Fig. 158 
 
 of rotation are shown in Fig. 157. The arrow (I a ) repre- 
 sents the direction of the armature current. Let this ma- 
 chine be operated as a motor by connecting it to some 
 source of energy, connecting the positive terminal of the 
 machine to the positive line, and the negative terminal of 
 the machine to the negative line. The direction of current 
 in the field and armature for this connection is shown in 
 Fig. 158. It will be seen by inspection that the direction of 
 current in the field winding has remained the same in the two 
 cases and that the direction of current in the armature has 
 changed. Now applying Fleming's dynamo rule to Fig. 157 
 and his motor rule to Fig. 158 remembering the direction of 
 current in the armature in one case is just the reverse of 
 what it is in the other, and the field current is the same in 
 both cases you will find the direction of rotation of the arma- 
 ture in Fig. 158 will be the same as in Fig. 157. 
 
 In the change from a generator to a motor, as shown in 
 Figs. 157 and 158, the polarity of the terminals of the motor 
 was the same as that of the generator. When the polarity of 
 
PRACTICAL APPLIED ELECTRICITY 
 
 the motor is just the reverse of that of the generator, the 
 current in the shunt-field winding will be reversed in direc- 
 tion and the armature current will not change. This will also 
 result in the direction of rotation of the armature remaining 
 the same. Hence, a shunt generator will always run in the 
 same direction when operated as a motor, as it did when it 
 was run as a generator. 
 
 To change the direction of rotation of a shunt generator 
 when it is changed to a motor, the connections of the arma- 
 ture or shunt-field winding must be reversed. 
 
 When a series generator is changed to a series motor, the 
 direction of rotation will be reversed, because the direction of 
 the current in the field winding and the armature bear the 
 same relation to each other in both cases and the motion will 
 be opposite as shown by the right- and left-hand rules. Chang- 
 ing the connection of the machine to the line will not change 
 the direction of rotation as the current in both the armature 
 and field winding is reversed when such a change is made. 
 Then in order to change the direction of rotation of the 
 armature, the connections of either the series field winding 
 or armature must be reversed, which will result in a change 
 in direction of either the magnetic field or of the armature 
 current, but not of both. 
 
 The compound generator will act, as far as direction of 
 rotation is concerned, when changed to a motor, the same as 
 though it were a simple shunt machine, provided the machine 
 is lightly loaded. If it is started under a heavy load there 
 will be an excessive current in the armature and series-field 
 winding, and if the magnetizing effect of the series-field 
 winding is greater than that of the shunt-field winding, the 
 machine will start up as though it were a series motor. 
 
 205. Armature Reaction in a Motor. Let us assume that a 
 shunt generator is operated as a shunt motor, the polarity of 
 the machine being the same in both cases. The current in 
 the shunt-field winding will remain constant in direction and, 
 as a result, the direction of the magnetic field of the machine 
 does not change. The direction of current in the armature, 
 however, changes and as a result the direction of the magnetic 
 field produced by it changes. When the brushes are in the 
 normal neutral plane, as shown in Fig. 143, the field produced 
 by the armature current is at right angles to that produced by 
 
DIEECT-CUEEENT MOTOES 
 
 197 
 
 the field current and it is acting downward, as shown in Fig. 
 159, instead of upward, as shown in Fig. 143. Since the mag- 
 netizing effects of the armature current and the field current 
 are present at the same 
 time, they form a resultant 
 field whose general direc- 
 tion is similar to that 
 shown in Fig. 160. It will 
 be seen that the magnetic 
 field in the case of a motor 
 is shifted in a direction op- 
 posite to the direction of 
 rotation, which is just the 
 reverse of what occurred 
 in the generator, as shown 
 in Fig. 144. This results 
 in the neutral plane of the 
 magnetic field being shift- 
 ed back of the normal 
 neutral plane, as shown by the line (FG) in Fig. 160. 
 
 206. Position of the Brushes on a Motor. Since the neutral 
 plane of the magnetic field is changed when the generator is 
 changed to a motor, the plane in which the brushes are placed 
 
 must be changed so that 
 p it will correspond more 
 
 A B (> / nearly to the position of 
 
 the neutral plane. The 
 brushes then will be given 
 an angle of lag in the case 
 of a motor while they were 
 given an angle of lead in 
 the case of a generator. 
 
 The demagnetizing turns 
 on the armature are in the 
 angle (26), as shown in 
 Fig. 146, and the cross- 
 magnetizing turns are those 
 outside of this double an- 
 gle. The turns in the dou- 
 ble angle (26) are still demagnetizing, although the current 
 through the armature has been reversed, for the following 
 
198 PEACT1CAL APPLIED ELECTEICITY 
 
 reason: When the machine is used as a generator the brushes 
 are in advance of the neutral plane, as shown in Fig. 145, 
 and when it is used as a motor they are back of the neutral 
 plane, as shown in Fig. 160. If the brushes were changed from 
 one position to the other without reversing the current in the 
 armature, the current in the turns located in the angle (20) 
 would be reversed in direction and the magnetizing effect of 
 the ampere-turns in this angle (20) would act with the mag- 
 netic field of the machine. The current in the armature, how- 
 ever, is reversed at the same time the position of the brushes 
 is changed and, as a result, the magnetizing effect of the 
 turns in the angle (20) does not change in direction. 
 
 The brushes are usually placed a little back of the neutral 
 plane in the case of a motor for the same reason they are 
 placed in advance of the neutral plane in the case of a 
 generator, as explained in section (192). 
 
 207. Torque Exerted on Armature. The torque of a motor 
 is equal to the product of the total force acting on the arma- 
 ture conductors times the distance of the conductors from the 
 center of the armature, or 
 
 T = F X L- (107) 
 
 ' 
 When the force (F) in the above equation is measured in 
 
 pounds and the distance (L) between the point of application 
 of this force and the center of the armature is measured in 
 feet, the torque (T) will be given in pound-feet. The follow- 
 ing equation can be used in calculating the torque in pound- 
 feet in terms of the total number of conductors (Z) on the 
 armature, the number of poles (p), the magnetic flux per pole 
 (3>),the number of paths in parallel through the armature (b), 
 and the total armature current (I a ). 
 
 .1174 XpXZx$Xla 
 
 T = (108) 
 
 108 X b 
 
 208. Mechanical Output of a Motor. The output of a motor 
 in foot-pounds per second is equal to the torque (T) in pound- 
 feet multiplied by the speed in revolutions per second (r.p.s.) 
 times 2 ?r. Since one horse-power is equal to 550 foot-pounds 
 per second, then the output of a motor in horse-power (h.p.) 
 can be calculated by the use of the following equation: 
 
DIRECT-CURRENT MOTORS 199 
 
 27r X T X (r.p.s.) 
 
 h.p. = (109) 
 
 550 
 
 If the speed is measured in revolutions per minute (r.p.m.), 
 then 
 
 27T X T X (r.p.m.) 
 
 h.p.= (110) 
 
 33000 
 
 209. Counter Electromotive Force. When a machine is 
 being operated as a motor, the armature is revolving in a 
 magnetic field and there will be an induced e.m.f. set up in 
 the conductors just the same as there would be if the machine 
 were operated as a generator. Since the relation between 
 the direction of motion of the conductors with respect to the 
 direction of the magnetic field in the case of a motor is 
 opposite to what it is in the case of a generator, the direction 
 of the current in the conductors remaining constant, the 
 induced e.m.f. in the armature of the motor will be just the 
 reverse of what it is in the case of the generator. This e.m.f. 
 opposes the flow of the electricity in the armature and hence 
 takes energy from it, just as a force that acts in a direction 
 opposite to the velocity of a body takes energy from the body, 
 hence the motor action. This induced e.m.f. acts in a direc- 
 tion just opposite to the impressed e.m.f. at the terminals 
 of the machine and for that reason it is called a counter 
 electromotive force. Its value depends upon the same factors 
 as the e.m.f. of a generator, and it may be calculated by the 
 use of equation (100). A counter e.m.f. is absolutely neces- 
 sary to the operation of a motor. 
 
 210. Normal Speed of a Motor. The current in the arma- 
 ture of a motor depends upon the resistance of the circuit, 
 and the effective electromotive force acting in the circuit. If 
 the impressed voltage on the machine be represented by (E), 
 the counter electromotive force by (E c ), and the effective 
 electromotive force by (E f ), then 
 
 E f = E EC (111) 
 
 The current (I n ) in the armature is equal to 
 
 Er 
 
 I a = - (112) 
 
 R, 
 
200 PBACTICAL APPLIED ELECTRICITY 
 
 or 
 
 E EC 
 
 (113) 
 
 Ra 
 
 In the above equations (R a ) represents the total resistance 
 between the terminals of the machine, neglecting the shunt 
 field. In a shunt machine (R a ) would be the resistance of the 
 armature, while in a series and compound machine (R a ) would 
 be the resistance of the series field and armature combined. 
 Since the current is dependent upon the counter electromotive 
 force, as shown in equation (113), the machine will run at 
 such a speed that the difference between the impressed voltage 
 (E) and the counter electromotive force will produce suf- 
 ficient current in the armature to produce the required torque 
 in order that the machine may carry its load. Thus, with an 
 increase in load on a machine there will be an increase in 
 torque required, and this increase in torque will mean an 
 increase in armature current if the field strength remains 
 constant. Now in order that the current in the armature 
 increase, the resistance (R a ) and impressed voltage (E) 
 remaining constant, the value of the counter e.m.f. must 
 decrease. The only factor in equation (100) that can change 
 is the speed, since the field strength, or flux per pole (<), is 
 supposed to remain constant and the other factors are gov- 
 erned by the construction of the machine and cannot be 
 changed without rebuilding. There will then be a reduction 
 in the speed of a machine with an increase in load current, 
 all other factors remaining constant. 
 
 211. Methods of Regulating the Speed of a Motor. The 
 speed of a motor may be regulated by any one, or certain 
 combinations of the following methods: 
 
 (a) Change in field strength produced by a change in field 
 
 current. 
 
 (b) Change in field strength produced by a change in the 
 
 reluctance of the magnetic circuit. 
 
 (c) Varying voltage over the armature by means of a 
 
 rheostat. 
 
 (d) Multi-voltage system. 
 
 (e) By changing the position of the brushes. 
 
 (a) A rheostat placed in series with the shunt field of a 
 
DIRECT-CURRENT MOTORS 
 
 201 
 
 Fig. 161 
 
 motor, as shown in Fig. 161, may be used to change its speed. 
 If the resistance of the shunt-field circuit be increased by 
 increasing the part of the resistance (R) in circuit, the field 
 current will be decreased and there will be a decrease in the 
 magnetic flux (<) per pole which 
 will result in an increase in speed, 
 all other quantities remaining con- 
 stant, in order that the required 
 counter e.m.f. may be generated in 
 the armature. The change in the 
 value of (<t>) due to a change in the 
 field current will depend upon the 
 
 degree to which the iron of the magnetic circuit of the ma- 
 chine is saturated. If the circuit is well saturated there must 
 be a relatively large change in field current to produce a 
 small change in speed. 
 
 There is a limit, however, to the amount you can weaken 
 the field of a machine as the armature reaction increases with 
 a decrease in field strength which results in serious sparking. 
 The effect of armature reaction can be neutralized as ex- 
 plained in section (191) and the allowable range in speed ob- 
 tainable by this method thus greatly increased. A number* 
 of different kinds of field rheostats are described in the chap- 
 ter on operation. 
 
 (b) The magnetic flux 
 in the magnetic circuit of 
 a machine can be changed 
 by varying the reluctance 
 
 V *J ! v "'"" v of the magnetic circuit. 
 
 JT T Field This is accomplished in the 
 case of a motor manufac- 
 tured by the Stow Manu- 
 
 162 
 
 facturing Company, in the 
 
 following way: The field cores are hollow and are provided 
 with movable iron cores. These cores are all connected 
 mechanically so that their position in the field coils can be 
 adjusted by means of a hand wheel on top of the machine. 
 By moving them toward or away from the armature there will 
 be a decrease or increase in the reluctance of the magnetic 
 circuit and, as a result, an increase or decrease in the flux ($) 
 per pole. This change in (3>) will produce a change in the speed. 
 

 202 PEACTICAL APPLIED ELECTKICITY 
 
 (c) If a rheostat (Ri) be placed in series with the armature 
 of a motor, as shown in Fig. 162, the voltage across the 
 terminals of the armature circuit can be varied by changing 
 the resistance in the rheostat. A change in impressed voltage 
 on the armature will mean a change in speed, because there 
 will be a change in the value of the counter e.m.f. required. 
 The Ward Leonard system, as described in section (213), is a 
 form of variable voltage control. 
 
 (d) In the multi-voltage method 
 
 fs/| a j n A of speed control, there are several 
 
 ~T" different voltages available from 
 
 Main J3 a4oVolt5 which the motor may be operated. 
 
 . r ^Volts Thus, as shown in Fig. 163, there is 
 
 a different voltage between the dif- 
 
 Ma,nD 6 4 lts l 
 
 ferent lines and these may be com- 
 bined, giving other voltages, which 
 Fig. 163 may be connected to the motor ter- 
 
 minals by means of a suitable switch, 
 
 or controller. This method is usually used in combination 
 
 with the field rheostat method. 
 
 (e) If the brushes of a machine be shifted from the neutral 
 plane of the magnetic field, there will be an increase in the 
 speed for the following reason: The counter e.m.f. between 
 the brushes of a motor is a maximum when the brushes are in 
 the neutral plane because the e.m.f. induced in all the con- 
 ductors, in series in the various paths through the armature 
 windings, are acting in the same direction. If the position of 
 the brushes be changed, it. will result in the e.m.f. induced in 
 some of the conductors in series opposing the e.m.f. in the 
 others; and the resultant e.m.f. will be less than in the pre- 
 vious case, all other conditions remaining constant. Now as 
 the brushes are shifted from the neutral plane, the speed must 
 increase in order that the counter e.m.f. between the brushes 
 may satisfy equation (113). This is not a practical method for 
 varying the speed, as excessive sparking usually results when 
 the brushes are moved very much from their proper position. 
 The brushes, in the case of a motor, can be placed in the 
 neutral plane by moving them back and forth, noting the 
 change in speed. The position giving a minimum speed will 
 correspond to the neutral plane (no load on the motor). 
 
DIRECT-CURRENT MOTORS 
 
 203 
 
 212. Inter pole Motor. In order to prevent a shift in the 
 position of the neutral plane of the magnetic field of a motor, 
 due to a change in armature current, which tends to distort 
 the field, commutating-poles, or interpoles, are used. These 
 poles are placed between the regular poles of the machine, 
 and the windings on them carry the load current. Their mag- 
 netizing effect counteracts that of the armature current and 
 the position of the brushes need not be changed with the 
 change in load on the machine. If the direction of rotation of 
 the armature be changed by changing the direction of the 
 armature current, the polarity of the interpoles will also be 
 changed and their magnetizing effect will still counteract that 
 of the armature current. 
 
 213. Ward Leonard System. In this system the field of 
 the motor (M) is connected directly to the main line and the 
 
 Fig. 164 
 
 armature is connected to an auxiliary generator (G), whose 
 voltage can be regulated by means of the field rheostat (R), 
 Fig. 164. In this arrangement the speed of the motor (M) is 
 controlled by a change in impressed voltage, which in turn 
 is controlled by the excitation of the generator (G). The 
 field current for' the generator (G) is taken directly from 
 the line and its value is regulated by means of the rheo- 
 stat (R). 
 
 214. Comparison of Methods of Speed Control. The field 
 rheostat method is perhaps the cheapest and simplest method 
 of speed control and for that reason is no doubt used more 
 than any of the others. It permits of a wide variation in 
 speed when used with the interpole motor and the change 
 in the speed can be made very gradually. 
 
 The change in reluctance method is quite satisfactory, but 
 
04 PRACTICAL APPLIED ELECTRICITY 
 
 the initial cost of the machine is usually prohibitive for 
 .general use. 
 
 The armature rheostat method is very little used, as there 
 is a large change in speed, with a change in load, and there 
 is an excessive loss in the resistance for large armature cur- 
 rents. 
 
 The Ward Leonard and multi-voltage systems are very sat- 
 isfactory in operation, but they are expensive to install. 
 
 A change in speed produced by shifting the brushes is 
 not practical on account of difficulties due to sparking. 
 
 215. Starting Motors. There is no counter e.m.f. generated 
 in the armature of a motor when it is stationary and if the 
 machine were connected directly to line a very destructive 
 current would exist in the armature. The value of this cur- 
 rent, just at the instant the circuit was closed, would be 
 equal to (E) divided by (R a ) if there were no resistance 
 in series with the armature. The resistance of the arma- 
 ture is usually very small and, as a result, the current would 
 be large. By placing a resistance (R x ) in series with the 
 armature, the current can be reduced to a safe value. Now 
 as the armature starts to rotate there will be a counter 
 e.m.f. generated and the effective e.m.f. acting in the circuit 
 will be reduced, which will cause a reduction in current, and 
 the speed will become constant in value when the effective 
 e.m.f. acting in the circuit is equal to the product of the 
 current and the total resistance, or 
 
 E EC = L (Ra + R x ) (114) 
 
 In the above equation (R a ) represents the resistance of the 
 armature and <R X ) the resistance connected in series with 
 the armature. If the resistance (R x ) be decreased, there 
 must be an increase in speed, the armature current (I n ) re- 
 maining practically constant, in order that the effective e.m.f. 
 (E EC) will be equal to the (I a R) drop in the armature 
 circuit. When all of the resistance (R x ) is cut out of the 
 circuit, the effective e.m.f. is equal to the armature current 
 (I a ) times the armature resistance, or 
 
 E E c = IaRa (115) 
 
 and 
 
 E EC 
 I a = - (116) 
 
 Ra 
 
DIRECT-CURRENT MOTORS 
 
 205 
 
 Supply 
 Mains 
 
 The field circuit of the motor must, of course, be closed .when 
 it is being started in order that the armature conductors 
 may cut lines of force and have a counter e.m.f. induced 
 in them, and also that the proper torque be generated to 
 cause the armature to rotate. 
 
 216. Starting Boxes, or , 
 
 Rheostats. A resistance 
 that can be connected in 
 the circuit leading to the 
 motor and so constructed 
 that it may be slowly cut 
 out as the motor speeds up, 
 is called a starting box, or 
 starting rheostat. A simple 
 starting rheostat is shown 
 in Fig. 165. The shunt field 
 is connected directly to the 
 supply mains and the arma- 
 ture is connected through 
 the resistance (R x ). When 
 
 Fig. 165 
 
 the switch (S) is first closed, all of the resistance (R x ) 
 should be in circuit and as the motor speeds up, it may be 
 gradually reduced and finally all cut out. 
 
 217. Dead-Line Release. In the operation of a shunt motor, 
 as shown in Fig. 165, the armature may be destroyed by an 
 excessive current resulting from the line becoming dead for 
 a short time, which results in the speed of the motor decreas- 
 ing immediately, and when the full line voltage is again ap- 
 plied the counter e.m.f., on account of the decrease in speed, 
 will not be of sufficient value to prevent an excessive cur- 
 rent in the armature. To prevent the above condition oc- 
 curring, the starting box can be provided with what is called 
 a no-voltage or dead-line release magnet, as shown in Fig. 
 166. The winding of this magnet may be connected in 
 series with the shunt field winding, as shown in the figure; 
 however, in adjustable speed motors, it is usually con- 
 nected directly across the line. The arm (A) is moved 
 from its initial position against the action of a coil spring 
 and it is held in the extreme right-hand position by the 
 magnet (M). If the current in the winding of (M) be reduced 
 to such a value that the magnet will no longer hold the arm 
 
206 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 (A), the arm will be released and it will return to its initial 
 position. This will result in the armature and field circuits 
 both being opened if the line to which the motor is connected 
 should become dead. The arm (A) must then be moved by 
 an attendant to its right-hand position in order to operate the 
 motor when the line becomes alive. 
 
 218. Overload Release. 
 The armature of a motor 
 may be burned out, due to 
 an excessive current pro- 
 duced by the motor being 
 overloaded, and the purpose 
 of the overload release is to 
 open the circuit or discon- 
 nect the motor from the 
 lire before the machine is 
 injured, due to an excessive 
 current. The overload re- 
 lease magnet winding car- 
 ries the armature current 
 and when this becomes ex- 
 cessive a piece of iron is 
 attracted, which shorts the 
 no-voltage release magnet 
 and allows the arm to re- 
 turn to its initial position. 
 
 A starting box equipped with an overload release is shown 
 in Fig. 167. 
 
 219. Combined Starting and Field-Regulating Rheostats. 
 In a rheostat of this kind a field-regulating resistance is 
 combined with a starting box. Such a rheostat as manufac- 
 tured by the Cutler-Hammer Manufacturing Company is 
 shown in Fig. 168. The movable arm consists of two parts 
 and their outer ends move over separate sets of contacts. 
 When the motor is being started, the arm is moved to the 
 extreme right-hand position and the lower portion is held 
 there by the no-voltage release magnet, while the upper por- 
 tion may then be moved back over the upper row of contacts 
 which are connected to the field-regulating resistance. A 
 diagram of this starting box is shown in Fig. 169. 
 
 220. Speed Regulation. The speed regulation of a motor 
 
 Fig. 166 
 
DIRECT-CUEEENT MOTOES 
 
 207 
 
 is the change in speed from full load to no . load expressed 
 as a percentage of the full load speed, the field resistance 
 and impressed voltage remaining constant. Thus, if the 
 speed of a shunt motor is 1000 r.p.m. at full load and 1050 
 r.p.m. at no load, its speed regulation is 
 1050 1000 
 
 - X 100 = 5 per cent 
 1000 
 
 In order that the speed of the machine may remain constant 
 with a change in load the field strength of the machine must 
 be changed. 
 
 Characteristics of the Shunt 
 Motor. The change in torque, 
 current, and speed that takes 
 place as the load on a shunt 
 motor changes is shown in Fig. 
 170. There is a decrease in 
 speed with an increase in load. 
 The current and torque both in- 
 crease at about the same rate, 
 with an increase in load, since 
 the field strength remains prac- 
 tically constant. 
 
 221. Characteristics of the Se- 
 ries Motor. The speed of a 
 series motor will drop off a 
 great deal more with an increase 
 
 in load than in the case of a shunt motor because there is 
 an increase in field strength with an increase in load. Care 
 should be taken in the operation of series motors to see that 
 their load never drops to zero while they are connected to 
 the source of energy, as their speed will become excessive 
 or they will "race." If the iron of the magnetic circuit is 
 worked near saturation or above the "knee" of the mag- 
 netization curve, the change in speed will not be as great 
 as it is when the iron is not so near saturation. The in- 
 crease in torque with an increase in load must necessarily 
 be greater than in the case of a shunt motor, as the decrease 
 in speed is greater. The torque is proportional to the arma- 
 ture current and field strength, and the field strength varies 
 almost directly a? the armature current, the series winding 
 
 Fig. 167 
 
208 
 
 PBACTICAL APPLIED ELECTRICITY 
 
 and armature being connected in series. If the iron is be- 
 low the knee of the magnetization curve the torque will 
 then vary practically as the square of the current; when, 
 however, the magnetic circuit is worked above the knee of 
 the curve, the variation in torque due to a change in current 
 becomes less. The change in torque, current, and speed that 
 takes place as the load on a series motor changes, is shown 
 
 in Fig. 171. 
 
 222. Characteristics 
 of the Compound Motor. 
 When the compound 
 motor is connected so 
 its two fields aid each 
 other, its characteristics 
 are between those of 
 the shunt and the series 
 motor. If the magnet- 
 izing action of the se- 
 ries field opposes that 
 of the shunt field, the 
 speed remains nearer 
 constant with an in- 
 crease in load than it 
 does for a shunt motor. 
 The torque does not 
 
 need to increase so rapidly as a result of the speed remaining 
 constant, as it does in the case of a shunt motor. The arma- 
 ture current must increase, since the field strength is de- 
 creased in order that the same torque be produced in the case 
 of a shunt and differential compound motor. 
 
 223. Adaptability of Different Motors. There are three 
 different classes of work to be performed by motors, each 
 requiring a different relation between motor torque, and 
 speed. Examples of these classes are as follows: 
 
 (a) When a motor is used on a crane or an elevator it 
 must be capable of developing a constant torque at a variable 
 speed, since it is desired to move a given weight at different 
 speeds. 
 
 (b) In some classes of work, such as the operation of a 
 motor used in driving generators at a constant speed, the 
 motor will be subjected to a varying load as the output of 
 
 Fig. 168 
 
DIRECT-CURRENT MOTORS 
 
 209 
 
 the generator is changed, but its speed is to remain constant 
 and hence it must be capable of developing a variable torque 
 in order that it may carry the load. 
 
 (c) In certain classes of work the motor will be required 
 to develop a variable torque at a variable speed. Such is 
 the case in street-car motors. The torque rsquired is a 
 maximum when the car is being started and the speed a 
 minimum, and as the speed increases the torque decreases. 
 
 Motors may then be divided into three classes, according 
 to the character of the work to be performed, and they must 
 develop either: 
 
 (a) Constant 
 torque at variable 
 speed. 
 
 (b) Variable 
 torque at constant 
 speed. 
 
 (c) Variable 
 torque at variable 
 speed. 
 
 The shunt and the 
 compound motor 
 meet the require- 
 ments in cases (a) 
 and (b), and the Figr - 169 
 
 series motor operated from a constant-potential line generally 
 fulfills the requirements for case (c). The only motor that 
 naturally meets the requirements in case (a) is the series 
 motor operated on a constant-current circuit. 
 
 224. Construction of Motors. The character of the work 
 a motor is to perform will determine to a great extent its 
 construction. The motor may be located in an exposed place; 
 or it may be in a room filled with steam or dust and, as a 
 result, it must be practically enclosed in order to provide 
 ample protection to the windings, etc. If a motor is to be 
 used in a street car, for example, its mechanical construction 
 would need to be quite different from one that was to be 
 used on an elevator, as the street-car motor would, no doubt, 
 be subjected to more mechanical abuse than the elevator 
 motor. 
 
210 
 
 PEACTICAL APPLIED ELECTRICITY 
 
 225. Railway Motors and Their Control. There are two 
 general methods for controlling railway motors, viz, 
 
 (a) The rheostatic method. 
 
 (b) The series-parallel method (in combination with 
 rheostat). 
 
 (a) The connection in the case of the rheostatic method 
 is shown diagrammatically in Fig. 172. Resistance is placed 
 
 in series with the various 
 motors and by cutting this 
 resistance in and out of cir- 
 cuit, the voltage impressed 
 upon the motor can be 
 changed. 
 
 (b) The series-parallel 
 method consists first in 
 placing two motors in series 
 with a resistance in circuit 
 with them, as shown in Fig. 
 173, then decreasing the re- 
 sistance until the motors 
 are connected in series di- 
 rectly across the line. This constitutes what is called a 
 running position as there is no (I2R) loss in a starting resist- 
 ance, the entire voltage being impressed upon the two motors. 
 The next connection places the motors in parallel and a 
 resistance in series with 
 them, as shown in Fig. 174. 
 This resistance is then grad- 
 ually cut out and the mo- 
 tors are finally operating 
 directly across the line, 
 which corresponds to the 
 final running position. 
 
 The control of the switches 
 governing the connections 
 may be accomplished di- 
 rectly by hand or by an 
 auxiliary control. In the 
 first case the changes in 
 
 Fig-. 170 
 
 Fig". 171 
 
 connections are made by a motorman on the car platform, who 
 moves the handle of a controller. This movement of the con- 
 
DIEECT-CUEEENT MOTOES 
 
 Supply 
 
 troller handle causes a cylinder inside the containing case to 
 rotate. This cylinder has a number of contact arms mounted 
 on its surface and these make contact with stationary fingers 
 as the cylinder is rotated. A controller manufactured by the 
 General Electric Company is shown in Fig. 175. A small handle 
 
 to the right of the main controller 
 
 handle, as shown in the figure, ena- 
 bles the motorman to reverse the di- 
 rection of rotation of the motors by 
 changing the connections. The com- 
 plete wiring diagram of a street car 
 is shown in Fig. 176. Fig . 172 
 
 When auxiliary devices are used 
 
 to control the connections of the various motors the system is 
 called a multiple-unit control. When this system is used, a 
 number of cars can be coupled together and the motors on all 
 
 Fig. 173 
 
 of them controlled from any car. The equipment of each car 
 consists of a series-parallel controller, whose electrical opera- 
 tion is similar to that just described, and so arranged that it is 
 controlled from master controllers that are located in the 
 motorman's cabs at the ends of the cars. The leads that 
 run from the motor controllers to the master controllers run 
 
 Fig. 174 
 
 the entire length of the train, the connection between cars 
 being made by means of suitable couplers. The operation 
 of any one of the master controllers will cause all of the 
 motor controllers to operate in the same way and thus all 
 
212 PEACTICAL APPLIED ELECTRICITY 
 
 of the various motor connections throughout the train are 
 the same. 
 
 In the Sprague-General Electric Multiple-Unit Control Sys- 
 tem, the master-controller circuit takes current direct from 
 the line and the motor controllers are operated by means 
 of solenoids. 
 
 In the Westinghouse 
 Electric Company's Multi- 
 ple-Unit Control System, 
 the motor controllers are 
 operated by compressed 
 air, the valves controlling 
 the air being governed by 
 the master controllers. 
 The master-controller cir- 
 cuit receives its current 
 from a storage battery. 
 
 226. Automobile Motors. 
 The series motor is uni- 
 versally used for automo- 
 bile work. The source of 
 energy is a storage battery 
 and the cells are so ar- 
 Fig - 175 ranged that they can be 
 
 connected in different ways, giving different voltages. This 
 variation in voltage, together with a series-parallel combina- 
 tion of different sections in the series field affords an easy 
 means of controlling the speed. Thus, if forty cells be used 
 they may be connected in four groups of ten cells each 
 and these groups then connected in parallel; as the speed 
 of the motor increases, the grouping of the cells can be 
 changed and also the series field connections. These changes 
 in connections are governed by a suitable controller so ar- 
 ranged that the driver of the machine can operate it by a 
 lever or hand wheel. 
 
 Automobile motors are very compact and usually con- 
 structed with a view to economy in weight. When they 
 are located under the car, they are of the enclosed type; 
 while if they are placed in an unexposed position, they can be 
 of the semi-enclosed or open type. In some cases two mo- 
 tors are provided, one being attached to each wheel through 
 
DIEECT-CUEEENT MOTOES 
 
 213 
 
 4 
 
 Fig. 176 
 
214: 
 
 PEACTICAL APPLIED ELECTRICITY 
 
 a suitable transmission, the wheels turning independent of 
 each other, while in other cases a single motor is employed, 
 the connection to the wheels being made by means of some 
 form of differential gear. The various parts of an automo- 
 bile motor used by the Woods Electric Company are shown 
 in Fig. 177. 
 
 Fig. 177 
 
 227. Elevator and Crane Motors. There are many dif- 
 ferent forms of elevator and crane motors on the market and 
 the electrical operation of all of them is practically the same. 
 In the majority of cases some kind of a brake is provided 
 so that the load may be held after it is raised. These brakes 
 may be either of the friction or of the dynamic type. 
 
 Fig. 178 
 
 The friction brake is usually controlled by a solenoid. When 
 the motor is operating, the solenoid is energized and the 
 brake does not act. If the motor is disconnected from the 
 
DIRECT-CURRENT MOTORS 215 
 
 line and the solenoid de-energized, the brake clamps a pulley 
 and prevents the armature turning. 
 
 In the dynamic brake the motor is converted into a gen- 
 erator and delivers current to some local circuit while it is 
 coming to rest, which results in the motor stopping quicker 
 than it would otherwise. The dynamic brake is usually used in 
 combination with the friction brake, the friction brake be- 
 coming operative after the action of the dynamic brake 
 ceases. A motor provided with a friction brake is shown in 
 Fig. 178. 
 
 228. Efficiency of a Motor. There are three efficiencies 
 'for a motor, namely, 
 
 (a) Efficiency of conversion. 
 
 (b) Mechanical efficiency. 
 
 (c) Commercial efficiency. 
 
 (a) The efficiency of conversion is the ratio of the total 
 mechanical power developed to the total electrical power 
 supplied (El), or 
 
 (P + stray-power losses) 
 
 Efficiency of conversion = - X 100 
 
 El 
 
 (117) 
 (P in the above equation is the power available at the pulley.) 
 
 (b) The mechanical efficiency is the ratio of the mechan- 
 ical power available at the pulley (P) to the total mechan- 
 ical power developed, or 
 
 P 
 
 Mechanical efficiency = X 100 
 
 (P + stray-power losses) 
 
 (118). 
 
 (c) The commercial efficiency is the ratio of the avail- 
 able output (P) to the input (El), or 
 
 P 
 
 Commercial efficiency = X 100 (119) 
 
 El 
 
 The commercial efficiency is by far the most important 
 of the three; it includes all the losses in the machine. 
 
 229. Determining the Commercial Efficiency by Test. The 
 commercial efficiency of a motor can be determined by meas- 
 
216 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 uring the electrical input by means of a voltmeter and an 
 ammeter, and at the same time measuring the mechanical 
 output. When the values of these two quantities are known, 
 they may be substituted in equation (119) and the efficiency 
 calculated. 
 
 A satisfactory way of measuring the output of the motor 
 is by means of a Prony brake. The construction and opera- 
 tion of this brake can best be explained by reference to 
 Fig. 179. The brake proper consists of two parts (C) and 
 (D) that are held together by two bolts (B^ and (B 2 ). The 
 
 bolts are provided with small 
 hand wheels (Hj) and (H 2 ) 
 by means of which the pres- 
 sure of the brake upon the 
 pulley can be varied. An 
 arm (A) is attached to the 
 brake and extends out at 
 right angles to the shaft 
 upon which the pulley (P) is 
 Fig. 179 mounted. When the brake is 
 
 in use, the outer end of the 
 
 arm (A) rests upon the platform of a pair of scales. The 
 torque exerted by the armature in pound-feet is equal to the 
 net reading of the scales in pounds multiplied by the hori- 
 zontal distance (L), in feet, between the point where the arm 
 (A) rests upon the scales and the center of the shaft. Call 
 the scale reading (W), then 
 
 T = W X L 
 and the output in horse-power will be equal to 
 
 27r X T X r.p.m. 
 h . p . = 
 
 or 
 
 33 000 
 
 2-rr X W X L X r.p.m. 
 h.p.=- 
 
 33000 
 
 (120) 
 
 (121) 
 
 (122) 
 
 The input, of course, will be in electrical units and either 
 the output or input must be changed before equation (119' 
 can be used in calculating the efficiency. 
 
DIEECT-CUEKENT MOTOES 
 
 [Note. The dead weight of the brake must always be sub- 
 tracted from the scale reading in order to obtain the net 
 weight or the value to be used in equation (122) ]. 
 
 Example. In the test of a motor by the Prony brake 
 method, the net scale reading was thirty pounds, the lever 
 arm of the brake was two feet, and the motor was running at 
 1000 r.p.m. What was its commercial efficiency if the input 
 was 91.0 amperes at 110 volts? 
 
 Solution. The output can be obtained by substituting in 
 equation (122), which gives 
 
 2:r X 30 X 2 X 1000 
 
 h.p. = 
 
 33000 
 
 376 992 
 
 = 11.42 
 
 33000 
 
 The output was then 11.42 horse-power or 8519.32 watts. The 
 input was 
 
 91 X 110 = 10 010 watts 
 and the efficiency was 
 
 8519.32 
 
 = 85.1 
 
 10 010.00 
 
 Ans. 85.1 per cent. 
 
 PROBLEMS ON DIRECT-CURRENT MOTORS 
 
 1. Calculate the torque in pound-feet, exerted by the 
 armature of a motor wound with 300 inductors (simplex lap 
 winding, singly re-entrant), and revolving in a four-pole 
 magnetic field, the flux (*) per pole being 4 000 000 maxwells 
 and the armature current 200 amperes. 
 
 Ans. 281.76 pound-feet. 
 
 2. If the speed of the armature in problem (1) is 1200 
 revolutions per minute, what is the horse-power output of 
 the motor? Ans. 64.3 horse-power. 
 
 3. Calculate the counter electromotive force generated for 
 the data given in problem (1) if the speed is 1200 r.p.m. 
 
 Ans. 240 volts. 
 
218 PRACTICAL APPLIED ELECTEICITY 
 
 4. Calculate the impressed voltage for the above motor, 
 if the armature resistance is .035 ohms, (I a ) being 200 am- 
 peres and (E c ) 240 volts. Ans. 247 volts. 
 
 5. The speed of a motor is 1200 r.p.m. when operating 
 under load and 1250 r.p.m. when operating without load, 
 what is its speed regulation in per cent? 
 
 Ans. 4.17 per cent. 
 
 6. Calculate the output of a motor in horse-power when the 
 input is 100 amperes at 110 volts and the commercial effi- 
 ciency of the machine is 90 per cent. 
 
 Ans. 13.27 horse-power. 
 
 7. At what speed must a motor run in order that its out- 
 put be 50 horse-power, the torque being 263.0 pound-feet? 
 
 Ans. 1000 revolutions per minute. 
 
 8. What is the average pull on each of the inductors in 
 problem (1) if the inductors are located 8 inches from the 
 center of the armature? Ans. 1.41 pounds. 
 
 9. The total armature resistance of a six-pole 250-volt 
 direct-current motor, including brushes, brush contacts, etc., 
 is .012 ohm. The winding on the armature is a simplex 
 singly re-entrant lap winding and composed of 600 inductors. 
 What is the flux (<) per pole when the machine runs at 900 
 r.p.m. and takes a current of 300 amperes? 
 
 Ans. 2 738 000 maxwells. 
 
 10. In testing a motor by the Prony brake method, the 
 following data were obtained. Calculate the commercial effi- 
 ciency for this particular load: 
 
 (Net) Scale reading (W) = 38.88 pounds 
 
 Length lever arm (L) =3 feet 
 
 Speed of armature, 900 revolutions per minute 
 
 Impressed voltage, 220 volts 
 
 Current input, 75 amperes Ans. 90+ per cent. 
 
CHAPTER XI 
 
 ARMATURES FOR DIRECT-CURRENT DYNAMOS 
 
 230. Armature. An electrical conductor, such as a sim- 
 ple loop of wire, moved in a magnetic field, so that there is 
 an e.m.f. induced in it, constitutes a simple armature. An 
 armature composed of a single turn of wire is shown in Fig. 
 127. The e.m.f. induced in such an armature is unsteady see 
 section (178) and in order that a practically steady e.m.f. 
 be induced more turns of wire should be used and these vari- 
 ous turns should be so located and connected with respect to 
 each other that the e.m.f. between the brushes remains almost 
 constant. 
 
 The armature of a commercial direct-current dynamo con- 
 sists of three principal parts, namely, 
 
 (a) The armature core (sections 231 to 233 inclusive). 
 
 (b) The commutator (sections 234 to 236 inclusive). 
 
 (c) The armature windings (sections 238 to 251 inclusive). 
 
 231. Armature Cores. The core of an armature serves a 
 double purpose: it supports the armature winding and it con- 
 ducts the magnetic flux from the face of one pole piece to 
 another. 
 
 Since the armature core is moved relative to the magnetic 
 field, it becomes magnetized in alternate directions, which 
 results in a loss due to hysteresis. There will also be a loss, 
 as explained in section (127), due to eddy currents. The 
 hysteresis loss can be reduced to a minimum by using a 
 grade of iron whose hysteretic constant is low, while the 
 eddy-current loss is reduced by building the armature cores 
 of thin soft iron or sheet steel disks insulated from each 
 other by rust, insulating varnish, or paper. The disks are 
 always placed in such a position with respect to the magnetic 
 field that their plane is parallel to the magnetic flux. 
 
 Armature cores are of two general types, smooth cores and 
 slotted, or tunneled, cores. In the smooth core type, the arma- 
 
 219 
 
220 
 
 PEACT1CAL APPLIED ELECTKICITY 
 
 ture windings are placed upon the surface of the cores, 
 while in the slotted, or tunneled, type, they are placed in slots 
 or openings cut in the outer edge of the core stampings. 
 The mechanical and electrical construction of the slotted, 
 or tunneled, type is better than that of the smooth core 
 
 Fig. 180 
 
 Fig. 181 
 
 type, because the length of the air gap in the magnetic circuit 
 is reduced, and the conductors are held rigidly in place, 
 which prevents their moving back and forth and the likeli- 
 hood of injury to the insulation on them is thus greatly 
 reduced. 
 
 232. Armature-Core Stampings. The stampings used in the 
 construction of armature cores assume a number of differ- 
 
 Fig. 183 
 
 ent forms, depending upon the size and kind of armature 
 for which they are intended. In the construction of small 
 armature cores the disks are punched in one piece, as shown 
 in Figs. 180 and 181. The disks used in the construction 
 of large cores are made in sections, as shown in Figs. 182 
 and 183, and these various sections are then mounted upon 
 
ARMATURES 
 
 221 
 
 an auxiliary support called a spider, which may assume a 
 number of different forms. A spider upon which the disks 
 
 J 
 
 Fig. 185 
 
 shown in Fig. 182 can be mounted is shown in Fig. 184. 
 Such a core would usually be used for a ring winding. A 
 spider upon which the disks shown 
 in Fig. 183 can be mounted is 
 shown in Fig. 185. The dovetail 
 notches or extensions on the stamp- 
 ings fit into dovetail extensions or 
 notches on the spider arms. The 
 various lamina? are held together 
 by means of bolts (B) and end 
 plates (Pi) and (P 2 ), as shown in 
 Fig. 188. 
 
 233. Ventilation. On account of 
 the heat generated in the armature 
 cores, due to hysteresis and eddy 
 currents in the iron, and the (I 2 R) 
 losses in the armature conductors, 
 some means of ventilation must be 
 provided in order to prevent an ex- 
 cessive temperature rise. The 
 means usually employed in venti- 
 lating the armajture cores, especially in the larger machines 
 is to separate the cone disks at certain intervals along 
 the axis of the core. These openings between the disks 
 
 Fig. 186 
 
222 
 
 PEACTICAL APPLIED ELECTEICITY 
 
 called ventilating ducts, can be made by placing a piece of 
 metal on edge, as shown in Figs. 187 and 188, and fastening 
 them to the disk. These ventilating ducts are usually spaced 
 from 2 to 4 inches apart. 
 
 Fig. 187 
 
 Fig. 188 
 
 234. The Commutator. The commutator usually consists 
 of a number of similar wedge-shaped pieces of copper clamped 
 between two rings, as shown in Figs. 189 and 190, and in- 
 sulated from each other by mica or other insulating material 
 whose wearing qualities are practically the same as that of 
 copper. Amber mica is usually used for this purpose. 
 
 Fig. 189 
 
 Fig. 190 
 
 The commutator shown in Fig. 189 is for a small machine, 
 while the one shown in Fig. 190 is for a large machine. 
 
 235. Commutator Risers. The various commutator seg- 
 ments are connected to the armature winding by means of 
 commutator risers. These risers consist of pieces of metal 
 that project radially from the end of the commutator toward 
 the surface of the armature. In the case of small machines 
 they are formed as a part of the commutator segment. In 
 large machines a piece of metal is soldered or brazed into a 
 
AEMATURES 223 
 
 groove cut in the end of the commutator bar before the com- 
 mutator is assembled. 
 
 236. Construction of the Commutator. In constructing the 
 commutator the segments and insulation are placed inside 
 a heavy clamping ring and the inside of the commutator is 
 turned down to the proper dimension. It is then clamped 
 between its own rings (Rj) and (R 2 ), Fig. 189, before the 
 first clamping ring is removed. When it is rigidly fastened 
 in place, the outer ring may be removed and the outer 
 surface turned down to the proper dimensions and form. 
 
 237. Brushes and Brush Holders. The brushes used on 
 dynamos are usually made from hard blocks of what is known 
 as graphitic carbon. In some special cases, however, metal 
 brushes are used, especially when a very low resistance 
 brush is desired, or they may be a combination of metal and 
 carbon. The carbon brushes have the advantage of wearing 
 well mechanically and they are self-lubricating, giving the 
 commutator a very smooth surface. They also have a higher 
 resistance than the metal, or combination brushes and, as 
 *a result, reduce the tendency for sparking to occur at the 
 commutator when the brush bridges two commutator seg- 
 ments connected to an element of the armature winding that 
 may be undergoing commutation. The tendency for spark- 
 ing at the commutator, due to the cause just mentioned, is 
 not very great in low voltage machines, such as those used 
 in electroplating and, as a result, copper or copper gauze 
 brushes are used, thus reducing the total resistance of the 
 circuit. 
 
 Brushes are usually mounted so that they make an angle 
 with the surface of the commutator, although in some cases 
 they are set radial, especially in cases where the direction 
 of rotation of the machine is to change, as in street-car 
 motors. 
 
 The brushes are supported in individual holders, and these 
 holders are mounted on arms called brush-holder arms, which 
 in turn are mounted on rings that are concentric with the 
 commutator and called rockers. The brush holders should 
 be so constructed that the pressure of the brush on the 
 commutator can be adjusted and the electricity be conducted 
 to the brush holders through a path other than that formed by 
 the spring used in holding the brush upon the commutator. 
 
224 
 
 PKACTICAL APPLIED ELECTKICITY 
 
 Fig. 191 
 
 The rockers supporting the brush-holder arms are mounted 
 
 on the front bearing in small machines, and on projecting 
 
 arms from the magnetic frame 
 in large machines. The rockers 
 are always so arranged that they 
 can be moved by a lever or a 
 specially arranged hand wheel, 
 which affords a means of ad- 
 justing them to their proper po- 
 sition on the commutator. A 
 brush and brush holder are 
 shown in Fig. 191. The brushes 
 are connected to the stationary 
 part of the holder by means of 
 
 flexible copper conductors. 
 
 238. Armature Windings. Armature windings may be 
 
 classified according to the manner in which they are placed 
 
 upon the core, as follows: 
 
 (a) Ring windings. 
 
 (b) Drum windings. 
 
 (c) Disk windings. 
 
 (a) In ring windings 
 the conductors are placed 
 upon a ring-shaped core, 
 the winding passing 
 through the interior of the 
 ring, as shown in Fig. 192. 
 These windings are some- 
 times referred to as hel- 
 ical windings. 
 
 (b) In drum windings 
 the winding is placed en- 
 tirely upon the surface of 
 the drum, when smooth 
 
 cores are used, or in slots or tunnels cut in the surface of the 
 core. Such an armature winding is shown in Fig. 193. 
 
 (c) In the disk windings the cores upon which the wind- 
 ing is placed are shorter and larger in diameter in propor- 
 tion than they are in the case of drum windings. The in- 
 ductors correspond to the spokes of a wheel and are con- 
 
 Fig. 192 
 
ARMATURES 
 
 225 
 
 nected in a manner similar to those in the drum winding. A 
 disk-wound armature is shown in Fig. 194. 
 
 In addition to the above classification of armature wind- 
 
 Fig. 193 
 
 ings, they may be grouped into two types, depending upon 
 whether the winding constitutes an open or closed circuit, viz, 
 
 Fig. 194 
 
 (a) Closed-coil windings. 
 
 (b) Open-coil windings. 
 
 (a) The closed-coil windings have all the inductors in- 
 
226 PEACTICAL APPLIED ELECTRICITY 
 
 terconnected, so that the e.m.f.'s induced in them are always 
 effective in producing a current in the external circuit, ex 
 cept when a certain part of the winding is undergoing com- 
 mutation. This type of winding gives a very steady current 
 and the difficulties due to sparking are considerably less 
 than in the open-coil type. 
 
 (b) The open-coil windings have the inductors and com- 
 mutator segments so arranged that the e.m.f.'s induced in 
 the windings are only effective in producing a current in 
 the external circuit when the coil is undergoing commuta- 
 tion. This type of winding does not give as steady a cur- 
 rent as the closed-coil type and considerable trouble is en- 
 countered in commutation due to sparking. The open-coil 
 winding is used mostly (in the case of direct-current ma- 
 chines) for constant-current arc-lighting machines. 
 
 239. Armature Inductors. That part of the armature wind- 
 ing in which an e.m.f. is induced is called an armature in- 
 ductor. The terms conductor and inductor have been used 
 in the same sense up to the present time, but in speaking 
 of armature windings from now on the term armature in- 
 ductor will be used. Thus, in the case of a ring winding, 
 as shown in Fig. 192, there will be one inductor per turn, it 
 being the outer portion of the turn, as that is the only part 
 of the turn in which there is an e.m.f. induced. In the drum 
 winding, as shown in Fig. 193, there will be two inductors 
 per turn, because both sides of the turn have e.m.f.'s in- 
 duced in them. 
 
 The e.m.f.'s induced in the conductors in the case of the 
 ring winding are all acting in series and in the same direc- 
 tion, the inductors being connected by the part of each turn 
 that passes through the ring. If this return portion of each 
 turn were placed on the outside of the cores, as in the case 
 of a drum winding, it would become an inductor and there 
 would be an e.m.f. induced in it, but the direction of the 
 induced e.m.f. would be such, if the two parts of the coil 
 were under poles of the sam^ polarity, that it would tend to 
 neutralize the e.m.f. in the other portion of the coil or in- 
 ductor. In order that the e.m.f. in the two parts of an arma- 
 ture coil, in the case of a drum winding, may act in series 
 and in the same direction, they are so placed on the core 
 that the two parts are under poles of opposite polarity. 
 
ARMATURES 227 
 
 240. Element of Armature Winding. The element of an 
 armature winding is that part of the winding which termi- 
 nates at two consecutive commutator segments, as the wind- 
 ing is being traced out. In a ring winding there may be a 
 commutator segment connected between all the turns, then 
 an element would consist of a single turn and one inductor. 
 The number of inductors and turns per element in the case 
 of a ring winding is the same, and the number of conductors 
 or turns per element will depend upon the relation of the 
 number of commutator segments (K) and the number of 
 inductors (Z). In the drum winding a commutator segment 
 may be connected between all the turns and an element 
 would consist of a single turn, or two inductors. There 
 will always be twice as many inductors per element as there 
 are turns in the case of drum windings. 
 
 241. Armature Coil. In winding armatures a number of 
 turns are usually placed together and insulated as a unit 
 and this unit, called a coil, is placed upon the armature core. 
 The method of forming and insulating the coils depends en- 
 tirely upon the kind of armature they are intended for, their 
 insulation being better and greater care is usually taken in 
 their construction when they are to be used on a high volt- 
 age machine. In some cases the winding is placed directly 
 on the armature core. 
 
 A coil may correspond to an element of the winding or 
 the number of inductors per coil may be greater or less 
 than the number of inductors per element. Thus, two or 
 more coils may be connected in series to form an element, 
 or taps may be taken off the coil, only part of the coil being 
 used for an element. 
 
 242. Number of Commutator Segments. In the case of a 
 simple ring winding, the maximum number of commutator 
 bars (K) that it is possible to have is the same as the num- 
 ber of turns or inductors on the armature cores. The num- 
 ber of bars may, of course, be less than the number of in- 
 ductors, as each element may be composed of a number of 
 inductors. In general, if (M) represents the number of 
 turns in each element of the winding and (Z) the total 
 number of inductors, the number of commutator segments 
 will be equal to 
 
22S PRACTICAL APPLIED ELECTRICITY 
 
 K = (123) 
 
 M 
 
 The number (M) can have any value so long as (Z) divided' 
 by (M) gives a whole number as a quotient. 
 
 The maximum number of commutator bars that it is pos^ 
 sible to have in a commutator to be used with a simple drunj 
 winding is equal to 
 
 Z 
 
 K = - (124) 
 
 2M 
 
 In the above equation, (M) represents the number of turns 
 in series in each element of the winding and since there are' 
 two inductors per turn for a drum winding, (2M) is the 
 total number of inductors per element. The number (M) 
 can have any value, even or odd, but (2M) will always be? 
 even and, since (K -r- 2M) must give a whole number, as in 
 the previous case, (Z) must be even. 
 
 243. Pitch of Winding and Field Step. It was explained 
 in section (239) that the two inductors composing a single 
 turn in the case of a simple drum winding had to be placed 
 in such a position on the armature that the inductors were 
 under poles of opposite polarity. In the case of a ring wind- 
 ing, as explained in section (239), the inductors can be placed 
 under a pole of the same polarity because they are con- 
 nected by a conductor that passes through the center of the 
 ring and in which there is practically no induced e.m.f. The 
 field step in the case of a winding is unity when the distance 
 between one inductor and the ne&t in order, in tracing 
 through the winding, corresponds very nearly to the distance 
 between the centers of adjacent unlike poles. The field step 
 then for a simple ring winding is zero and for a simple drum 
 winding is unity. It may be greater than these values for the 
 two windings, but the connections required to join the ends 
 of the inductors would be unnecessarily increased in length, 
 which would mean an increase in the cost of copper required 
 for the winding and an increase in the resistance of the 
 armature. 
 
 The pitch of a winding is the distance from one inductor 
 of the winding to the next inductor in order. This distance 
 is usually measured in terms of the number of inductors 
 passed over, or it may be measured in terms of the number 
 
AEMATUKES 229 
 
 of half coils, slots, or distance on the surface of the arma- 
 ture. An example would perhaps show more clearly the 
 exact meaning of the term "pitch." Let the inductors on a 
 certain drum-wound armature be numbered consecutively 
 around the armature starting with number (1). If inductor 
 number (1) is joined at the back end of the armature (end 
 opposite the commutator) to inductor (14), and inductor (14) 
 Is joined at the front end of the armature to inductor (27), 
 etc., the pitch of the winding would be the same at both ends 
 and equal to 13. The front pitch is represented by the 
 symbol (Y f ) and the back pitch by symbol (Y b ). These 
 pitches are both positive in sign when they are measured 
 in the same direction around the armature. If, in the above 
 case, inductor (1) be joined to inductor (16) at the back 
 end, and inductor (16) be joined to inductor (3) at the front 
 end, and inductor (3) be joined to inductor (18) at the back 
 end, etc., the front pitch would be negative and the back pitch 
 positive. Their values would be (Y b ) = 15 and (Y f ) = 13. 
 
 The average pitch (Yav) in any case is equal to the aver- 
 age of the front and the back pitches regardless of their signs. 
 For the first winding (Yav) would be [(13-f 13) -=- 2] = 13, 
 and for the second winding (Y a v) would be [(15 -f- 13) -r- 2] 
 = 14. The resultant pitch (Y r ) of any winding is the alge- 
 braic sum of the two pitches. For the first winding (Y r ) 
 would be (15) + (13) == 2. 
 
 The commutator pitch is the interval between the com- 
 mutator segments connected to an element of the winding 
 expressed in terms of the number of commutator segments. 
 
 244. Types of Ring Windings. There are two types of 
 ring windings: 
 
 (a) Spirally-wound ring windings. 
 
 (b) Series-connected wave-wound ring windings. 
 
 (a) In the spirally-wound ring armature, the winding forms 
 a closed helix, as shown in Fig. 192. There will be (p) points 
 
 on the commutator (p) represents the number of magnet 
 
 poles where brushes may be connected to conduct the elec- 
 tricity to and from the armature winding. The proper loca- 
 tion of the brushes is shown in the figure and the number 
 of paths (b) through such a winding is equal to the number 
 of poles (p). The current capacity of this winding will be 
 greater than that of a bipolar machine if the same size wire 
 is used in the winding: and the e.m.f.'s will be the same if 
 
230 
 
 PRACTICAL APPLIED ELECTKICITY 
 
 the field strength, speed, and number of inductors in series 
 are the same in both cases. The e.m.f. equation for such a 
 machine is 
 
 Z X * X P X r.p.m. 
 
 E= (125) 
 
 108 x 60 X b 
 
 The number of brushes can 
 be made less than the num- 
 ber of poles by permanently 
 connecting the various com- 
 mutator segments together 
 that are always at the same 
 potential. 
 
 (b) In the series -con- 
 nected ring winding, the va- 
 rious turns are connected in 
 series. In this arrangement 
 there will always be two 
 paths in parallel through the 
 armature, regardless of the 
 number of poles. Armatures 
 
 wound with this kind of a winding are called two-circuit, or 
 series-wound, armatures. Only one set of brushes iB required, 
 but a maximum of $p -f- 2) sets can be used. 
 
 In calculating the e.m.f. that will be developed in a wind- 
 ing of this kind, equation (125) can be used and (b) will 
 always be equal to 2. The armatures of the machines are 
 usually series wound when their output is to be at a high 
 voltage and low current, while if the output is to be at a low 
 voltage and large current, they are parallel wound. 
 
 245. Types of Drum Windings. Drum windings (closed- 
 coil) are of two kinds: 
 
 (a) Lap windings. 
 
 (b) Wave windings. 
 
 (a) A simple (simplex) lap winding is shown in Fig. 195 
 and a developed form of the same winding is shown in Fig. 
 196. It will be observed that the front and the back pitches 
 differ in sign, or the winding laps back upon itself. The num- 
 ber of paths (b) in parallel through an armature wound with 
 a simple (simplex) lap winding is equal to the number of 
 poles (p). The number of sets of brushes required in order 
 that all the inductors be effective in producing a current in 
 
 Fig. 195 
 
ARMATURES 
 
 231 
 
 the external circuit is equal to (p). Lap windings are usu- 
 ally used on armatures whose output is at a low voltage 
 and large current. 
 
 (b) A simple (simplex) wave winding is shown in Figs. 
 197 and 198. It will be observed that both the front and the 
 back pitches are of the same sign and the winding advances 
 around the armature in the form of waves. There will be 
 only two paths through an armature wound with a simple 
 (simplex) wave winding regardless of the number of poles. 
 Only two sets of brushes are required for such a winding, 
 
 ic id, j e | f | 9 | M t | j | k| i |m|a| b |c \d 
 Fig-. 196 
 
 but as many as (p) sets can be used. Wave windings are 
 usually used on armatures whose output is at a high volt' 
 age and low current. 
 
 If the front and the back pitches in a wave winding be so 
 chosen that in starting with a commutator segment and pass- 
 ing through an element of the winding in a clockwise direc- 
 tion you arrive at a segment to the right of the one from 
 which you started, the winding is said to be progressive; if 
 the segment is to the left of the one from which you started 
 the winding is said to be retrogressive. 
 
 If the front and back pitches in a wave winding be so 
 chosen that in starting with a given commutator segment 
 and, after passing in a clockwise direction through as many 
 elements of the winding as there are pairs of poles, you 
 arrive at a segment to the right of the one from which you 
 started, the winding is said to be progressive; and if the seg- 
 ments be to the left of the one from which you started, 
 the winding is said to be retrogressive. 
 
 When the average pitch of a winding differs considerably 
 
232 
 
 PEACTICAL APPLIED ELECTKICITY 
 
 from the number of inductors (Z) divided by the poles (p), 
 the winding is called a chord winding. 
 
 246. Multiplex Windings. 
 Armatures may be wound 
 with two or more independent 
 windings, the inductors and 
 the commutator segments of 
 the two windings being sand- 
 wiched between each other, 
 as shown in Fig. 199. A 
 winding composed of two in- 
 dependent windings is called 
 a duplex winding; one com- 
 posed of three independent 
 Y av =6 windings is called a triplex 
 197 5 winding, etc. The brushes 
 
 must, of course, be increased 
 
 in width, if the commutator segments remain the same in 
 breadth when a multiplex winding is used, in order that the 
 current may be collected from all the various windings at 
 the same time. 
 
 247. Re-Entrancy. In section (238) it was stated that a 
 winding which closes upon itself is called a closed-circuit wind- 
 ing. Such a winding is also known as a re-entrant winding, 
 because it re-enters upon itself. A winding is said to be singly 
 
 m|n|o|p|a|b|c|dJe|fJg|K|t[j|k|l|m|n| 
 Fig. 198 
 
 re-entrant when the entire winding must be traced through 
 before you return to the inductor from which you started. 
 If only one-half of the winding need be traced out before the 
 inductor from which you started is again reached, the wind- 
 ing is said to be doubly re-entrant. Likewise only one-third 
 of the winding is passed through in a triply re-entrant wind- 
 
ARMATURES 
 
 233 
 
 Fig. 199 
 
 ing before you return to the conductor from which you started, 
 
 and so on for multiply re-entrant windings. 
 The term re-entrancy as 
 
 used in the remainder of the 
 
 chapter has a meaning en- 
 
 tirely different than that just 
 
 given, it being used as a 
 
 factor in determining the 
 
 number of circuits between 
 
 positive and negative brushes. 
 
 In the above definition of re- 
 
 entrancy, there would be no 
 
 difference between the multi- 
 
 plicity and the re-entrancy of 
 
 a winding. A simplex or 
 
 multiplex winding, however, 
 
 may be singly or multiply re- 
 
 entrant, and the re-entrancy 
 
 in the case of a lap winding is equal to the total number of 
 
 paths through the armature divided by the product of the 
 
 number of poles and the multiplicity of the winding, and in 
 
 the case of the wave winding 
 it is equal tc the total num- 
 ber of paths divided by twice 
 the multiplicity of the wind- 
 ing. The winding shown in 
 Fig. 200 is simplex doubly re- t 
 entrant, and the one shown in 
 Fig. 199 is duplex singly re- 
 entrant. The number of paths 
 through the winding is the 
 same in both cases. 
 
 248. Number of Paths 
 Through Armature Windings. 
 As stated in section (244), 
 the number of paths in par- 
 
 allel (b) for a simplex spirally-wound ring is (p), and for a 
 
 simplex series-wound ring (2). When such windings are made 
 
 multiplex, the number of paths is increased, the number in 
 
 the second case being equal to the original number multiplied 
 
 by the multiplicity of the winding. Thus a triplex series- 
 
 Fig. 200 
 
234 PRACTICAL APPLIED ELECTRICITY 
 
 wound ring winding would have (3X2) paths in parallel, and 
 a duplex spirally-wound ring winding would have (2Xp) paths 
 in parallel. Winding tables are given in Chapter 20, which 
 show the relation between the multiplicity, the re-entrancy, 
 the number of paths, the number of inductors in series in 
 each path, etc. 
 
 A closed-coil drum winding must satisfy the following con- 
 ditions. No drum winding can have an odd number of in- 
 ductors, for that would be equivalent to not having a whole 
 number of turns. The even-numbered inductors may be re- 
 garded as the returns for the odd-numbered inductors, or 
 vice versa, and both the front and back pitches must always 
 be odd in simplex windings in order that you pass from an 
 odd to an even numbered inductor at one end of the arma- 
 ture and from an even to an odd numbered inductor at the 
 other end in tracing out the winding. 
 
 The front and back pitches should be approximately equal 
 and correspond in value to (Z <*- p) in order that the in- 
 ductors connected in series and moving under poles of oppo- 
 site polarity have their e.m.f.'s additive. 
 
 249. Choice of Front and Back Pitch for a Given Number 
 of Inductors. (A) Lap and wave windings in general. 
 
 (a) All the elements or coils composing the winding must 
 be similar, both mechanically and electrically, and must be 
 arranged symmetrically with respect to each other and the 
 armature core. 
 
 (b) In a simplex winding each inductor must be encoun- 
 tered only once and the winding must be re-entrant. 
 
 (c) If the winding is multiplex, each of the simplex wind- 
 ings composing it must fulfill condition (b). 
 
 (B) Choice of front and back pitch for lap windings. 
 
 (a) Front and back pitches must be opposite in sign. 
 
 (b) The front and back pitches must be numerically un- 
 equal, for if they were equal the coil would be short-circuited 
 upon itself. 
 
 (c) The front and back pitches must differ by 2 in the 
 case of a simplex lap winding; that is, 
 
 Y b -f Yf == 2 
 
 (d) The front and back pitches differ by 2 X in the case 
 
AEMATUKES 
 
 of a multiplex winding, (X) being the number of independent 
 simplex windings composing the multiplex winding. 
 
 (e) The number of inductors (Z) must be an even num- 
 ber. If the winding .is placed on a slotted armature the 
 number of inductors must be a multiple of the number or 
 slots. The number of slots may be even or odd. 
 
 (C) Choice of front and back pitches for wave windings. 
 
 (a) The front and back pitches must be alike in sign, and 
 odd. 
 
 (b) The front and back pitches may be equal, or they 
 may differ by two or any multiple of two. It is customary 
 to make them nearly equal to (Z-f-p). 
 
 (c) The number of inductors (Z) for a simplex winding 
 should comply with the equation 
 
 Z = P Yav 2 
 
 (d) And for a multiple winding: 
 
 Z = P Yav 2 X 
 
 250. Armature Winding Table. Tables I, J, and K in Chap- 
 ter 20 give the values of the various quantities for the differ- 
 ent types of armature windings. The symbols used in these 
 tables represent the following quantities: 
 
 . z = the total number of inductors on the armature 
 
 X = the number of independent windings 
 
 b = the total number of paths through the armature 
 
 b'i = the number of paths in parallel in each winding 
 
 m = the field steps 
 
 y = the resultant pitch 
 
 Yk= the commutator pitch 
 
 Y f == the front pitch 
 
 Y h = the back pitch 
 
 K = the number of commutator segments 
 
 g = the number of inductors per group 
 
 G = the total number of groups 
 Yav = the average pitch 
 
 Note. The tables given in Chapter 20 were made up by the 
 use of equations given in "Design of Dynamos" by S. P. 
 Thompson. 
 
 251. Equipotential Connections. The e.m.f.'s generated in 
 the various paths that are connected in parallel in any arma- 
 ture winding will, as a rule, differ in value due to inequali- 
 
236 PRACTICAL APPLIED ELECTRICITY 
 
 ties in winding, location in magnetic field, armature out 
 of center, etc. This difference in e.m.f. in the various paths 
 will result in unequal currents in the different paths through 
 the armature. In order to reduce this unbalanced condi- 
 tion as much as possible the points in the winding that are 
 supposed to be at the same potential are connected by heavy 
 copper leads, called equipotential connections. 
 
CHAPTER XII 
 
 STORAGE BATTERIES, THEIR APPLICATIONS AND 
 MANAGEMENT 
 
 252. The Storage Cell. A storage cell, secondary cell, 01 
 accumulator, as it is variously called, is a voltaic cell in 
 which a chemical action is first produced by an electrical cur- 
 rent through the cell from some external source of energy ; 
 after which the cell is capable of delivering a current to an 
 external circuit by means of a secondary or reversed chem- 
 ical action. The process of storing the electrical energy by 
 sending a current through the cell from some external source 
 of energy is called charging. When the cell is producing a 
 current in an external circuit or it is supplying energy it is 
 said to be discharging. 
 
 In charging a storage cell a larger voltage is required be- 
 tween the terminals of the cell than the cell is capable of pro- 
 ducing on discharge, on account of the internal resistance of 
 the cell and an action on the surface of the plates similar to 
 polarization in the primary cell. The (IR) drop in the cell 
 opposes the free flow of the electricity through the cell, both 
 on discharge and charge, and the energy the cell is capable 
 of supplying on discharge is less than the energy input to 
 the cell when it is being charged. No storage cell, as a re- 
 sult, can have an efficiency of 100 per cent, the efficiency 
 decreasing with an increase in internal resistance. The 
 greater the internal resistance the greater the variation in 
 the value of the terminal voltage with a change in load. 
 
 253. Types of Storage Cells. Storage cells may be divided 
 into two main groups, according to the kind of materials 
 used in the construction of the plates, viz, lead storage cells 
 (sections 254 to 274 inclusive), and non-lead storage cells 
 (sections 275 to 278 inclusive). 
 
 254. Lead Storage Cells. In the construction of the lead 
 storage battery, the cathode is made of lead peroxide (PbO 2 ) 
 and the anode of spongy metallic lead. These two plates, 
 
 237 
 
238 PRACTICAL APPLIED ELECTEICITY 
 
 or "grids," as they are called, are immersed in an electro- 
 lyte of dilute sulphuric acid. The lead peroxide and spongy 
 lead are called the active materials of the cell. They are 
 both converted in lead sulphate (PbSO 4 ), which is insoluble, 
 when the cell is being discharged, and this lead sulphate 
 is reconverted into lead peroxide and spongy lead when the 
 cell is being charged. 
 
 The electrode of a storage cell, which is the cathode on 
 discharge, is called the positive grid and the other electrode 
 is called the negative grid. 
 
 255. Action of a Lead Storage Cell While Discharging. 
 In discharging a lead cell, the electrolyte (H 2 SO 4 ) is split up 
 by the current into hydrogen (H) and sulphion (SO 4 ). The 
 hydrogen which is liberated at the cathode converts the 
 lead peroxide (PbO 2 ) into lead oxide (PbO). The lead oxide 
 immediately combines with a part of the electrolyte (H 2 SO 4 ), 
 forming lead sulphate and water. Lead sulphate (PbSO 4 ) 
 is formed at the anode by the sulphion (SO 4 ), combining 
 with the spongy lead (Pb). 
 
 The lead sulphate which is formed during the discharging 
 process is more bulky than the active materials themselves 
 and, as a result, there is an expansion in the plates of the 
 cell. There is also a decrease in the density of the elec- 
 trolyte on account of the absorption of the sulphion (SO 4 ) 
 by the active material. 
 
 The chemical action taking place in the cell can be easily 
 shown by the equation 
 
 Discharging (current from negative to positive grid) 
 
 Positive grid PbO 2 + H 2 SO 4 + H 2 = 2H 2 O + PbSO 4 
 
 Negative grid Pb + SO 4 = PbSO 4 
 
 256. Action of Storage Cell While Charging* In charging 
 a lead storage cell, an action takes place which is just the 
 reverse of that described in section (255). The lead sul- 
 phate (PbSO 4 ) on one grid is converted back to lead per- 
 oxide (PbO 2 ), the lead sulphate (PbSO 4 ) on the other grid is 
 converted back to spongy lead (Pb), the density of the elec- 
 trolyte increases and the volume of the active material 
 decreases. The following equations will serve to show the 
 chemical action that takes place in the cell when it is being 
 charged. 
 
 Charging (current from positive to negative grid) 
 
STORAGE BATTERIES 239 
 
 Positive grid PbSO 4 + 2H 2 O + SO 4 = 2H 2 SO 4 + PbO 2 
 Negative grid PbSO 4 + H 2 = H 2 SO 4 + Pb 
 
 257. Storage Battery Grids. Two general processes are 
 employed in the manufacture of storage battery grids, viz, 
 the Plante process and the Faure process. 
 
 258. The Plante Process. In the Plante process the 
 surface of a lead plate is subjected to the action of a suitable 
 acid which converts the surface of the plate into active mate- 
 rial. In the first process the lead plates were exposed to the 
 action of dilute sulphuric acid, and the action was accelerated 
 by making the plates being formed alternately the anode and 
 cathode of the electrolytic cell. The modern process is far 
 superior to the old method, the formation of the active mate- 
 rial being brought about in a much shorter time by adding a 
 small quantity of lead dissolving acid, such as acetic or nitric 
 acid, and increasing the area of the plates exposed to the 
 action of the acid, by cutting grooves in their surface. 
 
 259. Faure Process. In the 
 Faure process the active ma- 
 terial is manufactured in bulk 
 and introduced by a mechan- 
 ical process into openings in 
 the lead grids. The original 
 process, and one that is used 
 quite extensively at the pres- 
 ent time, consisted in mixing 
 litharge or a mixture of lith- 
 arge and red lead with dilute 
 sulphuric acid, and placing 
 the paste in suitable support- 
 ing frames, the combination Fig. 201 
 forming the grids. 
 
 260. Examples of Plante and Faure Plates. The grids 
 manufactured by the Gould Storage Battery Company, as 
 shown in Fig. 201, are a good example of the modern Plante 
 plate. Thick plates of lead of the proper dimensions are passed 
 over rapidly revolving rolls which consist of a large number 
 of thin disks separated from each other by thin washers. The 
 action of these disks is such that fins of lead are raised upon 
 the surface of the lead plates. Both surfaces of the plates are 
 subjected to the action of the spinning rolls, but central webs 
 
240 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 Fig. 202 
 
 and cross-ribs are left where the plate is in no way changed. 
 
 The purpose of these central webs and cross-ribs is to add 
 
 conductivity and strength to the plates. 
 
 The positive grid used in the sta- 
 tionary type of storage cell manu- 
 factured by the Electric Storage 
 Battery Company, which are often 
 called "chloride" cells, is shown in 
 Fig. 202. A casting is first made 
 of lead-antimony alloy, with numer- 
 ous holes in it, and small coils of 
 pure lead are placed in these holes. 
 These coils of lead are then con- 
 verted into active material by the 
 Plante process. 
 
 The 'negative grid used in the 
 stationary storage cell of the Elec- 
 tric Storage Battery Company is 
 shown in Fig. 203. Two plates of 
 pure lead with numerous holes in 
 
 them are pressed together over a block of active material 
 
 which squeezes out through the holes. While the plates are 
 
 still under pressure they are riveted together. In the "exide" 
 
 cell made by the Electric Storage 
 
 Battery Company, the grids are 
 
 cast of a lead-antimony alloy with 
 
 a large number of small openings 
 
 in them. The openings in the 
 
 plates that are to form the positive 
 
 grids are filled with a paste of red 
 
 lead and dilute sulphuric acid, and 
 
 the openings in the plates that are 
 
 to form the negative grids are filled 
 
 with a paste of litharge and dilute 
 
 sulphuric acid. 
 261. Comparison of Plante and 
 
 Faure Plates. The Plante plates 
 
 are more costly for a given output 
 
 than the Faure plates. They are 
 
 more bulky, heavier, and more easily injured by impurities in 
 
 the electrolyte. They are, however, able to stand a more 
 
 Fig. 203 
 
STOEAGE BATTEEIES 
 
 241 
 
 rapid charging and discharging without injury. They do not 
 lose their active material as easily as the Faure plates. They 
 are in general more durable and dependable than the pasted 
 plates and have longer life. The Faure plates are cheap, 
 light, and occupy a small space. They are not so easily dam- 
 aged by impurities in the electrolyte; but their efficiency is 
 less than the Plante plates for higher rates of discharge. 
 
 262. Capacity of a Storage Cell. The unit in which the 
 capacity of a storage battery is measured is the ampere-hour, 
 and the capacity is usually based upon the eight-hour dis- 
 charge rate. As an example, a 200-ampere-hour battery would 
 deliver a current of 25 amperes continuously for 8 hours. 
 Theoretically this same battery should deliver a current of 
 50 amperes for 4 hours, or a current of 12 amperes for 16 
 hours; but as a matter of fact the ampere-hour capacity of a 
 battery decreases with an increase in the rate of discharge. 
 The change in the capacity of a battery due to a change in 
 the discharge fate is given in Table No. IX. The 8-hour rate 
 is taken as a basis in figuring the output at other rates. 
 
 TABLE NO. IX 
 
 PERCENTAGE VARIATION OF THE CAPACITY OF A STORAGE 
 
 BATTERY DUE TO A CHANGE IN THE RATE 
 
 OF DISCHARGE 
 
 Rate in hours 
 
 Percentage of capacity at 8-hour rate 
 
 I'lante 
 
 Faure 
 
 Plante (+) 
 Faure ( ) 
 
 8 
 7 
 6 
 5 
 
 4 
 3 
 
 2 
 
 1 
 
 100.0 
 99.0 
 96.5 
 93.0 
 88.0 
 80.0 
 70.0 
 55.0 
 
 100.0 
 96.0 
 92.0 
 86.0 
 80.0 
 72.0 
 61.0 
 40.0 
 
 100.0 
 97.0 
 93.5 
 89.0 
 83.0 
 75.0 
 65.0 
 50.0 
 
 263. The Electrolyte. The electrolyte should be made of 
 sulphuric acid made of sulphur and not from pyrites. Acid 
 made from pyrites contains some iron and the presence of 
 this metal in the electrolyte is injurious to the plates. It is 
 not essential that the electrolyte be chemically pure, but it 
 should not contain any chlorine, nitrates, arsenic, mercury, 
 copper, platinum, nitric or acetic acid. The electrolyte should 
 
242 'PRACTICAL APPLIED EL.ECTKICITY 
 
 always be purchased from a very reliable chemical company 
 that will guarantee its being free from impurities which will 
 be injurious to the plates in the storage battery. 
 
 The acid may be purchased diluted until the specific gravity 
 is of the desired value for immediate use in the cell. In 
 some cases, however, it may be desirable to purchase the acid 
 and reduce its specific gravity at the point where it is to be 
 used. Only distilled or rain water should be used in diluting 
 the acid and the acid should always be poured into the water. 
 There will be considerable heat liberated and the solution 
 should be allowed to cool before a determination of the 
 specific gravity is made as there is quite a change in the 
 specific gravity due to a change in the temperature of the 
 electrolyte. The density of the acid to use will of course 
 depend upon the kind of cell it is to be used in, the ampere- 
 hour capacity of the cell, its rate of discharge and charge, etc. 
 The density that will give the best results for any particular 
 cell is, in the majority of cases, specified by the makers. 
 
 264. Density and the Hydrometer. The density 
 of any substance is the ratio of the weights of 
 equal volumes of the substance and water. Thus, 
 if the specific gravity of a certain quantity of 
 sulphuric acid is 1.25, it means that a certain 
 volume of the acid will weigh 1.25 times as much 
 as the same volume of pure water. 
 
 The hydrometer is an instrument for measuring 
 the density of liquid. It is placed in the liquid and 
 is so constructed that a portion of it projects above 
 the surface of the liquid. The amount projecting 
 FigT204 wiU vary with the density of the liquid and a 
 suitable scale attached or marked on the up- 
 wardly projecting portion will afford a means of determining 
 the density of the liquid direct from the scale reading. The 
 reading is taken at the surface of the liquid. The outline of 
 a hydrometer, is shown in Fig. 204. A small quantity of lead 
 shot in the lower portion gives the instrument the required 
 weight and serves to hold it always in an upright position. 
 
 265. Containing Vessel and Separators. There are a num- 
 ber of different kinds of containing vessels for the plates and 
 electrolyte of a storage cell, and perhaps the most important 
 of these are those made of rubber, glass, and lead-lined 
 
STORAGE BATTERIES 
 
 243 
 
 wooden tanks. The rubber containing vessel is used in the 
 construction of portable cells because it will stand more abuse 
 than glass and is much lighter. Glass containing vessels are 
 used for stationary cells of moderate capacity. The lead-lined 
 wooden tanks are used for very large cells as they are 
 stronger than either the glass or the rubber and the increase 
 in weight makes no great difference. 
 
 When the plates are placed in 
 the containing vessels, they are 
 positive and negative alternately. 
 This results in adjacent plates be- 
 ing of opposite polarity and some 
 means must be provided for sepa- 
 rating them. Perforated rubber 
 sheets are used in the smaller 
 cells, rubber sheets and thin 
 sheets of porous wood in medium 
 size cells, and glass rods in the 
 larger cells. The interior of a 
 cell is shown in Fig. 205. 
 
 266. Sulphation. In the section 
 describing the chemical action of 
 the storage battery, it was men- 
 tioned that lead sulphate was 
 formed when the cell was dis- 
 charged. This lead sulphate is 
 insoluble in sulphuric acid and oc- 
 cupies a larger volume than the 
 pure lead or lead peroxide which 
 forms it, and it is a non-conductor. 
 
 In discharging a storage battery, it should not" be allowed to 
 go beyond a point where a small part of the active material 
 is converted into lead sulphate. If the battery be over dis- 
 charged there will be an excessive amount of the sulphate 
 formed or as it is termed, an oversulphation. 
 
 The presence of the excessive amount of sulphate results 
 in the surface of the plates being covered with white crystals 
 and the pores of the plates are closed up due to the increase 
 in volume. The surface of the active material exposed is, as a 
 result, decreased due to the presence of the crystals, and the 
 increase in volume will cause the active material to be loos- 
 
 Fig. 205 
 
244 PKACTICAL APPLIED ELECTKICITY 
 
 ened from the grid, or it may result in the plate being bent 
 out of shape, which will result, in some cases, in the plates 
 being fractured and the active material falling to the bottom 
 of the cell as sediment. The distortion of the plates is known 
 as buckling. A high discharge rate results in a greater 
 expansion than a low rate and the active material is more 
 likely to fall away when the battery is being discharged at a 
 high rate than it is when discharged at a low rate. 
 
 267. Battery Troubles and Their Remedies. The following 
 troubles are perhaps the most important ones encountered in 
 the operation of a storage battery: 
 
 (A) Loss of capacity. 
 
 (B) Loss of voltage. 
 
 (C) Corrosion of electrodes. 
 
 (D) Buckling of plates. 
 
 (E) Shedding active material. 
 
 268. (A) Loss of Capacity. The loss of capacity may be 
 due to any one or all of the following causes: (a) sulpha- 
 tion; (b) loss of active material; (c) loss of electrolyte; (d) 
 sulphate between grid and the active material; and (e) con- 
 traction of active material on spongy lead plate. 
 
 (a) The causes of sulphation have already been discussed 
 but the means of treating sulphated plates will be given here. 
 To remove the sulphate, charge the battery at as high a rate as 
 possible without causing the temperature of the cell to exceed 
 110 Fahrenheit until the plates gas very freely, then reduce 
 the rate to the normal 8-hour rate and continue until the 
 plates again begin to gas. Then reduce to half the 8-hour 
 rate and continue until the plates gas. Now give the battery 
 a partial discharge and then recharge as just described. This 
 cycle of operations may have to be repeated a number of times 
 before all the sulphate is removed. 
 
 (b) Loss of active material is usually due to the plates not 
 being worked under normal conditions; if this is not the case, 
 the plates are poorly designed. This loss is due chiefly to 
 rapid charge and discharge, sulphation, and a long over- 
 charge. 
 
 (c) Loss of electrolyte due to evaporation may cause the 
 surface of the liquid to fall below the upper edge of the plates. 
 The remedy is obvious. 
 
 (d) In the Faure type of plates, sulphate may form between 
 
STORAGE BATTEEIES 245 
 
 the active material and the supporting grid, which greatly 
 increases the electrical resistance of the cell and decreases 
 the area of the active material. 
 
 (e) The active material on the spongy-lead electrode will 
 contract and such shrinkage will close up the pores and 
 greatly reduce the active surface. There are methods of 
 preventing this contraction in use by several companies. If 
 you think your battery trouble is due to this cause, it would 
 be best for you to get advice from the manufacturers of the 
 battery. 
 
 269. (B) Loss of Voltage. The causes of loss in voltage 
 are the same as those resulting in a loss of capacity and the 
 treatment of the cell for the two conditions is identical. 
 
 270. (C) Corrosion of Plates. The corrosion of the plates 
 is usually due to the presence of some injurious impurities in 
 the electrolyte and the only remedy is to change the electrolyte. 
 
 271. (D) Buckling of Plates. Any condition of operation 
 of the cell which will result in an unequal chemical action 
 over the surface of the plates will result in an unequal 
 expansion of the active material and hence, a tendency for 
 the plate to expand more in some spots than others. These 
 stresses which are set up in the plates relieve themselves by 
 changing the form of the plates. Buckling is usually due to 
 improper design and cannot be overcome except by recon- 
 struction. 
 
 272. (E) Shedding of Active Material. When the active 
 material on the plates drops off more rapidly than it should 
 which is indicated by the rapid accumulation of sediment in 
 the bottom of the cell the cell should be worked at a low 
 rate of discharge, never being discharged below 1.75 volts 
 and never being charged above 2.4 volts. 
 
 273. Management of a Storage Battery. There are a few 
 important rules that one should always bear in mind in the 
 care of a lead storage battery. 
 
 (a) Always use a pure electrolyte. 
 
 (b) Never allow the surface of the electrolyte to fall below 
 the upper edge of the plates. 
 
 (c) Always maintain the specific gravity at the value speci- 
 fied by the manufacturers. 
 
 (d) Keep cells well cleaned, never allow sediment to rise 
 until it is in contact with the lower edge of the plates. 
 
246 PRACTICAL APPLIED ELECTKICITY 
 
 (e) Keep all separators in place so that there is no danger 
 of the plates coming in contact with each other and shorting 
 the cell. 
 
 (f) Keep cells well insulated by placing them in trays 
 that are supported on insulators. 
 
 (g) Inspect all cells occasionally for leaks in the contain- 
 ing vessel and either replace the broken vessel by a new one 
 or repair it immediately. 
 
 (h) Always charge the battery as soon as possible after 
 discharge. 
 
 (i) Never overcharge the battery or after the negative 
 plates begin to gas, except as stated in section (268). 
 
 (j) Never allow the battery to" discharge below 1.75 volts 
 at the normal rate of discharge and 1.6 volts when discharg- 
 ing at the 1-hour rate. 
 
 (k) Watch the plates for signs of sulphation and if any 
 sulphate appears, treat them immediately as described in 
 section (268). 
 
 (I) Always keep the temperature of the battery below 110 
 Fahrenheit. 
 
 (m) Give the battery a prolonged over-charge occasionally 
 until free gassing of the negative plate has continued for one 
 hour. 
 
 274. To Put a Cell Out of Service. When a cell is to be 
 out of service for several months or for an indefinite period, it 
 can be treated as follows and will then need no attention until 
 it is desired to be used again. Fully charge the cell, then 
 discharge it for about two hours at the normal rate. After the 
 cell has been discharged, draw off the electrolyte and fill the 
 vessel with distilled water. Now again discharge the cell at 
 the normal rate until its terminals must be shorted to produce 
 the discharge current. Pour out the water and again fill the 
 cells, allowing them to stand for a day or so when this water 
 should be drawn off and the plates allowed to dry. To put the 
 cell back in service, the electrolyte should be placed in the 
 cell and the cell should be given a prolonged over-charge. 
 
 275. Non-Lead Storage Cells. Almost any primary cell may 
 be made to act more or less as a secondary cell; as, for 
 example, the gravity cell may be charged by passing a current 
 through it opposite to the direction the current passes through 
 the cell on discharge. Quite a number of cells have been 
 
STORAGE BATTERIES 247 
 
 devised in which metals other than lead is used for one or both 
 of the plates. Reynier made a cell in which the negative plate 
 was composed of zinc instead of lead, and this zinc was con- 
 verted into zinc sulphate when the cell was discharging, which 
 dissolved in the electrolyte. The electromotive force of this 
 cell was considerably higher than that of the ordinary lead 
 cell and it was quite a bit lighter, since for the storage of a 
 given amount of energy the weight of zinc required is much 
 less than that of the equivalent lead. This cell, however, is 
 not very satisfactory in operation, since there are trees of zinc 
 formed on the negative plate during the process of charging, 
 and these trees are likely to extend out from the negative 
 plate a sufficient distance to short-circuit the cell. There is 
 also a difference in the density of the electrolyte at the top 
 and the bottom of the cell, which results in the action on the 
 plates not being uniform. This difficulty was overcome to a 
 certain extent by placing the plates in a horizontal instead of 
 in a vertical position. Where the plates are horizontal, however, 
 there is an accumulation of the liberated gases upon the sur- 
 face of the plates and, as a result, an increase in the internal 
 resistance of the cell. 
 
 Waddell and Entz constructed a storage cell in which 
 copper and zinc are used as the plates and the electrolyte is 
 an alkali solution. When the cell is discharged, the positive 
 plate consists of porous copper and on charging, the elec- 
 trolyte is decomposed, metallic zinc is deposited on the 
 negative plate, the porous copper forming the positive plate is 
 oxidized, and the liquid forming the electrolyte is converted 
 into a solution of caustic potash. The electromotive force of 
 this cell is very low, it being only about .7 volt and, as a 
 result, approximately three times as many cells must be used 
 to give a given voltage as would be required if the lead cells 
 were used. This is a very serious objection to this particular 
 cell or to any other low voltage cell. 
 
 276. Edison Storage Battery. In the Edison battery the 
 active materials are oxides of nickel and iron, respectively, in 
 the positive and the negative electrodes, the electrolyte being 
 a solution of caustic potash in water. The retaining vessels 
 for these cells are made from sheet steel, their walls being 
 corrugated to add strength with a minimum weight. The 
 completed can is nickel-plated, which protects the steel from 
 
248 
 
 PEACTICAL APPLIED ELECTRICITY 
 
 rust and at the same time adds to the appearance of the cell. 
 There are a number of different types of Edison cells on the 
 market, but they differ only in the number of plates they 
 contain. Each positive plate consists of a grid of nickel-plated 
 steel holding 30 tubes filled with the active material, in two 
 rows of 15 tubes each, as shown in Fig. 206. The tubes are 
 made of very thin sheet steel, perforated and nickel-plated. 
 Each tube is reinforced and protected by small ferrules, eight 
 in number. These ferrules prevent expansion and thereby 
 retain perfect internal contact with the active material at all 
 times. The active material in the tubes is interspersed with 
 thin layers of pure metallic nickel in the form of leaves or 
 flakes. The pure nickel flake that is used is manufactured 
 by a special electrochemical process. 
 
 Each negative plate comprises 24 
 flat rectangular pockets supported 
 in three horizontal rows in nickel- 
 plated steel grids, as shown in Fig. 
 207. The pockets are made of thin 
 nickel-plated steel, perforated with 
 fine holes, each pocket being filled 
 with an oxide of iron very similar 
 to what is called iron rust. In the 
 construction of the negative plate 
 each pocket is subjected to a very 
 high pressure, so that it becomes 
 practically integral with the sup- 
 porting grid. 
 
 The positive and the negative 
 plates are hung alternately on two 
 connecting rods, the positive plates 
 being electrically connected to one 
 
 rod and the negative plates to the other. The plates are 
 properly distanced on these rods by nickel-plated steel' spac- 
 ing washers, and are held firmly in place and contact by 
 nuts screwed on both ends. In assembling the plates a 
 specially shaped lug is placed in the center of each of the 
 connecting rods, as shown in Fig. 207. These rods project 
 upward and are of sufficient length to protrude through open- 
 ings in the top of the containing can, thus forming the ter- 
 minals of the cell. There is always one more negative plate 
 
 Fig. 206 
 
STORAGE BATTEEIES 
 
 349 
 
 in the Edison cell than there are positive, just as there is in 
 the lead cell, which results in both outside plates being nega- 
 tive. Special insulators are used in separating the plates and 
 preventing them from coming into contact with the containing 
 can. 
 
 277. Chemistry of the Edison 
 Storage Battery. Starting with the 
 oxide of iron in the negative, green 
 nickel hydrate in the positive, and 
 potassium hydrate in solution, the 
 first charging of a cell reduces the 
 iron oxide to metallic iron while con- 
 verting the nickel hydrate to a very 
 high oxide, black in color. On dis- 
 charge, the metallic iron goes back 
 to iron oxide and the high nickel 
 oxide goes to a lower oxide but not 
 to its original form of green hydrate. 
 On every cycle thereafter, the nega- 
 tive charges to metallic iron and dis- 
 charges to iron oxide, while the posi- 
 tive charges to a high nickel oxide. 
 Current passing in either direction 
 (charge or discharge) decomposes 
 the potassium hydrate of the elec- 
 trolyte, and the oxidation and reduc- 
 tions at the electrodes are brought 
 about by the action of its elements. 
 An amount of potassium hydrate 
 equal to that decomposed is always 
 
 re-formed at one of the electrodes by a secondary chemical 
 reaction, and consequently there is none of it lost and its 
 density remains constant. 
 
 The eventual result of charging, therefore, is a transference 
 of oxygen from the iron to the nickel electrode, and that of 
 discharging is a transference back again. This is why the 
 "Edison" is sometimes called an oxygen lift cell. 
 
 When both electrodes become fully charged, the elements 
 of the decomposed potassium hydrate can no longer act on 
 them, but instead they react to produce hydrogen and oxy- 
 gen the elements of water which are given off as a gas. 
 
 Fig. 207 
 
50 PEACTICAL APPLIED ELECTEICITY 
 
 Nickel plates in the positive and mercury in the negative 
 do not take part in the chemical reaction but are used solely 
 to bring the particles of active material into good electrical 
 contact with the conducting support. 
 
 278. Care of an Edison Storage Battery. Edison storage 
 batteries are shipped in a discharged condition, and should 
 be given a long initial charge before being put into service. 
 The duration of this first charge should be about 15 hours at 
 the normal rate, and it is recommended by the company that 
 this overcharge be repeated once every two weeks for the 
 first two months, when the battery is in constant service. If, 
 however, the battery is not in constant service, it should be 
 given a long charge after every 12 complete charges and dis- 
 charges until five long charges have been put in. This con- 
 stitutes what might be called the forming process, and it is 
 advisable to repeat the long charges about every two months 
 throughout the life of the battery. 
 
 In charging an Edison battery, the seven-hour charge at the 
 normal rate is arbitrarily chosen as normal for the reason 
 that a battery will retain good efficiency up to this point. 
 This rate, however, is not fixed and may be varied at will, the 
 highest practical output being reached on a ten-hour charge, 
 which gives a maximum efficiency of about 30 per cent above 
 normal rated output. Overcharging is in no way harmful, 
 provided the temperature is not allowed to exceed 100 Fahren- 
 heit at any time while charging. The cells must be frequently 
 filled when they are overcharged and overcharging means a 
 waste of energy. The evaporation must be replaced with pure 
 distilled water, and under no circumstances use any acid. The 
 solution should never be allowed to go below the tops of the 
 plates, the proper height being one-half inch above the plates. 
 It is always advisable to fill the battery before charge as in 
 the process of charging the liquid is raised to a false level. 
 
 The electrolyte which is a 21 per cent solution of potash 
 (KOH) in a battery in constant service, being charged and 
 discharged each day, should be renewed once every eight or 
 nine months. 
 
 279. Commercial Applications of Storage Batteries. The 
 following list gives the principal uses to which the storage 
 battery may be placed: 
 
 (a) To supply energy to portable electrical apparatus. 
 
STORAGE BATTERIES 251 
 
 (b) As a source of constant potential and current in elec- 
 trical laboratories. 
 
 (c) As a source of energy in telephone and telegraph work. 
 
 (d) To supply energy for train-lighting. 
 
 (e) To reduce the fluctuations in the load on a generator, 
 by operating the battery and the generator in parallel. 
 
 (f) To supply energy during certain hours when the load 
 on a power plant is low and thus allow the generator to be 
 shut down. 
 
 (g) To supply energy and aid the generator in carrying the 
 maximum load (peak) which usually lasts only a few hours. 
 
 (h) To change froni a high to a low voltage by charging 
 the cells in series and discharging them in parallel, or vice 
 versa. 
 
 (i) As a means of subdividing the voltage of a main gen- 
 erator, enabling it to supply energy to a multi-voltage system. 
 
 (j) To supply energy for electrically driven vehicles and 
 boats. 
 
 280. Portable Storage Batteries. Practically all the bat- 
 tery companies manufacture a portable form of storage cell. 
 These cells are usually constructed so that they will be as 
 light and compact as possible, and mounted in a suitable 
 containing case outside the one holding the electrolyte, which 
 gives ample protection to the cell and affords a means of 
 easily carrying the cell, by providing this outer case with 
 some kind of a handle. The number of cells mounted in each 
 outer containing case may vary depending upon the particular 
 use to which the battery is to be placed. 
 
 The great objection to portable storage cells is their great 
 weight and this is almost prohibitive of their general use. 
 Portable cells are used in operating small lighting systems 
 such as occur on automobiles and launches, in operating spark 
 coils for gas engines, in operating small lamps and motors for 
 various special purposes, etc. 
 
 281. Storage Batteries in Electrical Laboratories. The 
 storage battery is a valuable source of energy in electrical 
 laboratories, as the regulation of the voltage and the current 
 can be accomplished by means of the adjustment of a simple 
 rheostat of some kind. The voltage of the battery can be 
 changed by changing the grouping of the cells, a maximum 
 voltage being obtained when they are all connected in series 
 
PEACTICAL APPLIED ELECTEICITY 
 
 and a minimum voltage when they are all connected in 
 parallel. When a large current is wanted at a low voltage, 
 it can be more easily obtained and at a less expenditure of 
 energy than if the same current were taken from a higher 
 voltage. The connections of jg^arging ar* ( d discharging board 
 are shown in Fig. 209. 
 
 282. Storage Batteries in Telephone and Telegraph Work. 
 Storage batteries have come into general use in telephone 
 exchanges since the introduction of what is known as the 
 common-battery telephone system. In this system instead 
 of each subscriber having a battery of two or more cells 
 placed in his instrument, these batteries are all combined in 
 one large battery located at the central office, and each sub- 
 scriber's line is supplied with current from this main or 
 central battery. The storage battery is preferable for this 
 main battery for the following reasons: Lower first cost; 
 smaller space required; lower internal resistance; more con- 
 stant electromotive force; rapidity of recharge, and low cost 
 of maintenance. Two batteries are usually placed in each 
 exchange so that one can be on charge and held in reserve 
 while the other battery is in use. 
 
 In telegraph work the storage battery may be used alone 
 or in combination with small generators in supplying current 
 to operate the telegraph instruments. 
 
 283. Storage Batteries for Train Lighting. The simplest 
 method of lighting a train by electricity is to install a small 
 dynamo on the locomotive, which may be driven by a small 
 steam engine or turbine. With this arrangement there is the 
 objection that the cars must be illuminated by some other 
 means when the locomotive is uncoupled. This has led to the 
 storage-battery system of supplying energy to each car sepa- 
 rately even though it be disconnected from the main train. 
 The battery is so connected that it is being charged when 
 connected to the main generator leads, provided the voltage 
 between the generator leads is greater than the terminal 
 voltage of the battery. When the generator voltage drops 
 below a certain point, due to any cause, the battery discharges 
 and the lamps continue to burn just as though the generator 
 were operating. The connections of the battery lamps and 
 the generator are controlled by a specially constructed switch 
 that is automatically operated. In some cases a small gen- 
 
STOEAGE 3ATTEKIE3 253 
 
 erator is mounted on each car and driven by a belt that passes 
 over a pulley on one of the axles. The generator in this 
 system is inoperative when the car is at rest and the battery 
 must necessarily carry the load. 
 
 284. Storage Battery and <d||erator in Parallel. Often the 
 load a generator is called upon to carry fluctuates in value 
 and in a great many cases it is desired that the voltage 
 between the lines remain as near constant in value as pos- 
 sible. With a fluctuating load there would necessarily be a 
 change in line voltage due to a change in the value of the 
 copper drop unless there was a change in the voltage at the 
 
 generator terminals that 
 
 + would counteract the cop- 
 
 I + 1 per drop. By connecting 
 
 ^ a battery in parallel with 
 
 Battery ; Load the generator, as shown in 
 
 - =c - | Fig. 208, the battery 
 
 -3-^ t charges when the load is 
 
 Fig. 208 light and will discharge 
 
 when the load is of such a 
 
 value that the voltage between the line wires is less than the 
 battery voltage. As a result, the copper drop in the leads 
 from the generator remains nearer constant in value and 
 there is a smaller fluctuation in the value of the line voltage 
 due to a change in load than there would be if no battery 
 were used. 
 
 285. Storage Battery to Supply Energy During Certain 
 Hours. In a great many generating plants, the energy the 
 generator is called upon to supply during certain periods is so 
 small that it would be poor economy to operate the generator 
 on so small a load. A storage battery can be installed of 
 ample capacity to carry the load during this period and the 
 plant entirely shut down. The output of a generating plant 
 is represented by curve (A), Fig. 210. It will be seen from 
 this curve that the load carried by the generator from about 
 6 P.M. to 5 A.M. is very small. By installing a storage battery 
 having the required k.w. hours' capacity, the generator can be 
 shut down during part of the night. 
 
 286. Storage Batteries to Aid Generators in Carrying the 
 Maximum Load. Assuming the load on a generating plant is 
 similar to that shown by curve (B) in Fig. 210, sufficient 
 
254 
 
 PBACTICAL APPLIED ELECTEICITY 
 
 generator capacity must be installed to take care of the 
 maximum load at any time without exceeding the allowable 
 overload capacity of the generators. This would result in a 
 large part of the equipment being practically idle during the 
 greater portion of the day, or a part of the machinery would 
 represent an investment from which there would be propor- 
 tionally a small income. By installing a storage battery, the 
 
 Ammeter 
 
 Battery \ 
 Rhoestat 
 
 Circuit-^ 
 BreaKer 
 
 Voltmeter 
 
 Voltmeter 
 Switch 
 
 Series 
 Parallel 
 Switches 
 
 Battery 
 Switch 
 
 Fig. 209 
 
 generator capacity can be reduced, the battery being charged 
 when the load on the plant is light and discharged in parallel 
 with the generators when the load exceeds the capacity of 
 the generators. The shaded portion of the curve in Fig. 210 
 represents what is called the peak of the load. 
 
 287. Storage Batteries Used in Changing Voltage. The 
 line voltage available in a great many cases is either too high 
 or too low for a given purpose and some means must be 
 employed for changing its value. An easy means of doing this 
 
STORAGE BATTERIES 
 
 255 
 
 is to use a number of storage cells and have them so arranged 
 that they may be readily changed from any connection to an- 
 other. Thus, if it is desired to reduce the voltage, the cells 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 
 
 z 
 
 
 
 
 
 
 . 
 
 
 - 
 
 - 
 
 
 
 r 
 
 - 
 
 
 
 fr 
 
 '$&>, 
 
 \ 
 
 
 
 ^ 
 
 
 
 
 
 
 f 
 
 
 
 
 
 ^ 
 
 
 
 
 '// 
 
 $M// 
 
 \\ 
 
 
 
 p 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 
 
 '//, 
 
 YW// 
 
 ^y 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 '//, 
 
 Wifa 
 
 A 
 
 
 
 -d 
 
 
 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
 % 
 
 '%> 
 
 '"hi 
 
 
 
 (0 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 \ 
 
 T\ 
 
 
 
 _j 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 1 
 
 
 
 
 I 
 
 / 
 
 
 v 
 
 _ 
 
 
 H 
 
 
 ^ 
 
 s" 
 
 
 
 
 
 
 
 
 
 
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 S 
 
 
 
 
 
 
 
 
 
 
 
 
 
 I 
 
 
 x 
 
 4- 
 
 - 
 
 
 
 
 
 Time in 
 
 Hour's 
 
 
 
 *~} 
 
 - 
 
 
 E 2 4 6 8 10 \i 1 4 6 8 10 1! 
 
 Midnight Noon Midnight 
 Fig. 210 
 
 L, 
 
 A*. **! / 
 
 Jj> 
 
 r 
 
 no 
 
 no 
 
 of a battery may be charged in series and then connected in 
 a number of groups and these groups in turn connected in 
 parallel. If it is desired to raise the voltage, the cells should 
 be charged in parallel and then connected in series for 
 discharge. 
 
 288. Storage Batteries 
 Used in Subdividing Voltage 
 of a Generator. The con- 
 nections of a battery for di- 
 viding the voltage of a gen- 
 erator are shown in Fig. 
 211. Supposing the genera- 
 tor (G) is a 220-volt ma- 
 chine and it is desired to Fig-. 211 
 obtain energy from it at 110 
 
 volts. This can be accomplished by connecting the battery 
 (B), which should have a voltage of about 220 volts, across 
 the leads from the main generator and connecting a lead (N) 
 to the center of the battery. With this connection there will 
 be a 110-volt pressure between each outside lead and the 
 lead (N). 
 
 289. Storage Batteries to Supply Energy for Electrically 
 Driven Vehicles and Boats. The storage battery is growing 
 
256 
 
 PEACTICAL APPLIED ELECTRICITY 
 
 in favor as a means of supplying energy to vehicles, such as 
 pleasure automobiles, heavy trucks, and street cars; and it is 
 also quite extensively used in small pleasure boats and sub- 
 marines. The battery is connected to the motors through 
 
 Fig. 212 
 
 specially constructed controllers, so arranged that the cells 
 are grouped to give a low impressed voltage on starting and 
 as the controller is advanced to successive positions, the 
 connections of the various cells are changed, all being con- 
 nected in series when the controller handle is at its final 
 position. A tray of six cells, as used in an electric automobile, 
 is shown in Fig. 212. 
 
CHAPTEE XIII 
 
 DISTRIBUTION AND OPERATION 
 
 290. Systems of Distribution. The power output of an 
 electrical generator at any instant is equal to the product of 
 the terminal voltage of the machine and the current supplied 
 by the machine. With a change in output there must be a 
 change in the value of this product and necessarily a change 
 in the value of either the current or voltage, or both. When 
 the power output of the generator changes due to a change 
 in the value of the current, the machine is said to be a 
 
 constant-voltage machine, 
 and the method employed 
 
 *' * Li- in supplying energy to the 
 
 M) QQQQ circuit connected to the ma- 
 chine is called a constant- 
 voltage, or parallel system 
 of distribution. If the out- 
 put of the machine changes 
 due to a change in the ter- 
 minal voltage, the current remaining constant, the method 
 employed in supplying energy to the circuit connected to the 
 machine is called constant-current, or series system of dis- 
 tribution. 
 
 291. Constant-Voltage Distribution. In the constant-volt- 
 age, or parallel system of distribution, the various devices that 
 are being supplied with energy are connected in parallel 
 across the two lines leading to the terminals of the generator. 
 A motor (M) and a number of lamps (L) are shown connected 
 in parallel to the terminals of the generator (G), Fig. 213. 
 With a change in the number of lamps or motors connected, 
 there will be a change in the value of the total resistance 
 between the two leads (Li) and (L 2 ) and, as a result, a change 
 in the value of the current output of the machine. Thus, for 
 
 257 
 
258 PRACTICAL APPLIED ELECTRICITY 
 
 example, if the generator is connected to ten incandescent 
 lamps each having a hot resistance of 220 ohms, there will 
 be a total resistance of (220 -r- 10) or 22 ohms between the 
 leads, and if the voltage of the machine is 110 volts, there 
 will be a current of 5 amperes supplied by the machine. Now 
 if 5 of the lamps are disconnected, the resistance between the 
 leads will be increased as the number of paths in parallel has 
 been decreased, and it will be equal to (220-7-5) or 44 ohms. 
 The current supplied by the generator in this case will be 
 2.5 amperes, the voltage remaining constant. When more 
 than ten lamps are connected, the combined resistance will 
 be less than the resistance of the ten and, as a result, the 
 current supplied by the generator will increase, which results 
 in an increase in the power output, it being equal to (E X I). 
 
 292. Constant-Current 
 
 Arc Lamps Distribution. In the con- 
 
 ~ stant-current, or series 
 
 system of distribution, the 
 various devices that are 
 being supplied with ener- 
 gy are connected in series 
 to the terminals of the 
 generator. A number of 
 Fig. 214 arc lamps and a motor 
 
 (M) are shown connected 
 
 in series in Fig. 214, and the combination connected to the 
 generator (G). If there is a change in the number of lamps 
 or motors connected in such a circuit there will be a change 
 in the value of the resistance of the circuit, and since the 
 construction of the generator (G) is such that it supplies a 
 constant current, there must be a change in the terminal volt- 
 age of the machine with a change in load. Thus, if there are 
 ten arc lamps connected in series and there is a drop of 90 
 volts over each lamp, the terminal voltage of the machine 
 must be (10X90) or 900 volts, neglecting the drop in the line 
 wires. If five of these lamps be disconnected from the line, 
 the circuit still being closed, the voltage required at the ter- 
 minals of the machine will be (5X90) or 450 volts. The cur- 
 rent in the circuit is the same in each case. The output of 
 the machine in the second case then would be only one-half 
 what it was when the ten lamps were in operation as the 
 
DISTRIBUTION AND OPERATION 
 
 259 
 
 Fig. 215 
 
 voltage has been reduced one-half, the current remaining 
 constant. 
 
 293. Series-Parallel System of Distribution. The series- 
 parallel system of distribution is a combination of the series 
 and parallel systems. A number of similar lamps may be 
 connected in series and the 
 combination then connected 
 to the supply leads, as 
 shown in Fig. 215. 
 
 The same current exists 
 in each lamp of a given set 
 and the drop in potential 
 over the various lamps that 
 may be connected in series 
 will be proportional to their 
 
 respective resistances. This system is usually used where 
 it is desired to operate a number of lamps or motors from a 
 line whose voltage is several times that required to operate 
 a single lamp or motor. A good example of such an arrange- 
 ment is the wiring in a street car where five similar 110-volt 
 
 lamps are connected in se- 
 LI ries and the group then con- 
 
 nected to the 550-volt source 
 of supply, as shown in Fig. 
 215. If one of the lamps in 
 any group should burn out 
 or for some reason be re- 
 moved from its socket, thus 
 opening up the circuit, the 
 remaining lamps of that 
 group would also be ex- 
 tinguished. 
 
 294. Edison Three -Wire 
 System of Distribution. 
 
 Two 110-volt generators, (G 1 ) and (G o ), are shown connected in 
 series and supplying current to a number of groups of incan- 
 descent lamps, Fig. 216. Each group of lamps consists of two 110- 
 volt lamps connected in series. If the two lamps of any group 
 have the same resistance there will be the same drop in 
 potential over each, since they both carry the same current, 
 the drop being equal to the product of the resistance between 
 
 Fig. 216 
 
260 
 
 PEACTICAL APPLIED ELECTRICITY 
 
 L, 
 
 the points considered and the current in the resistance. All 
 of the points numbered (1), (2), (3), etc., will be at the 
 same potential, since the drop over each of the upper 
 lamps is the same and equal to the drop over each of the 
 lower lamps. If these various points be connected by a con- 
 ductor there will be no change in the division of the current 
 
 through the various 
 branches or lamps. The 
 conductor connecting the 
 points (1), (2), and (3) 
 may be extended back and 
 connected between the two 
 generators, as shown in 
 Fig. 217, provided the ter- 
 minal voltage of the gen- 
 erators is the same, the 
 point (A) between them 
 La will be at the same poten- 
 
 Fi s- 217 tial as the points (1), (2), 
 
 and (3), and connecting all of these various points together 
 by the lead (N), which is called the neutral wire, will pro- 
 duce no change in the division of the line current through the 
 various branches of the load. Such an arrangement as that 
 shown in Fig. 217, is called the Edison three-wire system of 
 distribution. 
 
 There will be no current in the neutral wire when the 
 number of lamps in the upper set is the same as the number 
 of lamps in the lower set and the current in the leads (L^) 
 and (L 2 ) will be the same in value and in the direction indi- 
 cated oy the arrows in the figure. If the number of lamps 
 in the lower group be less than the number in the upper 
 group, there will, as a result, be a current in the neutral lead 
 and the direction of this current will be toward the gen- 
 erators, or toward the left, when the polarity of the machines 
 is the same as that shown in the figure. When the number 
 of lamps in the upper group is less than the number in the 
 lower group, the current in the neutral lead will be from the 
 generators or toward the right when the polarity of the 
 machines is the same as that indicated in the figure. The 
 current in the neutral lead will always be equal to the dif- 
 ference in the value of the current in the two outside leads 
 
DISTRIBUTION AND OPEEATION 
 
 (Li) and (L 2 ) and its direction will be just opposite to that 
 of the current in the outside lead that is greatest in value. 
 When there is no current in the neutral lead, the load is said 
 to be balanced and when there is a current in the neutral 
 lead it is said to be unbalanced. 
 
 The neutral lead in no case will carry a current greater 
 in value than either of the outside leads and, as a result, it 
 need not be greater in cross-sectional area than the outside 
 leads. Each outside wire in the Edison three-wire system 
 need be only one-fourth as large in cross-sectional area to 
 supply the same number of lamps with the same per cent 
 voltage drop as would be required in the simple 110-volt 
 system. Only one-fourth as much copper would be required 
 in the three-wire system as would be required in the 110-volt 
 system if no neutral lead was used, or each outside lead 
 would represent one-eighth 
 
 of the total copper re- + 75 L 
 
 quired in the 110-volt sys- - -x- 
 tem. Since the neutral ' 
 
 lead is usually made equal 
 in area to the outside 
 leads, there will be three 
 leads, each representing in 
 weight one-eighth of the 
 copper required for the 
 110-volt system, or the to- 
 tal copper required for the p. g 21g 
 three-wire system is three- 
 eighths of that required for the 110-volt system. 
 
 If no neutral lead were used, it would be impossible to 
 operate one lamp alone since there are two in series; but 
 with the neutral lead, the number of lamps that may be turned 
 on or off in either the upper or the lower groups is entirely 
 independent of the number of lamps turned on in the other 
 group. 
 
 295. Drop in Potential in the Neutral Wire. If the current 
 taken by the upper group of lamps in Fig. 217 be 75 amperes 
 and the current taken by the lower group be 50 amperes, 
 there will be a current of 25 amperes in the neutral lead and 
 the direction of these currents will be that shown by the 
 arrows in Fig. 218. Since the current in the neutral lead is 
 
262 PBACTICAL APPLIED ELECTEICITY 
 
 toward the generators, the end connected to the load must be 
 at a higher potential than the end connected to the gen- 
 erators. The load end of the upper lead (Lj) is at a lower 
 potential than the generator end and the load end of the 
 lower lead (L 2 ) is at a higher potential than the generator 
 end. The drop in potential in these various leads is repre- 
 sented by the dotted lines in Fig. 218, the potential falling 
 off along each lead in the direction of the current. Assuming 
 the voltage of each of the generators is 112 volts and that 
 this voltage remains constant regardless of the load, then the 
 voltage over the upper group of lamps will be equal to 112 
 minus the algebraic sum of the drops in the upper lead (L^) 
 and the neutral; while the voltage over the lower group of 
 lamps will be equal to 112 minus the algebraic sum of the 
 drop in the lower lead (L 2 ) and the drop in the neutral. The 
 drop in the neutral causes a decrease in the voltage over the 
 upper group of lamps and it tends to increase the voltage over 
 the lower group of lamps. The voltage over the smaller load 
 will be greater than the terminal voltage of the machine con- 
 nected to that load when the current in the neutral is greater 
 than the current in the ouside lead connected to the smaller 
 load, if the neutral and outside leads have the same resistance. 
 If a three-wire system be unbalanced and the fuse in the 
 neutral lead should blow or the neutral should be opened, the 
 outside leads remaining connected to the generators, there will 
 be a redistribution of the total voltage, between the two leads 
 (Li) and (L 2 ), over the upper and lower groups of lamps. The 
 drops over the two groups would bear the same relation to 
 each other as exists between the resistances of the two 
 groups, that is, the group containing the smaller number of 
 lamps or having the larger resistance will have the larger 
 drop over it. For example, if there be ten 220-ohm lamps 
 connected in parallel and forming one group and only one 220- 
 ohm lamp in the other group, the resistances of the two 
 groups would be in the ratio of 22 to 220. This would result 
 in the voltage over the single lamp being equal to 22 9 2 42 * 
 the total voltage between the outside leads when the neutral 
 lead was open. If the total voltage between the outside leads 
 is, say 220 volts, then the voltage over the single lamp will be 
 200 volts. This voltage is in excess of the value the lamp will 
 stand and, as a result, the lamp filament will be destroyed. 
 
DISTRIBUTION AND OPERATION 
 
 263 
 
 296. Three-Wire Generators. In the operation of the 
 Edison three-wire system as described in sections (294) and 
 (295), two generators are required, giving rise to an addi- 
 tional expense for machines as compared to the system using 
 a single generator; and on this account a special type of 
 machine has been devised which is known as a three-wire 
 generator. 
 
 The total voltage of any direct- 
 current generator can be divided 
 into two parts by placing a brush 
 midway between the negative and 
 the positive brushes of the ma- 
 chine. The coils short-circuited 
 by this additional brush would be 
 in a strong magnetic field in th6 
 ordinary machine and, as a result, 
 there would be considerable 
 trouble encountered in properly 
 
 commutating the current. This additional brush, however, can 
 be connected to a coil that is located in a weak magnetic field 
 and the commutation greatly improved by the arrangement 
 shown in Fig. 219, which consists of a four-pole field-magnet 
 frame wound for a bipolar machine, there being two adjacent 
 north poles and two adjacent south poles. The brushes (B A ) 
 
 Fig, 219 
 
 Fig. 220 
 
 and (B 2 ) represent the main brushes of the machine and the 
 brush (B.T) is the one to which the neutral lead is connected. 
 The brush (B ;5 ) is negative with respect to the brush (Bj) 
 and positive with respect to the brush (B 2 ). The magnetic 
 
264 
 
 PKACTICAL APPLIED ELECTKICITY 
 
 flux from the two north poles or into the two south poles is 
 not equal on account of armature reaction which crowds the 
 flux into the forward pole. This results in the voltage between 
 the neutral brush and one main brush being greater in value 
 than the voltage between the neutral brush and the other 
 main brush. 
 
 Another form of three-wire generator is shown diagram- 
 matically in Fig. 220. The armature winding is divided into 
 
 Fig. 221 
 
 the same number of parts as there are magnetic poles on the 
 machine. The alternate division points of the armature 
 winding are connected to one slip ring and the remaining 
 division points to a second slip ring. A coil of low resistance 
 and high inductance, called a reactor, is connected to two 
 brushes that make continuous contact with the two slip rings, 
 and a tap, which is taken off from the center of this coil, 
 forms the neutral connection. 
 
DISTRIBUTION AND OPEKATION 265 
 
 The number of slip rings may be reduced to one by placing 
 the reactor inside of the armature and allowing it to revolve 
 with the armature, the middle point being connected to the 
 slip ring. Three-wire generators may be flat or over-com- 
 pounded just as an ordinary generator to compensate for 
 armature and line drops. A machine manufactured by the 
 General Electric Company and provided with two slip rings 
 is shown in Fig. 221. 
 
 297. Dynamotors. The dynamotor is a machine having 
 one magnetic field and two armature windings. It is a com- 
 bination of generator and motor. Each of the armature wind- 
 ings is usually supplied with a separate commutator, the 
 electrical connections of the two windings being independent. 
 Either of these windings may be used as a generator or a 
 motor. The relation of the terminal voltage of the generator 
 side and the impressed voltage on the motor side will depend 
 upon the relation between the number of turns in the two 
 armature windings. If the number of inductors in the winding 
 of the generator armature winding is one-fourth the number 
 of inductors in the motor armature winding, then the voltage 
 of the generator will be practically one-fourth the voltage 
 impressed upon the motor armature. The current output of 
 the generator, however, will be practically four times the cur- 
 rent taken by the motor. This relation of current and volt- 
 age in the generator and the motor armatures results in there 
 being practically the same number of ampere-turns in each 
 armature winding when the machine is in operation, and since 
 the current in the generator armature winding will be in the 
 opposite direction around the armature core to what it is in 
 the motor armature winding, there will be practically no 
 armature reaction, the two magnetizing effects neutralizing 
 each other. 
 
 The dynamotor in the direct-current circuit corresponds to 
 the transformer in the alternating-current circuit, however, it 
 is not nearly so efficient as the transformer. 
 
 A dynamotor manufactured by the Crocker Wheeler Com- 
 pany is shown in Fig. 222. 
 
 298. Dynamotor as an Equalizer. The dynamotor is often 
 used to. equalize the difference in potential between the out- 
 side leads in a three-wire system when one side of the system 
 is carrying a larger load than the other. When the dyna- 
 
266 PRACTICAL APPLIED ELECTRICITY 
 
 mometer is thus used, it is called an equalizer; the wind- 
 ings on the armatures are the same and the machine can 
 be connected to the line as shown in Fig. 223. When the 
 two sides of the system are balanced there will be no 
 current in the neutral lead (N) and a small current will 
 pass through the two armature windings of the dyna- 
 motor in series, both armatures acting as motors. If one side 
 
 Fig. 222 
 
 of the system is carrying a larger load than the other, there 
 will be a greater drop in the leads connected to it and, as a 
 result, a lower voltage will exist over the larger load than 
 exists over the smaller load. The armature winding of the 
 balancer connected to the higher voltage will act as a motor 
 and drive the other armature winding which will act as a 
 generator, and the pressure of this generator will tend to 
 raise the voltage of the more heavily loaded side. When one 
 of the windings changes from a motor to a generator, the 
 current in it reverses in direction. The direction of the 
 currents in an unbalanced three-wire system that is being 
 supplied with energy from a main generator (G) is shown in 
 Fig. 223. The upper commutator of the balancer is connected 
 to the generator winding of the dynamotor and is supplying 
 current to the upper or larger load, and the lower commutator 
 is connected to the motor winding of the dynamotor and is 
 taking current from the lightly loaded side. 
 
DISTKIBUTION AND OPERATION 
 
 267 
 
 299. Motor-Generators, or Balancers. A motor-generator in 
 its simplest form consists of a motor mechanically connected 
 to a generator. The number of generators connected to any 
 motor is not limited to a single machine, but it may be any 
 number. Thus, a motor may 
 
 be electrically connected to ^ 
 
 a source of energy and be 
 operated as any ordinary 
 motor, its output being con- 
 sumed in driving a number 
 of generators of the same or 
 unequal voltages. These va- 
 rious generators can in turn Fig. 223 
 be connected and supply en- 
 ergy to a multi-voltage system, as shown in Fig. 224. 
 
 A motor-generator is quite often used in connection with a 
 three-wire system, the motor and the generator being similar 
 machines and rigidly connected together. The combination, 
 when so used, is called a balancer and its operation is prac- 
 tically the same as the dyuamotor previously described. The 
 connection of a balancer composed 
 of two simple shunt generators to a 
 three-wire system is shown in Fig. 
 225. The two machines composing 
 the balancer have their field con- 
 nections interchanged, that is, the 
 field of one machine is connected 
 to the terminals of the other. With 
 this arrangement of connections, 
 the voltage regulation is greatly im- 
 proved, and is further improved by 
 compounding the two machines 
 forming the balancer and connect- 
 ing them as shown in Fig. 226. 
 
 300. Boosters. When electrical 
 energy is being distributed from a 
 
 central station over long leads, there is a drop in volt- 
 age due to the resistance of the leads and, as a result, the 
 voltage at the receiving end of the line is less than it is at the 
 transmitting end. This loss in voltage can be compensated 
 for by connecting in series with the line a machine called a 
 
 Pig. 224 
 
268 
 
 PKACTICAL APPLIED ELECTKiCITY 
 
 Fig. 225 
 
 booster, whose action in the circuit is to produce an elec- 
 trical pressure which acts in series with the main gen- 
 erator pressure. When the electrical pressure of the 
 booster acts in opposition to the voltage of the main 
 generator, it is called a negative booster. The booster 
 may be driven by a motor connected to the same line 
 the booster is connected to, or to any other line, or it 
 
 may be engine -driven. 
 There are a number of dif- 
 ferent forms of boosters 
 but only two will be men- 
 tioned hare, the series and 
 the shunt. The connection 
 of a series booster in a line 
 is shown in Fig. 227. The 
 booster (B) is driven by a 
 compound motor (M) con- 
 nected as shown in the figure. The booster itself is nothing 
 more than a series generator in which the iron of the mag- 
 netic circuit will not be worked above the knee of the curve 
 when the maximum current which the feeder is to carry 
 passes through the series winding of the booster. When the 
 magnetic circuit of the machine is worked at such a flux 
 density, the relation between the terminal voltage of the 
 machine and the load cur- 
 rent la practically a L, 
 straight line. Now by prop- 
 erly winding the machine, 
 its terminal voltage may 
 be made to increase or de- 
 crease with a change in 
 
 current in the feeder just ^ 
 
 a sufficient amount to ex- Fig. 226 
 
 actly compensate for the 
 
 loss in voltage due to copper drop. 
 
 In charging a storage battery, the voltage of the line from 
 which current is to be taken in charging the battery may in 
 some cases be less than is required to give the battery a full 
 charge. In such a case a small shunt-wound generator (B) 
 may be connected in series with the battery, as shown in Fig. 
 228. The voltage of this generator will act in series with that 
 
DISTRIBUTION AND OPERATION 
 
 269 
 
 Fig. 227 
 
 of the line giving a resultant voltage sufficient to charge the 
 battery. A shunt generator when so used is called a shunt 
 booster and it may be either motor- or engine-driven. 
 
 301. Operation of Generators and Motors for Combined 
 Output. The load generating stations are called upon to carry 
 is, as a rule, not constant 
 
 in value throughout the 
 twenty-four hours of the 
 day. If one large generat- 
 ing unit were installed in 
 a station supplying a vary- 
 ing load, the efficiency of 
 the plant would vary be- 
 tween very wide limits on 
 account of the efficiency of 
 
 a generator varying with the load it is carrying. A generator 
 is usually designed so that it will have the maximum efficiency 
 at its rated full load, it decreasing in value with either an in- 
 crease or decrease in load. Now in order that the generating 
 equipment in a central station be operated at its maximum 
 efficiency, it should at all times be carrying a load something 
 
 near its full capacity. In 
 
 4 ^ _r L! modern central stations 
 
 this is accomplished by 
 using a number of genera- 
 tors, instead of a single 
 machine, their combined 
 capacity being sufficient to 
 carry the full load of the 
 station and so arranged 
 that they may all be con- 
 nected to the load at the same time. The number of genera- 
 tors in operation may be changed as the load on the station 
 changes and in this way each machine will operate on a load 
 corresponding to, or near, its maximum efficiency. 
 
 For a similar reason to that mentioned above, motors are 
 connected so that their outputs may be added, the number of 
 motors in operation depending upon the load. 
 
 302. Shunt Generators Connected for Combined Output. 
 Two simple constant-voltage shunt generators (Gi) and (G 2 ) 
 lire shown connected in parallel, in Fig. 229, to two heavy 
 
 Storage 
 Battery 
 
 Fig-. 228 
 
270 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 Fig. 229 
 
 leads (LJ) and (L 2 ) called bus-bars. The regulating rheostats 
 (Rj) and (R 2 ) in the field circuits should be adjusted so that 
 the total load connected to the bus-bars is properly divided 
 between the two generators. If the voltage regulation of the 
 two machines is not maintained, no 
 serious damage will result except 
 one machine will not carry its por- 
 tion of the load, the machine of 
 higher voltage carrying the greater 
 portion of the load. The voltage of 
 one machine may drop to such a 
 value that it will change to a motor 
 but still no serious damage will re- 
 sult as the shunt motor rotates in 
 the same direction as a shunt gen- 
 erator, the connections of the field windings and armature 
 leads remaining unchanged. 
 
 Two or more shunt generators may be operated in series, 
 as shown in Fig. 224, and supply energy to a multi-voltage 
 system or they may supply energy to a single voltage system, 
 they being connected in series so as to increase the total 
 voltage between the leads. 
 
 303. Series Generators Con- 
 nected for Combined Output. Two 
 series generators (Gi) and (G 2 ) 
 are shown connected in parallel to 
 the bus-bars (Lj) and (L 2 ), Fig-. 
 230. The two machines will oper- 
 ate satisfactorily in parallel so 
 long as their voltages remain the 
 same. If, however, the voltage of 
 one machine falls a small amount 
 
 due to any cause, such as a decrease in speed of its prime 
 mover, there will be a decrease in current supplied by it and, 
 as a result, a decrease in its field excitation, which results in 
 a further decrease in its voltage. This unbalanced condition 
 continues to grow until the lower voltage machine is con- 
 verted into a motor, and since the direction of rotation of a 
 series generator is opposite to what it is when used as a 
 motor, the results may be very serious to one or both ma- 
 chines. 
 
 Fig. 230 
 
DISTRIBUTION AND OPEEATION 
 
 271 
 
 Fig. 231 
 
 The above difficulty in operating two series-wound gen- 
 erators in parallel can be overcome to a certain extent by 
 allowing the armature current of one machine to pass through 
 the field of the other. With this arrangement, a decrease in 
 armature current of one machine causes a decrease in voltage 
 of the other machine and, as a result, 
 the first machine must carry its proper 
 share of the load. 
 
 The current in the various field 
 windings may be made independent of 
 the voltage of the different machines 
 by connecting the junctions of the 
 series windings and brushes by a low 
 resistance lead, called an equalizer, as 
 shown in Fig. 231. The polarity of 
 the points connected by the equalizer 
 should all be the same. When this connection is made, the 
 current in the various series windings is practicplly the same 
 provided they have the same resistance. It is impractical to 
 operate series generators in parallel and, as a result, ,it is 
 never done. 
 
 Series generators are operated in series in practice in 
 direct-current, high voltage power transmission. The gen- 
 erators and their fields are 
 all connected in series. 
 Such systems are used in 
 Europe and in the major- 
 ity of cases they are con- 
 stant-current systems, the 
 current being maintained 
 constant in value by spe- 
 cial regulating devices 
 which change both the 
 speed of the prime movers 
 and the position of the 
 brushes. 
 
 304. Compound Generators in Parallel. Compound gen- 
 erators may be operated in parallel very satisfactorily, the 
 connections being made as shown in Fig. 232. It is not 
 necessary that the capacity of the machines connected in 
 parallel be the same but they must have the same terminal 
 
 L, 
 
 Shunt 
 ^^-TftftTvfir^ ' 
 
 Fig. 232 
 
72 PRACTICAL APPLIED ELECTRICITY 
 
 voltage at all loads and the resistance of their series fields 
 must be to each other inversely as their capacities for the 
 same degree of compounding in order that the total load he 
 divided in proportion to their respective capacities as the load 
 changes in value. When it is desired to operate two machines 
 having different degrees of compounding, the series field of 
 the machine of higher compounding should be shunted with 
 a resistance, or sufficient turns in the series windings discon< 
 nected, so that its compounding will correspond to that of 
 the machine with which it is to operate. A resistance may 
 be connected in parallel with the series winding of one of the 
 machines, if the currents in the series windings are not in- 
 versely as the capacities of the two machines. 
 
 305. Operation of Shunt Motors in Series and Parallel. 
 Any number of shunt motors will operate satisfactorily in 
 parallel across a constant pressure, and each motor may be 
 connected to a separate load or to the same load. 
 
 When a number of shunt motors are operated in series 
 across a constant-pressure line, they must be rigidly connected 
 together. If they were not rigidly connected together and the 
 load was removed from one of the motors, it would race and 
 rob the remaining motors of their proper share of the total 
 voltage. It is not practical for this reason to operate shunt 
 motors in series unless they be rigidly connected together. 
 
 306. Operation of Series Motors in Series and Parallel. 
 Any number of series motors may be operated in series on 
 constant-current circuits and their operation is independent 
 of the load any of the motors may be carrying. Any motor 
 may be overloaded until it stops without interfering with the 
 other motors connected to the same line, since the current in 
 the circuit remains constant in value at all times. Series 
 motors will operate satisfactorily in series on constant-voltage 
 circuits provided they are rigidly connected together. An 
 example is to be found in starting a street car when the 
 motors are connected in series groups of two each. The 
 speed of each motor is the same in this case, provided none 
 of the wheels slip, and the voltage over each will be prac- 
 tically the same. If, however, the wheels to which one of the 
 motors is geared slip, this motor will speed up and rob the 
 other motor of its proper share of the line voltage and, as a 
 
DISTRIBUTION AND OPERATION 73 
 
 result, the motor having the lower voltage impressed upon it 
 will have its starting torque lowered. 
 
 Any number of series motors may be operated in parallel 
 from a constant-voltage line provided their loads are not dis- 
 connected, which would result in the motor racing and no 
 doubt destroying itself. 
 
 307. Operation of Compound Motors. Compound motors 
 are operated from constant-voltage lines in every case and 
 each has its own load. The speed regulation of the compound- 
 wound motor, when the series- and shunt-field windings are 
 differentially connected, is better than any other type of 
 direct-current motor. 
 
 308. Switchboard. A switchboard is a board, of insulating 
 material usually, upon which the indicating instruments and 
 the switches used in connecting various electrical circuits are 
 located. It is customary to divide a switchboard up into 
 sections called panels. If a switchboard be used in connect- 
 ing a number of machines to a certain load, it will be divided 
 into what are called generator panels and feeder panels. All 
 of the switches and instruments associated with each genera- 
 tor being mounted on the generator panels, and the instru- 
 ments and switches associated with the feeder circuits being 
 mounted on the feeder panels. The equipment most com- 
 monly found on a direct-current switchboard consists of volt- 
 meters, ammeters, wattmeters, ground detectors, circuit 
 breakers, fuses, rheostats, and switches. All of the above 
 equipment has been described with the exception of circuit 
 breakers, rheostats, ground detectors, and switches. These 
 devices will be discussed in the following sections. 
 
 309. Circuit Breakers. A circuit breaker is a switch that 
 may be closed against the action of gravity or a spring and 
 held in the closed position by means of a suitable latch, which 
 in turn is controlled by one or more solenoids. A solenoid 
 may be connected so that its winding will carry all or a 
 definite part of the total current the contacts of the circuit 
 breaker carry and its armature may be so adjusted that it. 
 will be drawn up and trip the latch when the current exceeds 
 a certain value. Such a circuit breaker is called an over- 
 load circuit breaker. 
 
 A solenoid may be so constructed that it will trip the latch 
 
274 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 of the circuit breaker when the current in the circuit is 
 reversed. Such a circuit breaker is called a reverse-current 
 circuit breaker. 
 
 A circuit breaker in which the latch is tripped when the 
 current falls below a certain value is called an under-load 
 circuit breaker. 
 
 A fourth form of circuit breaker is one having the solenoid 
 controlling the latch connected directly across the line and so 
 arranged thaf the breaker is opened automatically when the 
 voltage drops below a certain value. This form of circuit 
 breaker is called a no-voltage circuit breaker. Various com- 
 binations of the above forms of circuit breakers may be made 
 which will meet practically all requirements. An over-load 
 and no-voltage circuit breaker combined is shown in Fig. 233. 
 
 310. Rheostat. A rheostat is a 
 resistance whose value may be 
 varied. There are numerous forms 
 of rheostats, their construction in a 
 measure being determined by the 
 particular use to which they are to 
 be placed. A form of rheostat used 
 in regulating the shunt-field current 
 of generators is shown in Fig. 234. 
 This consists of a number of small 
 coils of wire connected in series 
 and their junctions joined to a 
 number of contact buttons over 
 which a metal arm passes. One 
 terminal of the rheostat is the arm 
 that moves over the contact but- 
 tons and the other terminal is one 
 of the end coils. The variation in 
 
 current that may be produced by such a rheostat will depend 
 upon the relation between the resistance of the circuit in 
 which the rheostat is connected and its own total resistance. 
 Such rheostats, as a rule, have rather a small current- 
 carrying capacity. 
 
 A rheostat composed of a number of carbon plates mounted 
 side by side is shown in Fig. 235. The resistance of this 
 rheostat is changed by varying the pressure between the 
 various plates of carbon between the end plates, by means of 
 
 Fig. 233 
 
DISTRIBUTION AND OPEEATION 
 
 275 
 
 a small handle shown in the figure. The resistance of this 
 rheostat is, as a rule, rather low, but its current-carrying 
 capacity is quite large. It 
 operates very satisfactorily 
 in low voltage circuits and 
 the variations in its resist- 
 ance can be made very 
 gradual. 
 
 Rheostats are usually 
 controlled from the switch- 
 boards when used in ad- 
 justing the field current of 
 machines and the control 
 is accomplished by a small 
 handle on the face of the 
 board, the rheostat being 
 usually mounted back of 
 the board. 
 
 311. Ground Detectors. A ground detector is an instru- 
 ment used in measuring the insulation resistance between any 
 line connected to the switchboard and ground. It is really a 
 special form of series voltmeter marked in some cases to read 
 directly in ohms. 
 
 312. Switches. Switches are devices that are connected in 
 
 Fig. 234 
 
 Fig. 235 
 
 a circuit to facilitate its being closed or opened. They may be 
 single-pole, double-pole, etc., depending upon the number of 
 circuits that are interrupted when the switch is opened. A 
 double-pole double-throw switch is shown in Fig. 236. This 
 switch is so constructed that the circuits are connected to it 
 back of the board upon which it is mounted. The size of the 
 
276 PRACTICAL APPLIED ELECTRICITY 
 
 jaws and blades of a switch will depend upon the value of the 
 current the switch is designed to carry, and the distance 
 between the various parts that are connected to the different 
 leads will depend upon the voltage. 
 
 313. Instructions for Starting a Generator or Motor. In 
 starting a machine make sure the commutator is perfectly 
 clean. Examine the brushes carefully to see that they are all 
 making good contact with the commutator and that they are 
 in their proper position, which should be indicated by a mark 
 on the rocker arm supporting them. If there happens to be 
 no such mark, their position must be adjusted after the 
 machine is in operation, it being indicated by a maximum 
 voltage in the case of a generator and a minimum speed in 
 
 Fig. 236 
 
 the case of a motor. They are, however, usually advanced 
 a little beyond this position in a generator and back of it in 
 a motor in order to reduce the tendency for sparking. Exam- 
 ine all connections and see that all screws and bolts are tight. 
 Fill the oil cups and see that they are supplying oil to the 
 parts they are supposed to lubricate. 
 
 If the machine is being started for the first time, make sure 
 that it turns over freely and that the armature is properly 
 balanced and that it is centrally located in the magnetic field. 
 After it has been thus inspected, the machine should be 
 started up and its speed increased gradually when possible, 
 with the switches all left open in the case of a generator. 
 If the machine is being started for the first time, it should 
 be run for a number of hours without load and the load then 
 
DISTRIBUTION AND OPEKATION 
 
 277 
 
 Fig. 237 
 
278 PRACTICAL APPLIED ELECTRICITY 
 
 gradually applied, the attendant being in readiness at all 
 times to disconnect or stop it if anything should go wrong. 
 
 314. Starting and Stopping Compound Generators that are 
 Operating in Parallel. A diagram of the wiring of a switch- 
 board used in connecting two generators in parallel and to a 
 common load or in connecting either generator to a separate 
 load is shown in Fig. 237. The left-hand panel is the gen- 
 erator panel for, say generator (Gi); the middle panel is the 
 generator panel for generator (G 2 ) ; and the right-hand panel 
 is the feeder or load panel. On each generator panel there is 
 mounted a wattmeter (W), a circuit breaker (CB), a main 
 generator switch, an equalizer switch, a field-regulating rheo- 
 stat (shown in the figure by the dotted circles), a voltmeter, 
 and an ammeter. The ammeter shunt is shown connected in 
 series with the lead from the generator and it should always 
 be connected in the lead that goes to the terminal of the 
 generator opposite the one to which the equalizer lead is 
 connected. If it were connected in the other lead it would not 
 necessarily indicate the current that really exists in the arma- 
 ture of the generator unless there was no current in the 
 equalizer. 
 
 The following apparatus is mounted on the feeder panel 
 shown in Fig. 237. Two lines (Li) and (L 2 ) are connected 
 to the central points of the double-pole double-throw switches 
 (S 3 ) and (S 5 ), one lead of each line passing through the cur- 
 rent coils of the two wattmeters (W 3 ) and (W 4 ). The outside 
 points of the switches (S 3 ) and (S 5 ) are connected to the 
 bus-bars of the two generators (Gi) and (G 2 ). The upper and 
 the lower contacts of the switch (S 4 ) are connected to the bus- 
 bars of the two generators and when this switch is closed the 
 two machines will be connected in parallel, provided the 
 terminals of the switch (S 4 ) that are connected when the 
 switch is closed are of the same polarity. A voltmeter (V c ) 
 is mounted on this panel and its terminals are connected to 
 the central points of the small double-pole double-throw switch 
 (S 8 ), which has its upper and lower contacts connected to the 
 terminals of the two generators (G) and (G 2 ). 
 
 Assuming now one machine is in operation and connected 
 to one or both of the loads and it is desired to connect the 
 idle machine in parallel with the one already in operation. 
 The two loads can be connected to one machine by closing the 
 
DISTRIBUTION AND OPERATION 279 
 
 switches (S 3 ), (S 4 ), (S 5 ), and the proper generator switch. 
 Bring the generator up to speed, close the equalizer switches 
 (S 6 ) and (S 7 ), and adjust its shunt-field current to such a 
 value that its terminal voltage is a little in excess of that 
 between the bus-bar to which the machine is to be connected. 
 This can be determined by noting the indications of the two 
 voltmeters (Vi) and (V 2 ), respectively, or the voltmeter (V c ) 
 may be thrown from one circuit to the other, by operating the 
 switch (S 8 ) and its indication noted when it is connected to 
 the two circuits. Using a single voltmeter eliminates the 
 possibility of an error due to the two separate voltmeters 
 not indicating the same, even though they be connected to 
 the same pressure. When the voltage of the incoming ma- 
 chine has been adjusted to the proper value, the main switch 
 may be closed and the field current adjusted to such a value 
 that the load is divided between the two machines in propor- 
 tion to their capacities. You should always be absolutely 
 sure that the points of the last switch you close in connecting 
 the machines in parallel is of the proper polarity, positive to 
 positive and negative to negative, before the switch is closed. 
 If the indications of the voltmeters depend upon the direction 
 of the current in their windings, and you are sure there has 
 been no change in the connections back of the board or at the 
 machines, you can then close the paralleling switch when all 
 of the voltmeters read in the proper direction. 
 
 When it is desired to disconnect a machine from the line, its 
 voltage is lowered by reducing its shunt-field current and, as 
 a result, it fails to carry its proper share of the load. The 
 main generator switch should be opened when the current 
 output of the generator has decreased to almost zero value. 
 The equalizer switch may then be opened and the machine 
 shut down. 
 
CHAPTER XIV 
 
 DISEASES OF DIRECT-CURRENT DYNAMOS 
 
 315. Sparking at the Brushes Due to Fault of the 
 Brushes. 
 
 (1) Brushes not set diametrically opposite. 
 
 (Rla) Should have been properly set at first while 
 at rest by counting bars, by measurement, or by use 
 of reference marks on the commutator. 
 
 (Rib) Can be done if necessary while running by 
 bringing the brushes on one side to the least 
 sparking point by moving the rocker arm and then 
 adjusting the brushes on the other side to the least 
 sparking point by moving the rocker arm and then 
 brush holder and then clamping. 
 
 (2) Brushes not set in neutral point. 
 
 (R2a) Move the rocker arm slowly back and foith 
 until the sparking stops. See (R58e). 
 
 (3) Brushes not properly trimmed. 
 
 (R3a) Brushes should be always kept properly 
 trimmed and set. If sparking begins from this 
 cause and dynamo cannot be shut down, bend back 
 the brushes and cut off loose and ragged wires if 
 metal brushes are used. Retrim as soon as pos- 
 sible after run is over. If there are two or more 
 brushes in each set, they may be changed one at 
 a time for new and properly trimmed ones during 
 the run on any low voltage machine. See number 
 (38). To trim, clean them from oil or dirt with 
 benzine, soda, or potash, then file or grind to a 
 
 Note. The list of dynamo diseases given in this chapter 
 was taken from a large chart, suitable for framing, that is 
 published by the Guarantee Electric Company, Chicago. 
 
 280 
 
DISEASES OF DIRECT-CURRENT DYNAMOS 281 
 
 standard jig and reset carefully as at (Rla), (Rib). 
 See (R38a) and (R38b). 
 
 (4) Brushes not in line. 
 
 (R4a) Adjust each brush of a given set until they 
 are all in line and square with the same commu- 
 tator bar, bearing evenly for their entire width, 
 unless purposely staggered. See (R13a). 
 
 (5) Brushes not in good contact. 
 
 (R5a) Clean the commutator of all dirt, oil or grit, 
 
 so that brushes touch. 
 
 (R5b) Adjust pressure by tension screws and 
 springs until light, firm, yet even contact is made. 
 Pressure should be about 1.25 pounds per square 
 inch. See number (38). 
 
 316. Sparking at the Brushes Due to Fault of the Com- 
 mutator or Magnetic Field. 
 
 (6) Commutator rough, worn in grooves or ridges. 
 
 (7) Commutator not round. 
 
 (R6a and R7a) Grind down the commutator with fine 
 sand paper (never emery in any form) laid in stock 
 curved to fit the commutator. Polish with a soft, 
 clean cloth. 
 
 (R6a and R7b) If too bad to grind down, turn off with 
 a special tool and rest while turning slowly in the 
 bearings, or remove the armature from bearings 
 and turn off with light cuts in lathe. 
 
 Note. Armature should have from ifa" to %" en( * 
 motion so as to distribute wear evenly and prevent 
 wearing in ruts or ridges. Brushes may be shifted 
 sideways occasionally to assist in distribution of 
 the wear. See number (31). 
 
 (8) One or more high commutator bars. 
 
 (R8a) Set the high bar down carefully with a mal- 
 let or block of wood, being careful not to bend, 
 bruise or injure the bar and then tighten the 
 clamping rings. If this does not remedy the fault, 
 file, grind or turn the high bar down to the level of 
 the other bars. The high bar may cause the 
 brushes to jump or vibrate so as to "sing." See 
 number (38). 
 
 (9) One or more low commutator bars. 
 
282 PRACTICAL APPLIED ELECTRICITY 
 
 (R9a) Grind the remainder of the commutator down 
 to a true surface so as to remove low spots. 
 
 Note. The insulation between the segments may be 
 high, due to its not wearing as fast as the metal of 
 the segments. Insulation should be turned down to 
 level of segments to remedy this fault. 
 
 (10) Weak magnetic field. 
 
 (A) Broken circuit in field. 
 
 (RlOa) Solder or repair broken connection. Re- 
 wind if the brake is inside of the winding. 
 
 (B) Short-circuit of the coils. 
 
 (RlOb) Repair if external and rewind if internal. 
 
 (C) Dynamo not properly wound or without proper 
 amount of iron. 
 
 (RIOc) No remedy but to rebuild. 
 
 317. Sparking at the Brushes Caused by an Excessive Cur- 
 rent in the Armature Due to an Overload. 
 
 (11) Generator. (A) Too many lamps on the circuit 
 
 ( constant-potential system ) . 
 
 (B) Ground and leak from short-circuit 
 on the line. 
 
 (C) Dead short-circuit on the line. 
 Motor. (D) Excessive voltage on a constant- 
 potential circuit. 
 
 (E) Excessive amperage on a constant- 
 current circuit. 
 
 (F) Friction. See section (321). 
 
 (G) Too great a load on the pulley. 
 See section (321). 
 
 (Rlla) Reduce the number of lamps and thus di- 
 minish the current called for. 
 
 (Rllb) Test out, locate the ground and repair. 
 
 (Rile) Dead short-circuit will or should blow the 
 safety fuse. Shut down the dynamo, locate and 
 repair the fault. Put in new fuse before starting 
 again. Fuse should not be inserted until the fault 
 is corrected, as it will blow again on starting up 
 the machine. 
 
 (Rlld) Use the proper value of current for a motor 
 and no other. 
 
DISEASES OF DIRECT-CURRENT DYNAMOS' 283 
 
 (Rile) Make sure you have the proper rheostat or 
 
 controlling switch. 
 (Rllf) Reduce the load to the proper amount for 
 
 rating of the motors. 
 (Rllg) Remedy any cause of trouble from undue 
 
 friction. See section (321). 
 
 318. Sparking at the Brushes Due to Fault of the Arma- 
 ture. 
 
 (12) Short-circuited coil in the armature. 
 
 (R12a) Look for copper dust, solder, or other cause 
 for metallic contact between commutator bars and 
 remove. 
 
 (R12b) See that the clamping rings are properly 
 insulated from commutator bars, and from car- 
 bonized oil and copper dust or dirt which may form 
 a short-circuit. 
 
 (R12c) Test for internal short-circuit or cross-con- 
 nection; if found, reinsulate the conductor, change 
 the connection, or rewind armature to correct. 
 
 (R12d) Examine the insulation of the brush holders 
 for the fault. Dirt, oil, or copper dust may form a 
 short-circuit from brush holder to rocker arm, and 
 thus short-circuit the machine. 
 
 (13) Broken circuit in the armature. 
 
 (R13a) Bridge the break temporarily by staggering 
 the brushes till the run is finished, then test out 
 and repair the fault. This is only a temporary 
 make-shift to try to stop the bar sparking during 
 a run when dynamo cannot be shut down. 
 
 (R13b) If the dynamo can be shut down, look for 
 broken or loose connection to the bar and repair. 
 
 (R13c) If the coil is broken inside, rewinding is the 
 only sure remedy. The break may be bridged tem- 
 porarily by hammering the disconnected bar until 
 it makes contact across the mica to the next bar 
 of the commutator. This remedy is of doubtful 
 value if done. The bars must be repaired and 
 insulation replaced again after fault is corrected. 
 
 (R13d) Solder the commutator lugs together or 
 bridge across them with piece of heavy wire and 
 thus cut out the broken coil. Be careful not to 
 
284 PRACTICAL APPLIED ELECTRICITY 
 
 short-circuit a good coil in soldering, and thus 
 cause sparking from a short-circuited coil, as in 
 number (12). 
 
 (14) Cross-connection in the armature. 
 
 (R14a) Cross-connections may have the same effect 
 as a short-circuit and they are to be treated as 
 such. See number (12). Each coil should show a 
 complete circuit with no connection to any other 
 coils. 
 
 319. Heating of the Armature. 
 
 (15) Overloaded or not centrally located between the 
 poles. 
 
 (16) Short-circuit. See numbers (11), (12), (13), and 
 (14). 
 
 (17) Broken circuit. 
 
 (18) Cross-connection. 
 
 (19) Moisture in the armature coils. 
 
 (R19a) Dry out the coils by slow heat, which may 
 be done by sending a current through the armature 
 regulated not to exceed the proper value. If not so 
 bad as to cause a short-circuit, cross-connection, or 
 too much heat, the moisture may be dried out by 
 the heat of its own current while running. 
 
 (20) Eddy currents in the armature core. 
 
 (R20a) The iron of the core may be hotter than the 
 coils after a short run due to a faulty armature 
 core, which should be finely laminated and the 
 lamime insulated. No remedy but to rebuild. 
 
 (21) Friction. 
 
 (R21a) Hot bars and journals may affect the tem- 
 perature of the armature. See section (321). 
 
 320. Heating of the Field Coils. 
 
 (22) An excessive current in the field circuit. 
 
 (R22a) Shunt machine. Decrease the voltage at the 
 terminals by reducing the speed, or increasing the 
 resistance of the field coils by winding on more 
 wire, or rewind them with finer wire, or put a 
 resistance in sertes with the field. 
 
 (R22b) Series machine. Shunt a portion of the 
 current, or otherwise decrease the current in the 
 field windings, or take off one or more layers of 
 
DISEASES OF DIRECT-CURRENT DYNAMOS 285 
 
 wire, or rewind the fields with a coarser wire. 
 Note. An excessive current nay be due to a short- 
 circuit or from moisture in the coils acting as a 
 short-circuit. See number (24). 
 
 (23) Eddy currents in the pole pieces. 
 
 (R23a) The pole pieces may be hotter than the field 
 coils after a short run due to faulty construction 
 or to a fluctuating current in the latter; regulate 
 and steady the current. 
 
 (24) Moisture in the field coils. 
 
 (R24a) The coils show a resistance lower than nor- 
 mal, which may be caused by a short-circuit or 
 contact with the iron of the dynamo. Dry out the 
 coils as in number (19). See note under (R22b). 
 321. Heating of the Bearings. 
 
 (25) Not enough or poor quality of oil. 
 
 (R25a) Supply plenty of good clean oil and see that 
 it feeds properly. Oil should be best quality min- 
 eral oil, filtered clean and free from grit. 
 
 Note. Be careful not to flood the bearings so as to 
 force oil upon the commutator, or into the insula- 
 tion of the brush holders, as it will gradually char 
 and gather copper dust and form a short-circuit. 
 See (R12b) and (R12d). 
 
 (R25b) Vaseline, cylinder oil, or other heavy lubri- 
 cant may be used if ordinary oil fails to remedy 
 the hot box. Use till run is over, then clean up 
 and adjust the bearings. 
 
 (26) Dirt, grit, or other foreign matter in the bearings. 
 (R26a) Wash out the grit by flooding the bearings 
 
 with clean oil until run is over. Be careful, how- 
 ever, about flooding the commutator or brush 
 holders. See note under (R25a). 
 
 (R26b) Remove the cap and clean the journals and 
 bearings, then replace the cap and lubricate well. 
 
 <R26c) After the run is over (or if shut-down is 
 made), remove the bearings completely, cool off 
 naturally, and polish everything free from grit, and 
 set up again. 
 
 (27) Rough journals or bearings. 
 
 (R27a) Smooth and polish in a lathe, removing all 
 
286 PRACTICAL APPLIED ELECTRICITY 
 
 cuts, burs, scratches, and tool marks, then make 
 new bearings (of babbitt or other metal) to prop- 
 erly fit. 
 
 (28) Journals too tight for bearings. 
 
 (R28a) Slacken the bolts in the cap, put in packing 
 pieces till run is over, then fit to smooth bearing 
 and easy rotation by hand (if the machine is 
 small). 
 
 (R28b) Turn down smooth and repolish the journal, 
 or ream or scrape the bearings until they fit prop- 
 erly. 
 
 (29) Bent or sprung shaft. 
 
 (R29a) Bend or turn the shaft true by caretul 
 springing or turning in lathe. 
 
 (30) Bearings out of line. 
 
 (R30a) Loosen the base of the bearings and shift 
 them until the armature turns freely by hand with 
 belt off and it is at the same time in the center of 
 the polar space. Remount, bolt, and dowel-pin 
 holes, and fit new dowels to allow new position to 
 be kept when bolts are drawn up tight. If shaft 
 need be raised or lowered, then pack up or trim 
 down the foot of the bearing to allow the proper 
 setting. 
 
 (31) End pressure of the pulley hub or shaft collars 
 against the bearings. 
 
 (R31a) See that the foundation ia level and that the 
 armature moves freely with a small amount of end 
 motion. 
 
 (R31b) If there is no end motion, then turn off the 
 shoulders on the shaft or file or trim off the ends 
 of the bearings until the necessary end motion is 
 obtained. 
 
 (R31c) Then line up the shaft, pulley, and belt so 
 that no end thrust is maintained on the shaft, but 
 the armature has free end play while in motion. 
 
 (32) Too great a load or strain on the belt. 
 
 (R32a) Reduce the load so that the belt may be 
 slackened and yet not slip. Avoid vertical belts if 
 possible. (Vibration and flapping of belt causes 
 lamps to flicker.) 
 
DISEASES OF DIEECT-CUKKENT DYNAMOS 287 
 
 (R32b) Use larger pulleys, wider and longer belts. 
 Run with slack side on top to increase the adhesion 
 and pull of belt without excessive tightening. Belt 
 should be tightened just enough to drive the full 
 load smoothly without vibration or flapping. 
 
 (33) Armature being not centrally located between the 
 poles. 
 
 (R33a) Bearing may be worn out, letting the arma- 
 ture move out of center and should be replaced. 
 See number (30). 
 
 (R33b) Center the armature in the polar space and 
 adjust the bearings to the new position. See 
 number (30). 
 
 (R33c) File out the polar space to give an equal 
 clearance all around the armature. 
 
 (R33d) Spring the pole away from the armature 
 and secure it in place. This will be a difficult if 
 not an impossible job in large and rigid machines. 
 322. Noise. 
 
 (34) The armature or pulley out of balance. 
 
 (R34a) The armature and pulley should have been 
 properly balanced when made. Their construction 
 may, however, be somewhat improved by mounting 
 them on knife edges and adding weight to the light 
 side until balanced. 
 
 (35) The armature strikes or rubs against the pole 
 pieces. 
 
 (R35a) Bend or press down and secure any project- 
 ing wires. Secure rigidly with proper tie bands of 
 strong wire. 
 
 (R35b) File out the pole pieces where armature 
 strikes. See numbers (30) and (33) for possible 
 remedies. 
 
 (36) The collars or shoulders on the shaft, hub, or web 
 of pulley strike or rattle against the bearing. 
 
 (R36a) The bearing may be worn out and too loose 
 and therefore rattle, new bearing needed. See 
 numbers (30) and (33). 
 
 (37) Loose screws, bolts, or connections. 
 
 (R37a) Tighten up all the screws, bolts, and connec- 
 tions to firm bearing and keep them so by daily 
 
2SS PRACTICAL APPLIED ELECTRICITY 
 
 attention. The jar and movement of dynamos 
 tends to work screwed connections loose when not 
 held by check nuts. 
 
 (38) Singing or hissing of the brushes. See numbers 
 (3), (4), and (5). 
 
 (R38a) Apply a little mineral oil or better yet vase- 
 line or hold a piece of stearic acid (adamantine) 
 candle to the commutator and then wipe off. Just 
 a faint trace of oil or grease is all that is needed. 
 
 (R38b) Lengthen or shorten the brushes in the 
 holder until firm yet gentle pressure is maintained 
 free from any hum or vibration. See numbers (3), 
 (6), (7), (8), (9), and (31). 
 
 (39) Flapping or pounding of the belts, joints, or lacing. 
 (R39a) Use an endless belt. If a laced belt must be 
 
 used, have square joints properly laced. 
 
 (40) Slipping of the belt due to an overload. 
 
 (R40a) Tighten the belt or reduce the load. See 
 number (32). 
 
 (41) Humming of the armature lugs or teeth as they 
 pass the pole pieces. 
 
 (R41a) Slope the ends of the pole pieces so that 
 the armature teeth- do not pass the edges all at 
 once. 
 
 (R41b) Decrease the magnetism of the fields or 
 
 increase the magnetic capacity of the teeth. 
 323. Speed Too High. 
 
 (42) The engine fails to regulate under a varying load. 
 (R42a) Adjust the governor to the ^proper regula- 
 tion if possible; if not, get a better engine. The 
 engine should regulate closely from "no load" to 
 "full load" with the proper steam supply. 
 
 (43) Series motor takes too much current for a given 
 load and the motor runs away. (Load on the series 
 motor is too small.) 
 
 (A) Series motor on a constant-current circuit. 
 (R43a) Put in a shunt and regulate until the proper 
 
 current is obtained. 
 
 (R43b) Use the proper regulator for controlling 
 the magnetism of the field for a varying load. 
 
 (B) Series motor on a constant-potential circuit. 
 
DISEASES OF DIEECT-CURRENT DYNAMOS 289 
 
 (R44c) Put in a resistance to cut down the current. 
 (R44d) Use the proper regulator or controlling 
 
 switch. 
 (R44e) Change to an automatic speed-regulating 
 
 motor. 
 
 (44) Shunt motor. 
 
 (A) Regulator or field rheostat not properly set. 
 
 (B) Voltage too high. 
 
 (R44a) Adjust the regulator or field rheostat to 
 
 control the speed. 
 (R44b) Use the proper voltage and the proper 
 
 rheostat. 
 
 324. Speed Too Low. 
 
 (45) Same as number (42). 
 (R45a) Same as (R42). 
 
 (46) Overloaded. 
 
 (R46a) See (Rlla) to (Rllg). 
 
 (47) Short-circuit in the armature. 
 (R47a) See (R12a) to (R12d). 
 
 (48) Striking or rubbing of the armature on pole pieces. 
 (R48a) See (R35a) and (R35b). 
 
 (49) Friction. 
 
 (R49a) See section (321). 
 
 (50) Weak magnetic field. 
 
 (R50a) See (RlOa), (RlOb) and (RIOc). 
 
 325. Motor Stops. 
 
 (51) Too great an overload. See (D), (E), (F), and (G) 
 under number (11). 
 
 (R51a) Open the switch, locate the trouble, and re- 
 move. Keep the switch open and the arm of the 
 rheostat in the position "off" while locating and re- 
 pairing trouble. Then close the switch and move 
 the arm gradually to the position "on" to see if 
 everything is correct. With a series motor, no 
 great harm will result from motor stopping or 
 failing to start. If it is a shunt motor on a con- 
 stant-potential circuit, the armature may and prob- 
 ably will burn out or the fuse blow. 
 
 (52) Very excessive friction. 
 
 (R52a) Same as (R51a). See section (321). 
 
290 PRACTICAL APPLIED ELECTRICITY 
 
 (53) Circuit open. 
 
 (A) Safety fuse melted. 
 
 (B) Broke wire or connection. 
 
 (C) Brushes not in contact. 
 
 (D) Switch open. 
 
 (E) Current fails or is shut off from the station. 
 (R53a) Open the switch, locate and repair the trou- 
 ble, and then put in the fuse. See (Rile). 
 
 (R53b) Open the switch, locate and repair the trou- 
 ble. See (13). 
 
 (R53c) Open the switch to repair the fault. See 
 number (3). 
 
 (R53d) Close the switch, but before doing so see 
 that the starting resistance is in circuit. 
 
 (R53e) Open the switch, return the starting lever 
 to the position "off," wait for the current, testing 
 from time to time by closing the switch and moving 
 the starting lever to the first closed-circuit position. 
 
 (54) Complete short-circuit of the field. 
 
 (R54a) Test for the fault and repair if possible. 
 Inspect the insulation of the binding posts and 
 brush holders. Poor insulation, oil, dirt, or copper 
 dust may cause a short-circuit. See number (12). 
 
 (55) Complete short-circuit of armature. 
 (R55a) Same as (R54a). 
 
 (56) Complete short-circuit of switch. 
 (R56a) Same as (R54a). 
 
 326. Motor Runs Backward or Against the Brushes. 
 
 (57) Wrong connections within the motor. 
 
 (R57a) Connect up properly, referring to the proper 
 diagram. If proper diagram is not to be had, try 
 reversing the connections to the brush holders. 
 Other changes may be made until proper connec- 
 tions are found for rotation desired, then connect 
 up permanently. 
 
 327. Dynamo Fails to Generate. 
 
 (58) Reversed residual magnetism. 
 
 (A) Reversed current in the field coils. 
 
 (R58a) Send a current from another machine or 
 from a battery through the field coils in the proper 
 
DISEASES OF DIRECT-CURRENT DYNAMOS 291 
 
 direction to correct the fault. Polarity may be 
 tested by a compass needle. If the connections of 
 the windings are not known, try one and test; if 
 not correct, reverse connections, try again, and test. 
 
 (B) Reversed connections. 
 
 (R58b) Connect up properly for rotation desired, 
 referring to the proper diagram of the connections. 
 See that connections for series coils (in compound 
 dynamo) are properly made as well as those for the 
 shunt coils. See number (57). 
 
 (C) Earth's magnetism. 
 (R58c) Same as (R58a). 
 
 (D) Proximity of another dynamo. 
 (R58d) Same as (R58a). 
 
 (E) Brushes not in the proper position. 
 
 (R58e) Shift the brushes until evidence of an im- 
 provement is given. The position of the brushes 
 for best generating power should be clearly under- 
 stood, and is generally at or near the neutral point. 
 
 (59) Too weak residual magnetism. 
 (R59a) Same as (R58a). 
 
 (60) Short-circuit in the machine. 
 
 (R60a) See numbers (12), (54), (55) and (56). 
 
 (61) Short-circuit in the external circuit. 
 
 (R61a) Lamp socket or other part of the line short- 
 circuited or grounded may prevent building up of 
 shunt or compound machines. Locate and remedy 
 the fault before closing switch. See numbers (54), 
 (55), and (56). 
 
 (62) Field coils opposed to each other. 
 
 (R62a) Reverse the connections of one of the field 
 coils and test. Compass should show pole pieces of 
 opposite polarity. If, after such a trial, dynamo does 
 not build up, try (R58a). If the polarity does not 
 then come up in proper direction, cross the field 
 connections or remagnetize them in the opposite 
 direction. See number (58A). 
 
 (63) Open circuit. 
 
 (A) Broken wire. 
 
 (B) Faulty connections. 
 
 (C) Brushes not in contact. 
 
292 PRACTICAL APPLIED ELECTRICITY 
 
 (D) Safety fuse melted or broken. 
 
 (E) Switch open. 
 
 (F) External circuit open. 
 
 (R63a) Locate and repair brake. See number (13). 
 (R63b) See (R58b). 
 (R63c) See (R5a) and (R5b). 
 (R63d) See (R53a). 
 (R63e) Close the field switch. 
 
 (R63f) Test out and repair with the dynamo switch 
 open until the repairs are completed. 
 
 (64) Too great a load on the dynamo. 
 
 (R64a) Reduce the load to pilot lamps alone (shunt 
 or compound machine). After dynamo comes up to 
 full voltage, as shown by pilot lamps, or voltmeter, 
 close the other circuits in succession and regulate 
 the voltage at the same time. See (Rlla). 
 
 (65) Too much resistance in the field regulator or field 
 rheostat. 
 
 (R65a) Gradually turn the regulating switch to cut 
 out the resistance and watch the pilot lamp or volt- 
 meter when the dynamo comes up to voltage, regu- 
 late, etc. 
 
 32IB. General Suggestions and Precautions. Never use ice 
 or water to cool off the bearings, as it may get into the 
 armature and ruin it, unless it has been made waterproof as 
 in the case of street-car motors. 
 
 Never shut down because of hot box until remedies for 
 troubles (25), (26), (28), and (32) have been tried and proved 
 useless. If absolutely necessary to shut down, get the belt 
 off as soon as possible. Do not allow shaft to "stick" in 
 stopping. Get the boxes or bearings out and cool them off 
 naturally as soon as possible and not in water, as this may 
 ruin them. Then scrape, fit, polish, clean the shaft, and test 
 for free turning by hand before belting up and starting again. 
 
 Cleanliness about a dynamo or motor is imperative. Dirt, 
 oil, or copper dust may prove a source of great annoyance or 
 damage. Small tools, bolts, or pieces of iron must be kept 
 away from a dynamo as they may be drawn into or fall upon 
 armature and ruin it. It is always best not to allow loose 
 articles of any kind to be placed upon any portion of a dynamo. 
 
DISEASES OF DIEECT-CUEEENT DYNAMOS 393 
 
 Brass or copper oil cans are best to use as they are non- 
 magnetic. 
 
 All the connections must be large, clean, and firm. Look 
 over and tighten the loose connections, screws or bolts, daily. 
 
 Always keep copper brushes raised from the commutator 
 when the dynamo is at rest. Poor, cheap oil is poor economy. 
 Use none but the best of mineral oils. All new oils should 
 always be filtered before using. 
 
 Keep cotton waste off the commutator. Use canvas or 
 cloth to wipe the commutator. 
 
 A piece of pine makes a good burnisher to use on the 
 commutator to keep it clean and smooth. 
 
CHAPTEE XV 
 
 ELECTRIC LIGHTING 
 
 329. The Electric Lamp. The electric lamp in its broadest 
 sense consists of a part of an electric circuit heated to incan- 
 descence, together with special regulating and controlling 
 devices. Electric lamps may be conveniently classified under 
 three heads, viz, 
 
 (a) Arc lamps (sections 330 to 333, inclusive). 
 
 (b) Glow lamps (sections 334 to 339, inclusive). 
 
 (c) Vapor lamps (sections 340 to 344, inclusive). 
 
 330. The Carbon Arc Lamp. If the ends of two carbon 
 rods that are connected to some source of electrical energy 
 be touched together and then drawn apart, there will be an 
 electric arc formed between them. This arc consists of a 
 column of very hot vapor which serves to conduct the elec- 
 tricity from the end of one rod to the other. The terminals 
 of the two rods will be wasted away as the arc continues to 
 burn, the two rods, however, are not consumed at the same 
 rate always. If the arc be formed by a direct current, the 
 ends of the carbons assume a form similar to that shown in 
 Fig. 238, the end of the positive becoming concave, and the 
 end of the negative pointed. The carbon rod forming the 
 positive terminal of the arc is consumed approximately twice 
 as fast as the rod forming the negative terminal. The cup 
 or concave portion of the positive carbon is called the crater; 
 it is extremely hot and the greater part of the light the arc 
 emits comes from this crater. The point of the negative 
 carbon is not nearly so hot as the crater of the positive 
 carbon, and it does not emit nearly so much light. As a 
 result of this difference in light emitted by the positive and 
 the negative terminals of the direct-current arc, the positive 
 carbon will be placed above the negative so that the light will 
 be cast downward, except in special cases; in the case 
 
 294 
 
ELECTRIC LIGHTING 
 
 295 
 
 of searchlights and projecting lanterns, the arc is arranged 
 as shown in Fig. 239. If the electric arc be formed by an 
 alternating current, the ends of both carbons are heated about 
 the same, the upper carbon being perhaps a little hotter than 
 the lower, due to the upward movement of the heated vapor. 
 As a result of the heating of the ends of the two carbons 
 being approximately equal, the light emitted from them will 
 be approximately the same. The two carbons of an alternat- 
 
 Fig. 238 
 
 Fig. 239 
 
 Fig. 240 
 
 ing current are wasted away approximately the same, the 
 upper one being consumed a little faster than the lower one. 
 An alternating-current arc is shown in Fig. 240. The light 
 emitted by the alternating-current arc lamp is not steady, but 
 pulsates in value with the change in the value of the alter- 
 nating current, there being two pulsations of the light for 
 each cycle of the current. 
 
 A direct-current arc makes practically no noise when it 
 is operating properly, while the alternating-current arc makes 
 a loud humming noise on account of the continuous con- 
 traction and expansion of the heated vapor, due to the varia- 
 tion in the value of the current, and the lamp mechanism 
 often vibrates, due to reversals in magnetism. 
 
 A carbon arc lamp consists of two carbon rods, which have 
 their distance apart controlled by a suitable mechanism that 
 is operated by solenoids, or by hand. 
 
 331. Regulation of Arc Lamps on Constant-Voltage and 
 Constant-Current Circuit. If an electric arc be connected 
 directly to a constant-voltage line, it will be impossible to 
 maintain the arc unless a resistance be connected in series 
 with the arc for the following reason. Assuming the arc is 
 operating satisfactorily on a constant-voltage line and that 
 the current decreases in value, due to an increase in length 
 
396 PRACTICAL APPLIED ELECTRICITY 
 
 Df the arc, caused by the ends of the carbon being consumed, 
 this decrease in current will cause a decrease in the size of 
 the arc unless an additional voltage be applied at the termi- 
 nals of the arc, but the required increase in voltage is not 
 available since the arc is operating on a constant-voltage 
 circuit and, as a result, the lamp would go out almost in- 
 stantly, or before the regulating mechanism has a chance 
 to act and bring the carbons nearer together. When the 
 circuit is once broken at the arc, the ends of the carbons 
 must be placed in contact with each other and then drawn 
 apart to re-establish the arc. 
 
 If the current producing the arc is increased in value, 
 there will be an increase in the size of the arc or a de- 
 crease in its resistance and the constant voltage applied to 
 the terminals of the arc would be more than sufficient to 
 produce the desired current and, as a result, the current would 
 continue to increase in value and would become excessive 
 almost instantly, or before the regulating mechanism has 
 time to operate and thus separate the carbons. 
 
 By placing a resistance in series with the arc, an increase 
 in current will cause an increase in drop over this resistance 
 and a decrease in current will cause a decrease in drop. If 
 the resistance is large enough in value, the change in the 
 drop over the resistance will more than balance the varia- 
 tion in the drop over the arc caused by a change in the cur- 
 rent, and the operation of the arc will be quite stable. A 
 resistance used for the purpose just described is called a 
 ballast. The ballast for alternating-current arc lamps is 
 usually a reactance coil, instead of a resistance, the react- 
 ance coil being formed by winding a coil on a laminated iron 
 core. 
 
 When arc lamps are operated on constant-current circuits, 
 no ballast is required, as the current remains constant re- 
 gardless of the position of the carbons, it being governed by 
 the generator, transformer, or regulator. The drop in poten- 
 tial over the arc, however, must be regulated in a series lamp 
 by means of a solenoid which controls the distance between 
 the carbons. 
 
 332. Multiple Arc Lamps. Multiple arc lamps require only 
 one solenoid for their operation. When the lamp is first 
 started, there is a large current in the circuit, the solenoid 
 
ELECTRIC LIGHTING 
 
 297 
 
 is energized and draws the carbons apart until the decrease 
 in current due to the increase in resistance of the arc weak- 
 ens the solenoid to such an extent that it no longer acts to 
 separate the carbons. If the current decreases in value, the 
 solenoid is weakened, which allows the ends of the carbons 
 to approach each other and the current is restored to its 
 original value, or if the current increases in value, the solenoid 
 acts to separate further the ends of the carbons and thus pre- 
 vent an excessive increase in current. 
 The circuit of a multiple direct-current 
 arc lamp is shown in Fig. 241. The 
 circuit is composed of the ballast or 
 steadying resistance (R),the two regu- 
 lating solenoids (Sj) and (S 2 ), and the 
 arc (A) between the ends of the car- 
 bons. The steadying resistance and 
 the solenoids are so constructed that 
 the number of turns in circuit can be 
 varied by changing a connection from 
 one tap to another on the various 
 coils. The armature (B), controlled 
 by the solenoids, actuates the upper 
 carbon, the lower being stationary. 
 The upper carbon is connected to the 
 positive terminal of the circuit. 
 
 333. Series Arc Lamps. In this 
 type of arc lamp no ballast or react- 
 ance is required in series with the arc 
 since the lamps are connected in 
 series and operate on a constant-cur- 
 rent circuit. The series lamp does not 
 
 regulate automatically, as the multiple lamp does, and a 
 second solenoid whose winding is connected in parallel with 
 the arc is required. The mechanical action of this second 
 solenoid is just opposite that of the solenoid connected in 
 series with the arc. The diagram of a series arc lamp is 
 shown in Fig. 242. When the lamp is first connected in the 
 circuit, the two terminals are connected by means of three 
 paths one through the starting resistance (SR), and the cut- 
 out (CO); a second through the series coil (C), adjusting 
 resistance (AR) and arc in series; and the third through the 
 
 Fig. 241 
 
298 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 winding of the coil (DC), which is called the differential shunt 
 on account of its winding being in shunt with the arc and its 
 action differential with respect to the series coil. The two 
 terminals of the lamp may be connected directly together 
 by closing the switch (S) which is usually located in the 
 top of the lamp. 
 
 The operation of this lamp, 
 which is typical of all series arc 
 lamps, is as follows: The series 
 solenoid is energized as soon as 
 the lamp is connected in circuit, 
 and the action of this solenoid 
 will draw the ends of the car- 
 bons apart, starting the arc and 
 opening the cut-out (CO). As 
 the carbons are drawn apart, the 
 arc voltage increases and the 
 current in the shunt solenoid 
 (DC) increases, and its action 
 tends to bring the carbons to- 
 gether, but it does not overcome 
 the action of the series coil 
 (SC), which tends to separate 
 the carbons. As a result of 
 these two solenoids acting at the 
 same time, the arc is adjusted so 
 that it takes a definite current, 
 and a definite voltage exists 
 
 across it. When the carbons are consumed, the shunt solenoid 
 brings them nearer together, as its current has increased, due 
 to the increase in voltage over the arc, and the current in the 
 series coil remains approximately constant. This action con- 
 tinues until the cut-out (CO) is closed and the current is 
 shunted through it. The shunt solenoid (DC) is short-cir- 
 cuited by the cut-out closing and there is no current in the 
 series solenoid (SC), the upper carbon is released and the two 
 come together. When the end ot the two carbons come to- 
 gether, the current is re-established in the series solenoid and 
 the lamp again picks up. If the carbons be entirely consumed, 
 the cut-out remains closed and the circuit of which the 
 
 Fig. 242 
 
ELECTEIC LIGHTING 299 
 
 lamp is a part is not opened, even though the lamp is not 
 operating. A dash pot (DP) dampens the movement of the 
 armature of the solenoids, which greatly improves the opera- 
 tion of the lamp. In some types of series arc lamps the 
 shunt and series windings are both placed on the same 
 spool instead of on two different ones, as shown in Fig. 242. 
 
 334. Glow Lamp. In all glow lamps the light is emitted 
 from a solid electrical conductor that is heated by an elec- 
 trical current to such a temperature that it emits light. The 
 lamps included under this head are the ordinary carbon-fila- 
 ment lamps, the different metal-filament lamps, such as 
 tungsten and tantalum, and the Nernst lamp. 
 
 335. Carbon-Filament Lamp. The common carbon-filament 
 incandescent lamp consists of a fine filament of carbon 
 mounted in a highly exhausted glass bulb, which may assume 
 a number of different forms, depending upon the particular 
 use of the lamp. The carbon filament is connected to the 
 external circuit by means of two short pieces of platinum 
 that are embedded in the glass. Platinum is used for mak- 
 ing these connections on account of it being capable of 
 withstanding a high temperature and it contracts and ex- 
 pands due to changes in temperature the same as glass, 
 which is quite an advantage in maintaining the vacuum in 
 the bulb containing the filament. 
 
 The method usually employed in the manufacture of the 
 carbon filament is as follows: Some of the fibrous sub- 
 stances such as cotton are thoroughly cleansed and then dis- 
 solved in a solution of zinc chloride by constant stirring, 
 forming a thick fluid which is freed from lumps by filtering 
 and from bubbles by heating almost to the boiling point under 
 pressure. This fluid is then "squirted" through a small hole 
 and allowed to pass into an alcohol bath, which immediately 
 hardens the gelatinous rod which can then be thoroughly 
 washed in water. This thread has the appearance of celluloid, 
 it is fairly tough, and may be cut into lengths and bent on 
 formers into any shape desired. They are then packed in 
 charcoal and carbonized in a furnace, after which they are 
 mounted on the platinum wires that are to form the terminals 
 and heated electrically by a current to a high temperature in a 
 vapor of hydrocarbon. The hydrocarbon vapor is decomposed 
 by the hot filament, which results in a deposit of carbon on 
 
300 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 the filament. This deposit will be greatest at the hotest 
 points in the filament, which will be at the points of highest 
 resistance, or smallest cross-section and, as a result, the fila- 
 ment is made more uniform in cross-section, and its resist- 
 ance slightly lowered, due to the increase in area. The above 
 process is called flashing. The completed filament is placed 
 in a glass bulb, which is exhausted by means of special 
 pumps and sealed. A mounting suitable to screw into a 
 lamp socket is then mounted on the bulb and the terminals 
 of the filament connected to the two parts of the mount- 
 ing, which make electrical contact with the two terminals of 
 the line when the lamp is screwed into the socket. 
 
 The resistance of a carbon filament when working under 
 normal conditions is approximately half what it is at ordi- 
 nary temperatures. 
 
 336. Metalized Carbon-Filament or 
 Gem Lamp. The filaments used in the 
 so-called metalized carbon-filament 
 lamps are carbon filaments that have 
 been subjected to an enormously high 
 temperature, both before and after 
 flashing, by means of a specially con- 
 structed electric furnace. The term 
 "metalized" is used on account of the 
 filaments acquiring a positive tempera- 
 ture coefficient when subjected to very 
 high temperatures. 
 
 337. Tantalum Lamp. The tantalum 
 lamp was invented by Dr. Bolton 
 chemist for Siemens and Halske who 
 discovered the peculiarities of tantalum 
 and the methods of obtaining the pure 
 metal. Tantalum is obtained by special 
 
 processes from the ores tantalite and columbite, the tantalite 
 being found principally in Australia and the columbite in 
 New England. Filaments of the desired size are drawn from 
 the pure ductile tantalum. The melting temperature of tan- 
 talum is approximately 2800 centigrade and its resistance 
 increases with a rise in temperature. The tensile strength 
 of tantalum is very high when cold, but when heated it be- 
 comes soft and after the filament has been burning a few 
 
 Fig. 243 
 
ELECTEIG LIGHTING 301 
 
 hours it becomes very brittle, which is the great disadvan- 
 tage of this kind of a filament. The filament of a tantalum 
 lamp to operate on a 110-volt circuit is a great deal longer 
 than the carbon filament, and special means must be provided 
 for mounting those long filaments, such as shown in Fig. 243. 
 
 The tantalum lamp gives a much whiter light than the 
 carbon-filament lamp on account of the high temperature 
 at which it operates. The life of a tantalum lamp is a great 
 deal less on an alternating-current circuit than it is on a 
 direct-current circuit and its life on an alternating-current 
 circuit depends upon the frequency. 
 
 338. Tungsten Lamp. The latest form of metallic-filament 
 lamp placed on the market is the tungsten lamp. It has only 
 been commercially used for about three years, but even in 
 that short time it has attained the highest position in the 
 field of incandescent lighting. 
 
 Tungsten is not a rare metal, having been used for a num- 
 ber of years in the manufacture of tool steel and armor 
 plate. Owing to the fact that as hitherto produced the metal 
 was very hard and brittle, it has not until recently been 
 obtained in a ductile form and consequently was not drawn 
 into wire as was tantalum. It has a very high melting point 
 about 3050 C. which allows the lamps to be operated at 
 the relatively high efficiency of 1.25 w.p.c. and even higher. 
 This makes the light emitted very much nearer a pure white 
 than any other incandescent lamp which has yet come into 
 commercial use. 
 
 There are four methods of forming the tungsten filament, 
 but the one in most general use in this country is the Auer, 
 or paste, process. This process starts with a pure tungstic 
 acid, obtained from some one of the various tungsten ores, 
 such as wolframite or scheelite. Tungstic acid is a yellow 
 powder, which must undergo several processes of purifica- 
 tion and reduction before it is finally reduced to the pure 
 metal. This metal is used in the form of a fine black pow- 
 der, which is mixed with a binding material in order to 
 form a putty-like mass that can be squirted through a very 
 small die, even as small as one-thousandths of an inch. A 
 die is very expensive, being made from a diamond, through 
 which a hole is drilled with a fine flexible steel needle. Its 
 life is very short on account of the wear which the hard 
 
302 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 metal gives the diamond and the enormous pressure of 30000 
 pounds per square inch, under which the filament is formed. 
 Thus only enough filaments for 1500 lamps can be formed 
 before the die is so badly worn that it must be rebored for 
 the next larger size filament, an operation which costs al- 
 most as much as a new die. 
 
 The filament while being squirted is looped back and forth 
 on a card, which, when filled, is laid aside to allow the fila- 
 ment time to dry. After drying, the filaments are cut into 
 loops, which resemble in shape the finished filaments. These 
 loops are placed in a tube furnace and baked at a cherry red 
 heat in an atmosphere of gas which contains no oxygen. 
 After baking for some time the more volatile constituents 
 of the binder are found to have been driven off and the fila- 
 ments are ready to be "formed." 
 
 _ They are now connected into an 
 
 electrical circuit by means of clips 
 and are gradually heated in an at- 
 mosphere of inert gas, until incan- 
 descence is reached, when the re- 
 maining binding material is volatil- 
 ized, leaving the pure metal fila- 
 ment. This last process causes the 
 filament to shrink somewhat, which, 
 however, has been allowed for in the 
 previous operations. 
 
 The formed filament is now 
 
 mounted on the center support and the two ends are welded 
 to the supporting wires in an atmosphere of forming gas. 
 After sealing the mount into the tubulated bulb, the lamp 
 follows practically the same process of exhaustion as the 
 tantalum lamp. 
 
 There has been recently discovered a means whereby tungs- 
 ten is rendered ductile, and wire-drawn filaments are the re- 
 sult. Tungsten wire has a tensile strength varying from 
 400 000 to 600 000 pounds per square inch, a value three to 
 four times that attained by tantalum wire. This wire can be 
 bent into any form and consequently can be mounted in such 
 a manner as to be more capable of withstanding shocks than 
 was possible with a filament made by the paste process. 
 
 Glower 
 Fig. 244 
 
ELECTEIC LIGHTING 
 
 303 
 
 EDI80N ***! 
 
 339. Nernst Lamp. The filament or glower of a Nernst 
 lamp consists of a small rod of porcelain-like material com- 
 posed of the oxides of zirconium and yttrium. This rod is a 
 good insulator at ordinary temperatures, but becomes a very 
 good conductor at a low red heat, and its resistance decreases 
 very rapidly as the temperature rises. If such a glower is 
 to be used some means must be provided for heating it until 
 it will become a conductor in starting the lamp, and a bal- 
 last resistance must be cdn- 
 nected in series with the 
 glower to prevent the current 
 becoming excessive after the 
 glower has started to con- 
 duct. A diagram of a single 
 glower lamp is shown in Fig. 
 244. When the lamp is first 
 connected to the line, the cir- 
 cuit is completed through the 
 heater coil and cut-out. As 
 the temperature of the glow- 
 er is raised, due to the action 
 of the heater, its resistance 
 is lowered, which permits the 
 
 ARMATURE SUPPORT 
 
 L.POST 
 
 BALLAST 
 CUT OUT COIL 
 ARMATURE 
 
 ^T^C: SILVER CONTACT STOP 
 - HOUSING 
 
 "CONTACT SLEEVE PORCELAIN 
 
 GLOBE HOLDING SCREW 
 
 HOLDER PORCELAIN 
 HEATER PORCELAIN 
 HEATER TUBE 
 
 Fig. 243 
 
 electricity to pass through 
 the glower, ballast, and cut- 
 out coil all in series. After a short time this current will 
 reach a value, due to decrease in the resistance of the glower, 
 sufficient to operate the cut-out and thus disconnect the heater, 
 and the glower will become incandescent. The ballast is com- 
 posed of fine iron wire placed inside of an exhausted glass 
 tube to prevent the iron oxidizing when it is heated. This 
 ballast increases in resistance with an increase in tempera- 
 ture, due to an increase in current and, as a result, automat- 
 ically tends to maintain the current constant. A Nernst lamp 
 is shown complete in Fig. 245. 
 
 340. Vapor Lamp. In the different forms of vapor lamp 
 the light is emitted from an incandescent or luminescent 
 column of vapor that conducts the electricity. The lamps 
 included under this head are the flaming-arc lamps, mercury- 
 vapor lamps, and the Moore tube. 
 
304 PRACTICAL APPLIED ELECTRICITY 
 
 341. Flaming Arc. In the carbon arc lamp the greater 
 part of the light is emitted from the ends of the intensely 
 heated carbons, the arc itself emitting only a pale violet 
 light. If the carbons between which the arc is formed be 
 impregnated with metallic salts, or rods of metal, or metal 
 oxide be used instead of carbon, an arc will be formed which 
 is highly charged with metal vapor. The light emitted by 
 such an arc comes mostly from the incandescent particles in 
 the metal vapor, very little coming from the terminals ot 
 the rods forming the arc. Arc lamps employing impregnated 
 carbons or metal rods instead of carbons to form the arc 
 are known as flaming arcs. 
 
 One of the materials most commonly used in combination 
 with carbon is calcium, which gives the light emitted by the 
 arc a highly brilliant yellow color. Carbons impregnated 
 with stroncium give a red light, and those impregnated with 
 titanium or barium give a white light. There are many 
 different forms of electrodes for the flaming arc lamps, con- 
 sisting of different metals and combinations. 
 
 342. Bremen Flaming-Arc Lamp. The Bremer lamp is one 
 of the oldest and is the most efficient of the different flam- 
 ing arc lamps on the market. The carbons in this lamp are 
 placed parallel or slightly inclined to each other, instead of 
 being placed in the same plane with their axes coinciding, 
 which results in a larger arc being formed between them. 
 This arrangement of the carbons gives the lamp an additional 
 advantage over the other arrangement, since there is no 
 lower carbon in the path of maximum illumination. In the 
 construction of the lamp, a magnet is provided which creates 
 a magnetic field that acts on the arc and deflects it down- 
 ward, thus preventing its climbing up the carbons, and at the 
 same time giving a longer and larger arc and a better 
 distribution. 
 
 343. Mercury-Vapor Lamp. The mercury-vapor lamp con- 
 sists of a highly exhausted glass tube with two platinum 
 wires sealed in its ends. One of these wires is connected 
 inside the tube to a piece of iron or graphite that forms the 
 anode and the other is connected to a pool of mercury that 
 forms the cathode. In starting such a lamp a high electro- 
 motive force or a special starting device is required, but 
 after the lamp is once started a current of several amperes 
 
ELECTRIC LIGHTING 
 
 305 
 
 can be easily maintained by a pressure of from 30 to 100 
 volts. The mercury vapor in the tube gives off a bright 
 light that is deficient in the longer wave-lengths, or red. The 
 lack of the longer wave-lengths results in an unpleasant 
 distortion of color. 
 
 The lamp may be started by tilting the tube, it being nor- 
 mally at an angle to the horizontal, which allows the mercury 
 to extend from one end to the other and complete the cir- 
 cuit, and the circuit is maintained through the mercury vapor 
 when the metallic mercury circuit is broken by the tube be- 
 
 Fig. 246 
 
 ing allowed to return to its normal position. A spark may be 
 caused to pass through the tube, due to the action of an in- 
 duction or kick coil which ruptures the medium and starts 
 the lamp. A third means of starting is to place an auxiliary 
 positive electrode near the negative electrode to be used in 
 starting and the connection is then transferred to the other 
 positive electrode after the lamp is started. 
 
 The lamp is operated on alternating current by connect- 
 ing the negative electrode of the lamp to the middle point 
 of a transformer winding and having two positive electrodes 
 located at the same end of the tube and connected to the 
 
306 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 two ends of the transformer winding. A mercury-vapor lamp 
 is shown complete in Fig. 246. 
 
 344. Moore Tube. The Moore tube resembles the mer- 
 cury-vapor lamp in that it consists of a conducting vapor en- 
 closed in a glass tube and the light is emitted from incan- 
 descent particles in the vapor stream. The tube from which 
 the light is emitted may be of any length up to about 200 
 feet, of any desired form, and its diameter may be as large 
 as 1% inches. Two graphite electrodes are sealed in the 
 ends of this tube, which is filled with air, carbon dioxide, 
 nitrogen, or other suitable gas. The secondary winding of a 
 
 Fig. 247 
 
 Fig. 248 
 
 transformer is connected to the graphite terminals in the 
 ends of the tube, the primary winding being connected to 
 the source of power, as shown in Fig. 247. The vacuum in 
 the tube becomes more and more perfect, which decreases 
 the efficiency of the lamp, and some means must be provided 
 for regulating the vacuum, which is done as follows: A 
 separate tube (t) projects downward from the main one, 
 as shown in Fig. 247, and is connected with what is called a 
 feeder valve. This feeder valve, shown more in detail in 
 Fig. 248, consists of a solenoid connected in series 
 with the primary winding of the transformer. The iron 
 plunger (I) is fastened in a glass displacement tube and it 
 is raised or lowered, due to a change in the current in the 
 solenoid. In the end of the tube (t) there is cemented a 
 carbon plug with a very small opening in it, which is nor- 
 
ELECTKIC WIRING 307 
 
 mally covered with mercury. If the displacing tube be moved 
 up, due to the action of the solenoid, the mercury recedes, 
 uncovering the opening in the carbon plug and allowing a 
 small amount of gas to enter the tube. 
 
 With an increase in vacuum there is a decrease in resist- 
 ance and an increase in current in the secondary winding 
 of the transformer, and also a corresponding increase in 
 current in the primary winding. This increase in current 
 causes the feeder valve to operate and the vacuum is re- 
 stored to normal by admitting gas. The secondary voltage 
 required will depend upon the length of the main tube. 
 
 345. Units of Illumination. The luminous intensity of a 
 source of light is measured by comparing it with a source of 
 unit intensity, and the unity commonly employed for meas- 
 uring luminous intensity is the candle-power. The unit of 
 candle-power is equal to 1.111 hefner units. 
 
 The Hefner lamp, so-called from its inventor, is a specially 
 constructed lamp that burns pure amyl acetate. The wick 
 and the tube holding the wick are of definite dimensions and 
 in using the lamp the wick is adjusted so that the flame is 
 a prescribed height. The intensity of a beam of light in a 
 horizontal plane from such a lamp is called a hefner unit or a 
 hefner. 
 
 The illumination or the amount of light falling on an ob- 
 ject is measured in a unit called the foot-candle. A foot- 
 candle is the normal illumination produced by one unit of 
 candle-power at a distance of one foot. 
 
 The mean horizontal intensity is the average intensity in 
 all directions in a horizontal plane that passes through the 
 source of light. In the case of incandescent lamps this plane 
 is taken perpendicular to the axis of the lamp. 
 
 The mean spherical candle-power is the average candle- 
 power taken in all directions around the source of light. 
 
 346. Photometry. The measurement of light emitted by 
 a lamp is called photometry. This is always accomplished 
 by comparing the beam of light from a given lamp with the 
 beam of light from a standard lamp, and the device used for 
 making this comparison is called a photometer. The inten- 
 sity in different directions can be measured by placing the 
 lamp in different positions with respect to the photometer. 
 Lighting measurements are all based upon the law of in- 
 
308 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 verse squares, which can be explained by reference to Fig. 
 249. A source of light is shown at (L) and four rays of 
 light (Ri), (R 2 ), (R 3 ), and (R 4 ) are shown emanating from 
 (L) and forming a pyramid. Three cross-sections through 
 this pyramid and perpendicular to its axis are shown at (A), 
 (B), and (C). These three cross-sections and the light (L) 
 are all equally spaced and, as a result, the cross-section (B) 
 is four times that of (A), and (C) is nine times that of (A), 
 etc., or the cross-sections between the four rays increase as 
 the square of the distance the cross-sections are from the 
 source of light. Since the same total number of rays pass 
 through each area, the intensity per unit of area varies in- 
 
 Fig. 249 
 
 x, 
 
 Fig. 250 
 
 versely as the square of the distance from the source of light. 
 
 The Bunsen photometer is one of the oldest and simplest 
 forms of photometers and also one of the most efficient means 
 of comparing the intensities of different sources of light. The 
 construction of this photometer can best be explained by ref- 
 erence to Fig. 250. A sheet of white paper, the center por- 
 tion of which is made transparent by being treated with 
 paraffin or some other similar substance, is mounted inside 
 a box (B), as shown in the figure. This sheet of paper is 
 called the screen (C) of the photometer. 
 
 The two sides of this screen are viewed simultaneously 
 through the sight piece (S) by the aid of the two mirrors 
 (Mj) and (M 2 ) which are so mounted that they make an angle 
 of about 140 degrees with each other and equal angles with 
 the plane of the screen. The light falling on either side of 
 
ELECTRIC LIGHTING 309 
 
 this screen is not all reflected, a part passing through the 
 translucent spot in the center. When the illumination on 
 both sides of the screen is the same, an equal amount of 
 light is transmitted through the screen in both directions, 
 and if the lights on the two sides are of the same hue the 
 spot in the center and the remainder of the screen should 
 appear of the same color. 
 
 The photometer is used as follows: Two lamps, whose in- 
 tensities are to be compared, are located a known distance 
 apart on what is known as the photometer bench. The box 
 (B), Fig. 250, is placed between the two lamps so that its 
 axis (XiXo) coincides with the line connecting the cen- 
 ters of the two sources of light and so arranged that it can 
 be moved along this line. It is then moved until the two 
 parts of the screen have the same appearance. When this 
 balance is obtained, the distance the center of each source 
 of light is from the screen is determined and the relation 
 of the intensities is calculated by applying the law of inverse 
 squares given above. If the candle-power of one lamp is 
 known, the candle-power of the other one can be easily de- 
 termined, as follows: 
 
 Let (S s ) represent the candle-power of the standard lamp. 
 
 Let (S x ) represent the candle-power of the lamp being 
 tested. 
 
 Let (D s ) represent the distance the screen is from the 
 standard lamp. 
 
 Let (Dx) represent the distance the screen is from the lamp 
 being tested. 
 
 Sx D S 2 
 Then 
 
 S s D X 2 
 
 D S 2 
 and Sx= S s (126) 
 
 347. The Specific Consumption of Lamps. The specific 
 consumption of a lamp in practice is always specified by giv- 
 ing the watts consumed in the lamp per spherical candle- 
 power of light emitted. The specific consumption of different 
 types of lamps is given in Table X. 
 
310 PRACTICAL APPLIED ELECTRICITY 
 
 TABLE NO. X. 
 
 APPROXIMATE SPECIFIC CONSUMPTION OF DIFFERENT TYPE 
 
 LAMPS 
 
 Watts per Mean 
 Spherical Candle- 
 Type of Lamp Power Remarks 
 
 Direct-current series 1.0 
 
 Direct-current multiple 2.4 
 
 Alternating-current series... 1.7 No outer globe 
 
 Alternating-current multiple. 2. 5 No outer globe 
 
 D. C. Bremer flaming arc... .196 48 volts over arc 
 
 A. C. Bremer flaming arc... .226 48 volts over arc 
 
 Carbon-filament lamps 3.0 to 3.5 
 
 Tantalum lamps 1.8 to 2.2 
 
 Tantalum lamps 1.8 Direct current 
 
 Tungsten 1.25 
 
 Nernst 2.95 Six glower 
 
 Nernst 3.92 Single glower 
 
 Mercury-vapor 48* See note (A) 
 
 Moore tube 1.7* See note (B) 
 
 Note (A) : The candle-power is measured perpendicular 
 to the axis of the tube. 
 
 Note (B) : This value corresponds to a vacuum in the 
 tube of approximately .10 millimeters of mercury. 
 
 348. Distribution Curves. The distribution of light from 
 a source through any plane and in different directions can 
 be represented graphically, and such a graphical representa- 
 tion is called a distribution curve. The distribution curve, 
 about a four-candle-power lamp in a vertical plane, is shown 
 in Fig. 251. The intensity in different directions being pro- 
 portional to the distance, the curve is from the center. The 
 form of the filament, bulb, shades, and reflectors all have an 
 influence in determining the shape of the distribution curve. 
 
 349. Calculation of illumination. If a 16-candle-power 
 lamp (L) be placed 8 feet from the plane (A), as shown in 
 Fig. 252, the illumination per unit area on the plane (A) at 
 the point (B) would be equal to (16-^-82) = 14 foot-candle, 
 since the intensity varies inversely as the square of the 
 distance. In general, to get the illumination at any given 
 
 *Watts per candle-power. 
 
ELECTEIC LIGHTING 
 
 311 
 
 point, the candle-power in the direction measured must be 
 divided by the square of the distance from the light to the 
 point illuminated. 
 
 When the surface illuminated is not at right angles to the 
 light, the values of illumination obtained above must be mul- 
 tiplied by a reduction factor, which takes into account the 
 angle at which the rays of light strike the surface, Thus, 
 
 ~Fis. 251 
 
 if a lamp (V) be placed 8 feet above the horizontal plane 
 (H), as shown in Fig. 253, and it is desired to determine 
 the illumination at the point (B), 6 feet from the vertical 
 line through the lamp, you should proceed as follows: The 
 distance (0 the point (B) is from the lamp is equal to 
 
 I = V/V2 + h2 
 
 The value of (?) in Fig. 253 is equal to 
 1= V82 + 62 = 10 
 
 Assuming the intensity of the light from the lamp (L) along 
 the line (I) is 20 candle-power, then the illumination on a 
 surface (P) at the point (B) perpendicular to the line 
 (I) would be equal to 
 
 20 1 
 
 Illumination = = foot-candle 
 
 102 5 
 
PRACTICAL APPLIED ELECTRICITY 
 
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ELECTEIC LIGHTING 
 
 313 
 
 The illumination of } foot-candle on the surface (P) is to 
 be distributed over a larger area when the horizontal plane 
 is considered. The ratio of the illumination per unit of area 
 on the horizontal plane to the il- 
 lumination per unit area on the 
 plane (P) is equal to the inverse 
 ratio between a unit area in the 
 plane (P) and the projection of this 
 unit area on the horizontal plane. 
 This ratio is equal to the cosine of 
 
 ft 8 Feet 
 
 I 
 
 B 
 
 /B7 
 
 Fig. 252 Fig. 253 
 
 the angle between the plane (P) and the horizontal plane, 
 which is the same as the angle between (I) and a vertical 
 line through the lamp. The constants by which the intensity 
 in candle-power along the line (0 must be multiplied to 
 obtain the illumination on the horizontal for different values 
 of (h) and (v) are given in Table No. XI. The illumination 
 on the horizontal plane for the above example would be 
 equal to 
 
 20 X .008 015 = .1603 foot-candle 
 
 When the source of light consists of a number of lamps, the 
 illumination for each lamp can be determined and the re- 
 sultant illumination obtained by addition. 
 
 TABLE NO. XII 
 
 REQUIRED ILLUMINATION FOR VARIOUS CLASSES OF SERVICE 
 
 Intensity of 
 Illumination 
 Class of Service in Foot-Candles 
 
 General illumination of residences 1 to 2 
 
 Reading 1 to 3 
 
 Auditoriums and theaters 1 to 4 
 
 Churches 2 to 4 
 
 Bookkeeping and clerical work 3 to 5 
 
 General illumination of stores 2 to 5 
 
 Engraving and drafting 5 to 10 
 
 Street lighting by electricity 05 to .06 
 
314 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 The illumination required for various classes of service is 
 given in Table No. XII. 
 
 350. Shades, Reflectors, and Diffusers. Often the distribu- 
 tion from a source of light is undesirable and the intrinsic 
 brilliancy of the source may be too great for the best effect 
 
 135* 
 
 150 
 
 Fig. 254 
 
 or greatest comfort, which results in the use of shades, re- 
 flectors and diffusers. A shade is used to modify the light 
 and is placed between the source and the eye. It may act 
 
 as a reflector or diffuser. A 
 reflector serves to re-direct 
 the light and thus change 
 the distribution, and it may 
 act as a shade in certain 
 directions. A diffuser is 
 intended to decrease the 
 intrinsic brilliancy and to 
 reduce the glare, and in so 
 doing act as a shade or 
 reflector. The arc lamp is 
 usually enclosed in two 
 globes when used for in- 
 terior lighting, in order to reduce the intrinsic brilliancy. The 
 change in shape of the distribution curve, shown in Fig. 251, 
 due to the use of a holoplane reflector, is shown in Fig. 254. 
 The reflector and lamp are shown in Fig. 255. 
 
 351. The Effect Different Colored Walls Have Upon the 
 General Illumination. In rooms not larger than approxi- 
 
 Fig. 255 
 
ELECTRIC LIGHTING 315 
 
 mately 15 feet by 15 feet, the color of the walls will have 
 considerable effect upon the general illumination when the 
 lamps are used without shades or reflectors. The effective 
 illumination in rooms with different colored walls is obtained 
 by multiplying the illumination given directly by the lamp 
 by the factor given in Table No. XIII. 
 
 TABLE NO. XIII 
 FACTORS FOR OBTAINING EFFECTIVE ILLUMINATION 
 
 Illumination 
 Color Wall Factor 
 
 White paper 3.3 
 
 Orange paper. 2.0 
 
 Yellow paper 1.67 
 
 Yellow painted wall 1.67 
 
 Pink paper (light) 1.56 
 
 Green paper (emerald) 1.22 
 
 Brown paper (dark) 1.15 
 
 Blue-green paper 1.14 
 
 Chocolate paper (deep) 1.04 
 
CHAPTER XYI 
 
 ELECTRIC WIRING 
 
 352. Wiring in General. The term "electric wiring" is 
 usually considered to mean the proper placing of electrical 
 conductors to form a complete metallic circuit for conducting 
 the electrical energy to and from the points where it is gen- 
 erated and consumed. The above use of the term, however, 
 is rather narrow and it should include in addition to the 
 proper placing of the electrical conductors, the calculation of 
 the proper size of conductors to meet given requirements; the 
 selection of the proper materials; a consideration of the 
 proper location of the service mains, meters, outlets for 
 lamps, panel boards, switches, controlling devices, etc., and a 
 thorough understanding of the requirements of the inspection 
 department under whose jurisdiction the work is being done. 
 
 353. Factors Determining the Size of Conductors. The 
 problem in electric wiring is the transmission of a certain 
 amount of energy from one point to another, and it is usually 
 desired that this transmission be effected with a minimum 
 loss and at the same time keep the initial cost within a rea- 
 sonable value. 
 
 The drop in electrical pressure between any two points 
 connected by an electrical conductor is equal to the product 
 of the current in the conductor connecting the two points and 
 the resistance of the conductor, or volts drop equals (R X I). 
 This drop in pressure in volts multiplied by the current in 
 amperes gives the value of the power loss in watts in the 
 conductor, or power loss in watts equals (R X I) times (I), 
 which equals (I 2 R). The current in a conductor forming part 
 of the circuit connecting a given load to its source of energy 
 is fixed by the voltage of the generator and the resistance 
 of the load. Since the value of the current in the expression 
 for the power loss in a conductor is to be fixed for any given 
 
 316 
 
ELECTRIC WIRING 317 
 
 voltage, the only way to reduce the loss is to reduce the value 
 of the resistance (R). 
 
 The resistance of a conductor composed of a given material 
 and at a constant temperature varies directly as the length 
 and inversely as the cross-sectional area. The length of a 
 conductor connecting a load and generator is usually deter- 
 mined by the distance between them (in some cases the 
 conductor may be a great deal longer than this distance on 
 account of its not following a direct path), and, as a result, the 
 resistance can be reduced only by an increase in the cross- 
 section of the conductor. An increase in cross-section, the 
 length remaining constant, means a like increase in weight, 
 and hence an increase in cost. The loss in the conductors 
 in any circuit may be made very small by an increase in their 
 cross-sections, but, as pointed out above, the cost of the con- 
 ductors is increasing at the same time the loss is decreasing. 
 In practice, a reasonable loss, usually expressed in per cent, 
 is allowed and the size of the conductor required to carry the 
 current is figured from this value. 
 
 Neglecting the loss in the conductors, there is another 
 important factor to consider in the determination of the 
 proper size of conductors to use, and that is the allowable 
 rise in temperature of the conductor caused by the loss in 
 it. The rise in temperature due to a given loss will depend 
 upon the rate at which the heat generated in the conductor 
 is radiated, which in turn will depend upon its insulation and 
 mechanical protection. The allowable current-carrying ca- 
 pacity for different size copper wires has been established 
 by the Underwriters, and Table G, Chapter 20, gives a 
 complete set of these values. It must be understood that 
 the percentage drop in voltage is not taken into account in 
 this table. 
 
 In some cases the size of the conductor is determined by 
 the mechanical requirements; it, however, should never be 
 smaller than the size determined by the electrical require- 
 ments. 
 
 354. Choice of Material to Use as a Conductor. From the 
 standpoint of loss in the line, the choice of a material to use 
 as a conductor is governed by its resistance. In order that 
 the loss be small, the specific resistance must be low. This, 
 however, does not mean that the materials of lowest specific 
 
318 PRACTICAL APPLIED ELECTRICITY 
 
 resistance will be used, as their cost may be a great deal 
 more than that of some material having a higher specific 
 resistance. If the specific resistance of a material which we 
 shall caH (A) is twice that of a material which we shall call 
 (B), and the cost of the material (A) per unit volume is 
 just one-half that of material (B), then the cost of the two 
 conductors, one each of the (A) and (B) materials, of the 
 same length and having the same resistance, will be the same. 
 As far as the loss in the conductors and the initial cost are 
 concerned, there would be no choice in the above case. The 
 conductor composed of material (A) would be larger than 
 the one composed of material (B), and more material would 
 be required to insulate it; a larger conduit would be required 
 to accommodate it if it be placed in a conduit; and it would 
 be bulkier and more than likely harder to handle. The tensile 
 strength of one material might be such that it would not 
 meet the mechanical requirements although it fulfills the 
 electrical requirements. Thus a long span across a stream 
 would be made of steel wire on account of its high tensile 
 strength and not for electrical reasons. The material that 
 seems to meet best all the requirements for a conductor, 
 except in special cases, is copper, and for this reason copper 
 is usually used. The supply of copper and its cost are also in 
 its favor as compared to silver, which is electrically better. 
 
 355. Calculation of the Resistance of a Conductor. The 
 resistance of any conductor (neglecting changes in tempera- 
 ture) can be determined if its dimensions and the value of the 
 specific resistance of the material composing it are known. 
 The equation used in making this calculation is 
 
 Kl 
 
 R - (127) 
 
 d2 
 
 In the above equation (K) represents the mil-foot resistance, 
 or it is the resistance of a portion of the conductor one foot 
 in length and having a circular cross-section one-thousandth 
 of one inch in diameter; (I) is the length of the conductor 
 in feet; and (d) is the diameter of the conductor in mils (the 
 mil is equal to the one-thousandth part of one inch). 
 
 Example. Calculate the resistance of a conductor, com- 
 posed of commercial copper having a mil-foot resistance of 
 
ELECTEIC WIEING 319 
 
 (10.8), 500 feet in length, and having a diameter of 325. mils. 
 (This corresponds to a No. 0, B. & S. gauge wire). 
 
 Solution. Substituting in equation (127), the values of (K), 
 (t) and (d) given in the problem, gives 
 10.8 X 500 
 
 R = = .05112 
 
 325 X 325 
 
 Ans, .05112 ohm. 
 
 If the length of a circuit is given, the value of (Z) to sub- 
 stitute in equation (127) is equal to twice the length of the 
 circuit; or if the length of the circuit be represented by the 
 letter (L) the value of (I) is equal to (2L). 
 
 356. Calculation of Size of Conductor When Allowable Drop 
 and Current Are Given. If the drop in potential (E), in volts, 
 that is to occur in any circuit when there is a definite cur- 
 rent in the circuit, and the current of (I) amperes are both 
 given, the resistance of the circuit in ohms is equal to 
 
 E 
 R = (128) 
 
 I 
 
 Knowing the resistance of the circuit and its length, the size 
 of the conductors required can be determined by substituting 
 in the following equation: 
 
 I X K X 2L 
 d2 = (129) 
 
 Since from equation 
 
 and from equation (127) 
 
320 PRACTICAL APPLIED ELECTRICITY 
 
 i 
 and 
 
 I X K X 2L 
 
 E 
 
 Example. The voltage at the terminals of a generator is 
 112 volts, and it is desired to transmit 50 amperes over a 
 circuit 450 feet in length with a drop in voltage not to exceed 
 two per cent. What size of conductor is required if it be 
 composed of copper having a mil-foot resistance of 10.8? 
 
 Solution. Tbe drop in voltage (E) is equal to two per cent 
 of 112, or 
 
 E = .02 X 112 = 2.24 volts 
 
 Substituting the value of (E) just obtained, and the value of 
 (I), (L), and (K) in equation (129), gives 
 50 X 10.8 X 2 X 450 
 
 2.24 
 Solving this equation, gives 
 
 d2 = 215 170 
 and 
 
 d = 464 mils 
 
 Referring to a table giving the diameters of different size wire 
 you will find a No. 0000 B. & S. gauge is the size having 
 a diameter practically the same as the value just obtained. 
 In case the value of (d) obtained is less than the diameter of 
 a No. 14 wire, the No. 14 wire should always be used, or in 
 no case use a wire smaller than No. 14, B. & S. gauge, except 
 in the wiring of fixtures. 
 
 Tables L, M, and N, Chapter 20, give the proper size 
 conductors to use on 50-, 110-, and 220-volt circuits, when 
 the distance to the center of distribution and the current the 
 conductor is to carry are given, the loss in each case being 
 two per cent. The following example will illustrate the use 
 of the tables: 
 
 Example. A current of 100 amperes is to be supplied to a 
 number of incandescent lamps from a generator whose ter- 
 minal voltage is 220 volts with a loss not to exceed two per 
 cent. What size conductor should be used when the gen- 
 erator and lamps are 200 feet apart? 
 
 Solution. Referring to Table N, Chapter 20, and pass- 
 
ELECTRIC WIEING 321 
 
 ing along the horizontal lire corresponding to 100 amperes 
 until you strike the vertical column headed 200, which cor- 
 responds to the distance to the center of distribution, you 
 will find that a No. B. & S. gauge wire is the proper size 
 to use. 
 
 In some cases the percentage loss to be allowed in the line 
 may be different from that given in the tables, and the size 
 wire can be determined as follows: The percentage loss 
 allowed should be divided by two, giving a constant which 
 we shall call (C). Then determine the size wire required by 
 means of the tables, on the assumption that the loss is two 
 per cent, divide the circular-mil area of the wire thus obtained 
 by the constant (C), and look up the size of wire having a 
 circular-mil area corresponding to or next larger than this 
 result. 
 
 Example. It is desired to transmit 100 amperes from a 
 220-volt generator a distance of 200 feet with an allowable 
 loss of five per cent. What size wire should be used? 
 
 Solution. The constant (C) is equal to 5 divided by 2, or 
 
 C = 5 -f- 2 = 2.5 
 
 Referring to Table N, Chapter 20, we find that a No. 00 
 B. & S. gauge wire would be required if the loss were only 
 two per cent. The circular-mil area of a No. 00 B. & S. 
 gauge wire is, from Table C, equal to 133 100, and this value 
 divided by (C), or 2.5, gives the circular-mil area of the wire 
 to be used. 
 
 Circular-mil area = 133 100 ~ 2.5 = 53 240 
 diameter = 230.7 mils 
 
 A No. 3 B. & S. gauge wire has a diameter of 229.4 mils, 
 so that it should be used. 
 
 357. Motor Wiring Formula. The size of wire required to 
 supply energy to a direct-current motor can be calculated 
 as follows: Assuming the horse-power, efficiency, and the 
 voltage of the motor are given, the current that must be sup- 
 plied when the motor is operating under full load can be 
 determined by substituting in the following equation: 
 
 h.p. X 746 100 
 
 1 = -X (130) 
 
 E F 
 
322 PRACTICAL APPLIED ELECTRICITY 
 
 In the above equation (h.p.) represents the horse-power of 
 the motor, (E) the voltage the motor is designed to operate 
 on, (F) the efficiency of the motor in per cent, and (746) is 
 the number of watts per horse-power. Having determined 
 the value of the current (I), the size of wire required can be 
 determined as in section (356). The size of conductor used 
 should be such as to allow for a 25 per cent overload on the 
 motor, the current in the conductor not exceeding the values 
 given in Table G, Chapter 20. 
 
 Example. A 50-horse-power direct-current motor is to be 
 supplied with current from a 220-volt generator over a line 
 250 feet in length and having such a resistance that the drop 
 in voltage shall not exceed 4 per cent. What size wire should 
 be used, the efficiency of the motor being 90 per cent? 
 
 Solution. Substituting directly in equation (130) gives 
 
 50 X 746 100 
 
 I = - - X = 188. + amperes 
 220 90 
 
 When the motor is carrying a 25 per cent overload the cur- 
 rent in the leads will be equal to 1.25 times 188, or 
 
 Overload current = 1.25 X 188 = 235 amperes 
 
 Since the maximum value of current given in Table N, 
 Chapter 20, is less than 235 amperes, the size wire can be cal- 
 culated as follows: The size of wire required to carry 235 
 amperes with a 4 per cent drop will be the same as the size 
 of wire required to carry 117.5 amperes with a 2 per cent 
 drop. Referring to Table N, we find, that with a current of 
 120 amperes and a distance of 250 feet, a No. 000 B, & S. 
 gauge wire is required. Referring to Table G, we find that 
 No. 000 B. & S. gauge wire cannot be used to carry 235 am- 
 peres except when insulations other than rubber are used. 
 The size of wire required, if it is insulated with rubber, would 
 be a 300 000 circular-mil cable. 
 
 358. Methods of Wiring and Rules Governing Same. The 
 rules and requirements governing the proper installation of 
 electrical conductors and the kind of material that must be 
 used vary in different localities. In the majority of cases 
 the rules and requirements of the National Board of Fire 
 Underwriters as published in the National Electric Code are 
 
ELECTKIC WIRING 323 
 
 followed. In some municipalities there are certain ordinances 
 in force, or the power company may have certain require- 
 ments that must be met before they will supply electrical 
 energy. The National Electric Code should, however, be fol- 
 lowed at all times unless there are other requirements in 
 force. 
 
 There is a supplement to the National Electric Code that 
 contains a complete list of all the fittings that are approved 
 by the Underwriters, and in no case should fittings be used 
 that do not appear in this supplement unless by special per- 
 mission. 
 
 There are several methods of wiring that are approved by 
 the National Board of Fire Underwriters, viz.: 
 
 (a) Open, or exposed, work. 
 
 (b) Moulding work. 
 
 (c) Concealed "knob and tube" work. 
 
 (d) Interior conduit and armored cable work. 
 
 359. Open, or Exposed. Work. This method of wiring is 
 perhaps the cheapest of any of the methods given, and it is 
 at the same time one of the safest and best methods when 
 properly installed. It is used a great deal in mills, factories, 
 etc., where the appearance of the wires on the ceiling or walls 
 is of no great importance. The wires used in this method 
 of wiring may be either rubber covered or provided with 
 slow-burning weatherproof insulation. Rubber insulation 
 should always be used when the wire is in a damp place, such 
 as a cellar, and either weatherproof or rubber insulation may 
 be used to protect it against corrosive vapors. When installed 
 in dry places and for voltages below 300, the wires should 
 always be rigidly supported on non-absorptive, non-combustible 
 insulators that separate them 2% inches from each other 
 and 1/2 inch from the surface over which they pass. For 
 voltages from 300 to 500, the wires should be separated 4 
 inches from each other and 1 inch from the surface over 
 which they pass. If the wiring is in a damp place, the wires 
 should always be at least 1 inch from the surface over 
 which they pass, even if the voltage be below 300 volts, the 
 other distances being the same as above. The wires should 
 always be protected by porcelain tubes or short pieces of 
 flexible tubing when they pass over pipes or other material, 
 
324 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 as shown in Fig. 256. It is usually best to place the wires 
 above the pipes rather than under them. The wires, when 
 they run vertically on the walls, should be protected by a 
 suitable boxing or run in a pipe, as shown in Fig. 257. There 
 should be a clearance of at least 1 inch around the wires 
 when they are placed inside the box, which should be closed at 
 the top, and the holes in the top of the box where the wires enter 
 should be bushed with porcelain tubes. If the wires be placed 
 inside a pipe, they should each be encased in a piece of flexible 
 
 -Gas Pipe 
 
 Fig. 256 
 
 Fig. 257 
 
 tubing that will extend from the insulator below the end of the 
 pipe to the first one above it. Porcelain tubes should -always 
 be used when the wires pass through walls and floors. These 
 tubes should be long enough to reach all the way through 
 the wall or floor, except in special cases, when a piece of pipe 
 may be used with a long porcelain bushing put into it from 
 each end and cemented in place. 
 
 360. Moulding Work. In this class of work the wires are 
 placed in grooved pieces of wood that are provided with a 
 wooden cap that is fastened to the body of the moulding after 
 the wires have been put in place. The dimensions of this 
 moulding are governed by the requirements of the Under- 
 writers, and the number of grooves is usually two or three, 
 depending upon whether it is to be used on a two- or three- 
 wire system. The capping can be made to correspond in 
 design and color to the other woodwork in a building or 
 room, which makes it less conspicuous. 
 
ELECTEIC WIEING 
 
 325 
 
 Moulding work is extensively used alone and in combination 
 with other classes of work, there being numerous fittings on 
 the market that can be used in changing from one system to 
 the other. It cannot be used in damp places, or in rooms 
 where it will be subjected to fumes, or in concealed work or 
 elevator shafts. Approved rubber covered wire should be 
 used when it is placed in moulding. The same precautions 
 should be taken in protecting the wires in this class of work 
 where they pass through floors and ceilings as were men- 
 tioned for open, or exposed, work. A device known as a 
 kicking box, Fig. 258, is usually used in protecting the wires 
 at the points where they enter or emerge from the floor. 
 
 Fig. 258 
 
 Fig. 259 
 
 Metal mouldings, such as those shown in Fig. 259, are used 
 quite extensively at the present time, on circuits requiring 
 not more than 600 watts and where there is a difference in 
 potential not to exceed 300 volts. Special fittings must be 
 used with this kind of moulding so that it is continuous both 
 mechanically and electrically. The moulding should be 
 grounded, or the rules governing its installation are prac- 
 tically the same as those governing the installation of conduit 
 work. 
 
 361. Concealed "Knob and Tube" Work. Concealed "knob 
 and tube" work is fast disappearing on account of the great 
 danger of fire due to short-circuits between the wires that 
 are placed in the walls and floors. This class of wiring is 
 quite cheap and it is extensively used in frame buildings in 
 localities where the Inspection Departments will permit. The 
 wires for this class of work must have an approved rubber 
 insulation and be supported by means of knobs or tubes on 
 
326 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 the joist and studding. When the wires are run in a direction 
 perpendicular to the direction in which the joists run, holes are 
 drilled in the joists and porcelain tubes, with a shoulder on one 
 end, are driven into these holes, through which the wires are 
 passed, as shown in Fig. 260. The knobs should support the 
 
 wires at least 1 inch from 
 the surface over which they 
 run; these knobs should 
 not be farther apart than 
 Fig. 260 4^ feet and the wires fast- 
 
 ened to them in an approved 
 
 manner. Split knobs are usually used for this class 
 of work, as the wires are no longer approved by 
 the underwriters. The various wires should be at 
 least 5 inches apart at all times when supported on 
 the knobs, and it is best to have the wires 
 run on separate joist or studding when pos- 
 sible, as shown in Fig. 261. Porcelain tubes 
 should always be used where the wires pass 
 through walls and ceilings, and the knobs 
 should be so located that there is no strain 
 on the tubes. Each wire must be encased 
 in a piece of flexible tube at all outlets, 
 switches, distributing centers, etc., and this 
 piece of tubing should be of sufficient length 
 to extend from the last insulator and project 
 at least 1 inch beyond the outlet, as shown in 
 Fig. 260. When wires cross pipes or other 
 wires, they should be insulated by means of 
 porcelain tubes or pieces of flexible tubing, as 
 shown in Fig. 256. 
 
 362. Interior Conduit and Armored Cable 
 Work. Armor cable consists of rubber-covered 
 wire that is protected from mechanical injury 
 by two layers of flexible steel armor, which 
 also serves to protect the wire to a certain 
 extent from dampness, Fig. 262. A lead covering 
 is often placed between the insulation on the wire and the steel 
 armor, which protects the enclosed conductors from dampness. 
 Leaded armor cables can be used for all classes of work, and 
 the unleaded cable can also be used for all classes where it 
 
 Fig. 261 
 
W 
 
 ELECTEIC WIEING 327 
 
 is not exposed to dampness. Leaded cables may be buried in 
 the walls or floors, but reasonable care must be exercised in 
 installing the unleaded cable to protect it from being exposed 
 to moisture. Special fittings are on the market for con- 
 necting the ends of the armor to metal outlet boxes. The 
 armor should be cut away 6 or 7 inches from the end 
 of the wires so that switches, fixtures, etc., may be properly 
 connected. 
 
 In new work, holes 
 are drilled in the joists 
 and studding and the 
 cable is pulled into 
 place, it being fastened 
 by means of special Fig. 262 
 
 straps of metal. Ar- 
 mored cable is used quite extensively in the wiring of old 
 buildings, as it can be put into different places regardless of 
 its coming in contact with pipes, etc. 
 
 In conduit work approved rubber-covered wire must be 
 used and it is drawn into a system of iron piping that is 
 installed and connected to all outlet and cut-out boxes before 
 the wires are put in place. The conduit must never have an 
 inside diameter of less than .625 inch and in installing it no 
 bends or elbows should have a radius less than 3.5 inches, 
 nor should there be more than the equivalent of four quarter 
 bends from outlet to outlet. The conduits should be cleaned 
 out before the wires are drawn in and it is often advisable 
 to blow a small quantity of soapstone into them, which will 
 reduce the friction of the wire on the surface of the pipe to 
 a minimum. This system of wiring is the safest, most satis- 
 factory, and in the long run no doubt the most economical 
 method of installing wires. 
 
 363. Service Wires. When the electrical energy is sup- 
 plied from a source outside the building, certain precautions 
 must be taken in bringing the wires into the building. When 
 the wires are overhead and are taken into the building above 
 the basement, they must be provided with drip loops and pass 
 through insulating tubes in the wall that slope so their out- 
 side end is lower than the inside end. Such an arrangement 
 is shown in Fig. 263. When the wires are brought into the 
 basement from an outside service that is overhead, they 
 
328 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 should be placed in a metal conduit with its outside end bent 
 over and provided with a suitable fitting, thus forming a 
 drip loop, as shown in Fig. 264. When the outside wires are 
 underground and are brought into the basement, they 
 should be placed in metal or porcelain tubes that are tightly 
 sealed afterwards. The leads pass directly to the cut-out, 
 then to the main switch, both of which should be enclosed 
 in a suitable cabinet, and from the switch to the meter, and 
 
 t-Out 
 
 Fig. 263 
 
 Fig". 264 
 
 then to the main distributing center. A three-branch dis- 
 tributing center for a three-wire system is shown in Fig. 
 265. The gaps in the various leads are for fuses. 
 
 364. Location of Outlets, Switches, and Distributing Board. 
 The various distributing boards from which the branch cir- 
 cuits emanate should always be located as near the center 
 of the load as possible, so that the circuits will be practically 
 the same length. These boards are mounted in either metal 
 boxes or wooden boxes with fireproof lining, depending upon 
 the kind of work. Each branch circuit is provided with a 
 double-pole switch and properly fused. A three-wire distrib- 
 uting board is shown in Fig. 266 and a two-wire board in 
 Fig. 267. A main switch and fuses are placed in the leads 
 connecting the board to the source of energy. 
 
 The switches in the various branch circuits outside the 
 
ELECTEIC WIRING 
 
 329 
 
 distributing board should be located in such positions that 
 they will be convenient to operate. They should, as a rule, 
 in light wiring be placed near a door and on the side nearest 
 the door handle. 
 
 The location of the outlets will depend upon the location of 
 the lamps, kind of lamps arc or incandescent location of 
 motors, etc. A chart of the standard symbols for wiring 
 plans, as adopted and recommended by the National Electrical 
 Contractors' Association of the United States, is given in 
 Chapter 20. 
 
 Fig. 265 
 
 Fig. 266 
 
 365. Installing Arc Lamps and Fixtures. Arc lamps should 
 be insulated from inflammable material, and at all times sur- 
 rounded with a glass globe surrounding the arc and securely 
 fastened in place. Approved rubber-covered wire should be 
 used and it should be supported on porcelain or glass insu- 
 lators in constant-current systems that hold the wire at least 
 1 inch above the surface over which the wire passes, and 
 these wires should never be nearer each other than 8 inches, 
 except in cut-out boxes and in the lamps. 
 
 Fixtures, when supported from the gas piping or from any 
 grounded metal work of the building, must be insulated from 
 such metal by an approved insulating joint placed as neai 
 the walls or ceiling as possible. The cross-section of an 
 insulating joint is shown in Fig. 268. 
 
 366. Electric Heaters. All electric heaters must be pro 
 tected by cut-out and controlled by indicating switches. These 
 
330 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 switches should be double pole except when the device con- 
 trolled does not require more than 660 watts. Heaters must 
 always be in plain sight unless special permission be given 
 by the Inspection Department having jurisdiction. Stationary 
 heaters, such as radiators, ranges, plate warmers, etc., must 
 be placed in safe locations, isolated from inflammable ma- 
 terials, and always treated as sources of heat. 
 
 Fig. 267 
 
 Fig. 2G8 
 
 367. Electric Generators and Motors. All generators and 
 motors should be located in dry places. They should never 
 be installed in places where a hazardous process is carried 
 on, in dusty places, or in places where they are exposed to 
 inflammable gases or flying of combustible materials. 
 
 Generators and motors should always be insulated from the 
 surrounding floor on wooden bases. When it is impossible 
 to insulate them for any reason, the Inspection Department 
 having jurisdiction may permit the omission of the insulating 
 frame, in which case the frame should be permanently and 
 effectively grounded. 
 
 368. Electrical Inspection. No attempt has been made in 
 this chapter to give all the details that must be observed in 
 the proper installation of electrical conductors, it being left 
 to the engineer in charge, who should have a copy of both 
 the National Electric Code and its supplement, which contains 
 a list of approved fittings and materials. The Inspection 
 Department under whose jurisdiction the work is being done 
 
ELECTKIC WIRING 331 
 
 should be consulted freely, as it will often save time and 
 trouble in cases where doubtful work has been suspected, and 
 the inspector requires the floors to be taken up or the plaster 
 knocked off in certain places to satisfy himself that the work 
 was properly done. 
 
 * I 
 
CHAPTEE XVII 
 
 THE ALTERNATING-CURRENT CIRCUIT 
 
 369. Definition of an Alternating Electromotive Force or 
 Current. An alternating electromotive force or current is 
 one that changes in value, and reverses in direction at certain 
 regular intervals. Such an electromotive force would be 
 induced in a loop of wire that was resolved in a magnetic 
 field, as shown in Fig. 126. An alternating current would 
 exist in a closed circuit connected to the terminals of such a 
 coil by means of two brushes and slip-rings, as shown in 
 Fig. 127. 
 
 370. Hydraulic Analogy of 
 an Alterating Current. The 
 
 alternating current in an 
 electric circuit can be com- 
 pared to the flow of water in 
 a closed pipe connected to a 
 cylinder in which there is an 
 oscillating piston operating, 
 as shown in Fig. 269. If 
 the arm (A) be moved at a 
 constant angular velocity 
 
 there will be a flow of water through the pipe similar to that 
 represented by the curve in Fig. 270. The length of the hori- 
 zontal line (AB) corresponding to the time of one complete 
 revolution of the arm (A), and the length of the ordinate of 
 the curve, or vertical distance from a point on the line (AB) 
 to the curve, at any instant, represents the rate at which the 
 water or liquid is passing a given cross-section of the pipe, 
 or the current in the pipe. 
 
 371. Cycle Frequency Alternation Period Synchronism 
 Phase Displacement. When an alternating pressure or cur- 
 
 332 
 
 Fig. 269 
 
THE ALTERNATING-CURRENT CIRCUIT 
 
 333 
 
 90 
 
 ISO 
 Fig. 270 
 
 B 
 
 270 360 
 
 rent has passed through a complete set of positive and nega- 
 tive values, starting from any value and again returning to 
 that value in the same direction, the pressure or current has 
 completed what is called a cycle. A complete cycle is shown 
 by curve (E) in Fig. 271, which represents an alternating 
 electromotive force. The 
 e.m.f. is zero at (A), in- 
 creases to a maximum posi- 
 tive value at (C), decreases 
 to zero at (D,) and reverses 
 in direction, increasing to a 
 maximum negative value at 
 (E), and then decreases to 
 zero at (B), which completes 
 the cycle, it passing through 
 a similar set of values in the 
 next equal interval of time. 
 
 The number of cycles the pressure or current passes 
 through in one second is called the frequency. Thus a 60-cycle 
 electromotive force or current would be one that parsed 
 through a complete set of positive and negative values 60 
 times per second. 
 
 An alternation is half a 
 cycle, and corresponds to a 
 complete set of positive or 
 negative values of e.m.f. or 
 current. There will be just 
 twice as many alternations 
 in a given time as there are 
 cycles, or a frequency of 60 
 cycles would mean 120 al- 
 ternations per second. 
 
 The period of an e.m.f. or 
 current is the time in sec- 
 onds required to complete one cycle. Thus the period of a 
 60-cycle e.m.f. or current would be % of a second and of a 
 25-cycle e.m.f. or current i/ 5 of a second. 
 
 Two electromotive forces or currents are said to be in 
 synchronism when they have the same frequency. 
 
 Any number of e.m.f.'s or currents are said to be in phase 
 when they pass through corresponding values of their re- 
 
 360 
 
334 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 
 
 90' 
 
 D 
 
 180 270 360 
 
 Fig. 272 
 
 spective cycles at the same time. Thus the current (I), 
 and the e.m.f. (E), Fig. 271, are in phase because they both 
 pass through corresponding values of their cycles at the same 
 time. 
 
 Any number of e.m.f. 's or currents are said to be displaced 
 in phase when they do not pass through corresponding values 
 
 of their respective cycles at 
 the same time Thus the 
 current (I) and the e.m.f. 
 (E), Fig. 272, are displaced 
 in phase, and this phase dis- 
 placement may be measured 
 in degrees by determining 
 the difference in the degrees 
 represented by the two 
 points where the curves 
 cross the horizontal line 
 
 (AB). The total length of the line (AB) corresponds to 360 
 degrees, and if the distance between the two points where 
 the curves (E) and (I) cross the horizontal line is % of the 
 length of the line (AB), the e.m.f. and current represented by 
 these two curves are displaced in phase by % of 360 degrees, 
 or 45 degrees. The current lags the e.m.f., because the current 
 curve is shown as crossing the horizontal line (AB), as you 
 pass along the line from left to right, after the e.m.f. curve. 
 This phase displacement may be expressed in time as well 
 as degrees. Thus the time interval between when the current 
 and e.m.f. are zero, as shown in Fig. 272, is % of a period or 
 (1 -f- 8 X frequency) of a second. The displacement in prac- 
 tice is usually measured in degrees rather than time. 
 
 372. Chemical and Heating Effects of an Alternating Cur- 
 rent. It was mentioned in Chapter VIII that the chemical 
 effect of an alternating current was zero. This is due to the 
 fact that the current exists in the circuit in one direction for 
 the same time that it exists in the opposite direction and as a 
 result of this reversal in direction there will be a chemical 
 action taking place first in one direction and then in the 
 opposite direction, and the resultant chemical action will be 
 zero. 
 
 The power expended in heating a conductor at any instant 
 is equal to the product of the resistance of the conductor and 
 
THE ALTERNATING-CURRENT CIRCUIT 
 
 335 
 
 the square of the current in the conductor. In an alternating- 
 current circuit the current is constantly changing in value 
 and, as a result, the power expended in heating the conductors 
 is changing in value, it at any instant being equal to the 
 product of the resistance and the square of the current at 
 that particular instant. In order to obtain the total heating 
 effect of an alternating current, it is necessary to add up all 
 of the instantaneous heating effects. The heating effect of 
 a current is independent of the direction of the current in the 
 circuit. 
 
 373. Sine Wave E.M.F. or Current. If a simple loop of 
 wire be revolved at a constant rate in a uniform magnetic 
 field, there will be an induced e.m.f set up in the coil, which 
 will reverse in direction and change in value as the coil 
 rotates. The value of the induced e.m.f. will vary as the 
 direction of motion of the coil changes with respect to the 
 magnetic field, it being a maximum when the two sides of 
 the loop move perpendicular to the magnetic field and zero 
 when the two sides of the loop move parallel to the magnetic 
 
 
 , 
 
 ^ 
 
 
 
 ^ 
 
 , 
 
 
 
 
 
 / 
 
 :\ 
 
 \ 
 
 
 
 
 
 f 
 
 1 
 
 3 
 
 \ 
 
 \ 
 
 
 -- 
 
 ^ 
 
 r 
 
 H 
 
 \ 
 
 \ 
 
 / 
 
 \ 
 \ 
 
 $ 
 
 / 
 
 / 
 
 / 
 
 N > \ 
 
 \ 
 
 * 
 
 / 
 NI 
 
 
 A 
 
 
 c 
 
 
 \ 
 
 
 
 / 
 
 3< 
 
 
 ^ i 
 
 ^ 
 
 "y 
 
 
 *-w - 
 3 
 
 s 
 
 
 
 1 
 
 50* 
 
 Sv 
 1 
 
 \A 
 
 70* 
 
 
 
 
 Fig. 273 
 
 field. The e.m.f. induced in the coil for positions between 
 those just mentioned will bear a definite relation to the 
 maximum e.m.f., and this relation can be determined as fol- 
 lows: The rate at which the two sides of the loop are mov- 
 ing perpendicular to the field decreases in value from a ver- 
 tical position and becomes zero for a horizontal position of 
 the coil when the field is vertical, as shown in Fig. 273. The 
 movement of the coil at any instant can be resolved into 
 two parts, one parallel to the magnetic field and the other 
 perpendicular to the magnetic field. It is the part that is per- 
 
336 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 pendicular to the magnetic field that results in an e.m.f. being 
 induced in the coil, and this part is proportional to the sine of 
 the angle the path of the two sides of the coil make with the 
 magnetic field. The sine of this angle will vary as the pro- 
 jection of the coil on the vertical plane. If the projection 
 when the coil is in a perpendicular position be taken as rep- 
 resenting the maximum e.m.f., the e.m.f. for other positions 
 will correspond to the projection of the coil upon the vertical 
 plane for those positions. Let a complete revolution be rep- 
 resented by the horizontal line (AB), it corresponding to 360 
 
 degrees, then the relation 
 of the e.m.f.'s for various 
 angular positions can be 
 laid off on ordinates drawn 
 vertically through points 
 on the line (AB), which 
 correspond to the angular 
 displacement of the coil 
 
 360 
 
 from a position perpendic- 
 ular to the field. The values 
 for the 45 positions are the 
 only ones shown in the fig- 
 ure; the remaining ones, 
 however, are determined 
 in the same way. Such a 
 curve is called a sine 
 
 curve, since its ordinates vary as the sine of the angle rep- 
 resented by the point on the line (AB) through which the 
 ordinate passes. An e.m.f. or current whose value varies as 
 the ordinate of a sine curve is called a sine e.m.f. or current. 
 The following calculations are all based on a sine curve. The 
 e.m.f. and current curves met with in practice are very sel- 
 dom sine curves, but approach a sine curve quite often. 
 
 374. Maximum, Average, and Effective Values of E.M.F. 
 and Current. The maximum value of an alternating e.m.f. or 
 current is the value represented by the ordinate of the e.m.f. 
 or current curve having the greatest length. Thus in Fig. 
 274 the maximum e.m.f. occurs at 90 and 270, it being op- 
 posite in direction for the two positions but having the same 
 value. 
 
 The average value of an alternating e.m.f. or current is 
 
THE ALTERNATING-CURRENT CIRCUIT 337 
 
 equal to the average of all of the instantaneous e.m.f.'s or 
 currents for a complete alternation, starting with zero value 
 and returning to zero value. For a true sine wave the aver- 
 age e.m.f. and current are always .636 times their maximum 
 value. This relation is determined by finding the area of a 
 positive or negative loop of the e.m.f. or current curve and 
 dividing this area by the distance between the two points 
 where the curve crosses the horizontal line. The rectangles, 
 shown by the shaded portions in Fig. 274, have each the same 
 area as one loop of the sine curve, and the altitude of this 
 rectangle is .636 times the maximum ordinate of the sine 
 curve. 
 
 The effective value of an alternating current is numerically 
 equal to a steady direct current that will produce the same 
 heating effect in a given time as is produced by the changing 
 alternating current. If a conductor has a resistance of (R) 
 ohms and there is an alternating current in the conductor, 
 the power expended in heating the conductor at any instant 
 is equal to the value of the current at that instant squared, 
 times the resistance in which the current exists. Adding up 
 all of these instantaneous heating effects for a certain time 
 gives the total heating effect. This resultant or total heating 
 effect could be produced by a steady direct current as well 
 as by an alternating current. Now the value of the steady 
 direct current required to produce the same heating effect as 
 is produced by the alternating current corresponds in value 
 to the effective alternating current 
 
 I2R = average i2R, 
 or 
 
 12 = average i2 
 and 
 
 I = V average i2 
 
 Note Small letters are used to represent instantaneous 
 values. 
 
 For a sine wave the square root of the average of the in- 
 stantaneous values squared is equal to .707 times the max- 
 imum current. 
 
 Average value = .636 maximum value 
 Effective value = .707 maximum value 
 Effective value = 1.11 average value 
 
338 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 The effective value divided by the average value is equal to 
 1.11, which is called the form factor of the wave. The above 
 relations hold true for sine waves only. 
 
 Fig. 275 
 
 Fig. 276 
 
 375. Vector Representation of Alternating E.M.F.'s and 
 Currents. A vector quantity is one having both direction and 
 magnitude; it may be represented by a line, called a 
 vector, drawn in a definite direction corresponding to the 
 direction of the quantity it represents and having a length 
 corresponding to the value of the vector quantity to a suitable 
 scale. Thus a current of 10 amperes and an e.m.f. of 10 volts, 
 displaced in phase by 30 degrees, would be represented as 
 shown in Fig. 275. 
 
 These vectors can be thought of as rotating, and one 
 revolution corresponds to 360 degrees. The counter-clockwise 
 direction of rotation is taken as positive. In representing 
 alternating e.m.f.'s and current by vectors, the effective values 
 are the ones usually used. 
 
 376. Addition and Subtraction of Vectors. Two vectors are 
 added in the same way as two forces are added in determining 
 the resultant force. The two vectors (E^ and (E 2 ), shown in 
 Fig. 276, are added by completing the parallelogram, as shown 
 by the dotted lines, and drawing the diagonal gives the re- 
 sultant (E). Its direction is that indicated by the arrowhead. 
 
 Two vectors are subtracted by reversing one and adding 
 them. Thus if it is desired to know the value of (E l E 2 ), 
 shown in Fig. 276, the vector (E 2 ) is reversed in direction and 
 then added to the vector (E^) ; the direction of the vector 
 (E), representing the difference, is shown in the figure by the 
 arrow head. 
 
 377. Factors Determining the Value of an Alternating Cur- 
 rent. The current in a circuit upon which there is a steady 
 
THE ALTERNATING-CURRENT CIRCUIT 
 
 339 
 
 direct voltage impressed is equal to the value of the impressed 
 voltage in volts divided by the total resistance in ohms. In 
 an alternating-current circuit upon which there is a constant 
 effective pressure impressed, the value of the effective current 
 is determined not by the resistance alone but by the combined 
 effects of the resistance, inductance, and capacity, if they all 
 be present in the circuit. If there is no inductance or capacity 
 in the circuit, then the same law holds for the alternating- 
 current circuit as is true for the direct-current circuit. The 
 current in the alternating-current circuit will be equal to the 
 impressed voltage divided by the resistance of the circuit 
 
 Fig. 277 
 
 -UO 
 
 when the effects of the inductance and capacity are exactly 
 equal, they acting in opposition to each other, as will be 
 explained later. 
 
 378. E.M.F.'s Required to Overcome K:sistance. The e.m.f. 
 at any instant required to overcome the resistance of a circuit 
 is equal to the product of the current at that instant and 
 the resistance of the circuit, or (IR). If there be an alternat- 
 ing current, as represented by the curve (I) in Fig. 278, in a 
 circuit, the e.m.f. at any instant required to produce this cur- 
 rent is equal to (IR) and varies directly as the current or 
 passes through corresponding values at the same time. The 
 current and e.m.f. will, as a result, be in phase, and the curve 
 (E r ) represents the impressed e.m.f. required to produce the 
 current (I). 
 
 379. Hydraulic Analogy of Inductance. If the electric cur- 
 rent in an alternating-current circuit be represented by a fluid 
 that flows through a pipe, as shown in Fig. 279, due to the 
 
340 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 M 
 
 alternating pressure that is created by the pump (P), then an 
 inductance in such a circuit can be represented by a fluid 
 motor (M) similar to that shown in the figure. When such 
 
 a motor is connected in 
 the circuit, considerable 
 time will be required for 
 the current of liquid to 
 reach a maximum steady 
 value if a constant pres- 
 sure be applied to the cir- 
 cuit by the pump, on ac- 
 count of the inertia of the 
 wheel (W) that is attached 
 to the fluid motor. Alter 
 the pressure has been ap- 
 plied to the motor for some 
 time, the motor will have 
 
 reached a speed such that it offers practically no resistance 
 to the flow of the liquid through it. If, however, there be a 
 change in the pressure produced by the pump, there will be 
 a tendency for the current of liquid to change in value, and 
 the action of the fluid motor will always be such as to tend 
 to prevent a change in the 
 current that is, if the cur- 
 rent tends to increase in 
 value due to an increase in 
 pump pressure, the motor 
 will oppose this increase, 
 and if the current tends to 
 decrease in value, due to a 
 decrease in pump pressure, 
 the motor will tend to pre- 
 
 Fig. 279 
 
 360 
 
 vent this decrease. The ac- 
 tion of the motor at all times 
 
 is such as to tend to prevent any change in the value of the 
 current in the circuit of which it is a part. 
 
 The motor in the hydraulic problem just discussed corre- 
 sponds in action to the inductance of an alternating-current 
 circuit in which there is an alternating current. In the 
 hydraulic problem, if an alternating pressure be applied to the 
 motor instead of a direct pressure, its direction of rotation 
 
THE ALTERNATING-CUEEENT CIRCUIT 341 
 
 will change twice per cycle of the impressed pressure. The 
 direction of rotation, however, will not change at the same 
 instant the pressure produced by the pump changes on ac- 
 count of the inertia possessed by the moving parts of the 
 fluid motor. The motor will continue to rotate in a given 
 direction for some time after the pressure has been reversed 
 in direction. The velocity of the paddle wheel of the motor 
 determines the value of the current of liquid through it, and 
 the direction of rotation of the paddle wheel determines the 
 direction of the current. Since the velocity of the fluid motor 
 is not a maximum when the pressure of the pump is a max- 
 imum, it reaching a maximum velocity in a given direction 
 after the pressure produced by the pump has reached its 
 maximum value in the same direction, and the velocity of the 
 motor is zero after the pressure of the pump is zero, the cur- 
 rent of liquid in the circuit must lag the pressure. 
 
 380. Phase Relation of E.M.F. to Overcome Inductance and 
 the Current in an Alternating-Current Circuit. Assume there 
 is a circuit containing inductance alone, and that there 
 is a current in this circuit represented by the curve (I), 
 Fig. 280. The magnetic field created by the current at any 
 time will depend upon its instantaneous value. Thus the 
 magnetic field or lines of force associated with the current 
 will be a maximum when the current is a maximum, will de- 
 crease or increase in value with a decrease or increase in the 
 value of the current, and will reverse in direction at the same 
 time the current reverses in direction. Since the above rela- 
 tion exists between the current in the circuit and the magnetic 
 flux produced by the current, a second curve ($) may be 
 drawn, as shown in Fig. 280, whose ordinate at any instant will 
 represent to a suitable scale the magnetic flux at that instant. 
 With a change in the magnetic flux associated with the cir- 
 cuit, there will be an induced e.m.f. set up in the circuit, 
 which at any instant is proportional to the rate at which the 
 flux is changing with respect to the circuit, or the rate at 
 which the conductor forming the circuit is cutting the lines of 
 force. By investigating curve (3>) it is seen that the flux is 
 changing at its greatest rate when it is zero in value and is 
 changing at a minimum rate when it is at its maximum value; 
 or the induced e.m.f. in the circuit is zero at the points (C) 
 and (E) and is a maximum at the points (A), (D), and (B). 
 
342 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 The value of the induced e.m.f. at any other time during the 
 cycle will depend upon the rate at which the flux is changing 
 in value, and its direction will, according to Lenz's Law, al- 
 ways be such as to oppose a change in the value of the current 
 in the circuit. Thus, if the current be increasing in value in 
 the positive direction, as it is between the points (A) and (C), 
 the induced e.m.f. acts in such a direction as to oppose this 
 change in the current, or it acts in the negative direction. If 
 the current be decreasing in value in the positive direction, 
 the induced e.m.f. opposes this decrease, or it acts in the 
 positive direction.. The curve (ei) represents the e.m.f. 
 induced in the circuit. If the circuit has no resistance (a 
 theoretical condition), the only e.m.f. required to produce the 
 current (I) in the circuit would be one that would overcome 
 the e.m.f. (ei). Such an e.m.f. would be represented by the 
 curve (Ei), whose ordinates are at each instant equal to 
 those of (ei) but opposite in sign, or (Ei) acts opposite to 
 (ei), and will produce the current (I). From the relation 
 of the curve (I) and (Ei) in the figure, it is seen that the 
 current and impressed e.m.f. in an inductive circuit are dis- 
 placed in phase by 90 and that the current lags the e.m.f. 
 
 381. Hydraulic Analogy 
 of Capacity. The hydraul- 
 ic analogy of a condenser 
 is shown in Fig. 281. A 
 flexible rubber diaphragm 
 (D) is stretched across a 
 specially constructed 
 chamber (C) which is con- 
 nected to a pump (P), as 
 shown in the figure, that 
 produces an alternating 
 pressure. When the dia- 
 phragm (D) is in its nor- 
 mal position, it offers no opposition to the flow of the 
 liquid through the pipe in either direction. As soon, how- 
 ever, as the diaphragm is displaced from its neutral posi- 
 tion, it sets up a reaction which opposes the flow of the 
 liquid, and this reaction will increase in value as the dia- 
 phragm is displaced more and more, finally reaching a value 
 equal to the pressure, causing the liquid to flow through 
 
 Fig. 281 
 
THE ALTEENATING-CUKEENT CIRCUIT 
 
 343 
 
 the pipe, and when the reaction becomes equal to the acting 
 pressure there will be no current. If, now, the current be re- 
 versed in direction, the diaphragm will return to its normal 
 position, and while it is returning, it will act 'in the same 
 direction as the current. When the diaphragm has reached 
 its normal position and it is forced to the opposite side, it 
 will immediately react upon the current and tend to stop it, 
 and this reaction will finally reach such a value that there 
 will be no current in the circuit. It is seen, then, that the 
 diaphragm acts with the current one-half of the time and in 
 opposition to it one-half of the time. The reaction of the 
 diaphragm corresponds to the electrical pressure at the 
 terminals of a condenser connected in an alternating-current 
 circuit, and it has a maximum value when the current is zero 
 and a zero value when the current is a maximum. 
 
 382. Phase Relation of the E.M.F. to Overcome the Effect 
 of Capacity and the Current in an Alternating-Current Circuit. 
 The current in a circuit containing capacity alone may be 
 represented by a curve such as (I), Fig. 282. The flow of 
 liquid through the chamber (C), Fig. 281, could be repre- 
 sented by such a curve, and 
 since the reaction of the 
 diaphragm corresponds to 
 the e.m.f. at the terminals 
 of the condenser, the phase 
 relation of the e.m.f. and 
 the current can be deter- 
 mined by an investigation 
 of Fig. 281, carrying the op- 
 eration through a complete 
 
 cycle. The position of the diaphragm must be normal 
 when the current is a maximum, say at the point (C), 
 Fig. 282, as it produces no opposition to the flow of 
 liquid. As the diaphragm is extended to either side, its 
 reaction increases and it opposes the flow of liquid, or if 
 the current is in the positive direction, the action of the 
 diaphragm is negative. If the current reverses in direction 
 when it has reached a zero value and starts to increase in 
 value in the negative direction, the diaphragm will act with 
 the current or they will both be negative. When the di- 
 aphragm has reached its normal position, its reaction is zero 
 
 180" 270 
 Fig. 282 
 
 360 
 
344 PRACTICAL APPLIED ELECTRICITY 
 
 and the current is a maximum, and at this point the reaction 
 of the diaphragm changes sign and the current starts to 
 decrease in value in the negative direction. While the cur- 
 rent is decreasing in value in the negative direction, the reac- 
 tion of the diaphragm is increasing in value in the positive 
 direction. The current again reverses in direction after reach- 
 ing zero value and starts to increase in the positive direction, 
 the reaction of the diaphragm decreasing in value in the posi- 
 tive direction, which completes the cycle. The curve (e c ), 
 Fig. 282, represents the reaction of the diaphragm, or the 
 electrical pressure at the terminals of a condenser connected 
 in an alternating-current circuit carrying a current (I). Since 
 the curve (e c ) represents the reaction in the circuit, the e.m.f. 
 required to overcome this reaction must be equal in value and 
 opposite in direction to it at each instant. The curve (E c ) 
 then represents the e.m.f. required to overcome the effect of 
 the capacity in a circuit and produce the current (I). It is 
 seen by an inspection of the curves that the current (I) leads 
 the impressed e.m.f. (E c ) by 90 degrees. 
 
 383. E.M.F. Required to Overcome Combined Effects of 
 Resistance, Inductance, and Capacity. By comparing the 
 curves (Ei) and (E c ) in Figs. 280 and 282, it is seen that 
 they are displaced in phase by 180 degrees, or the e.m.f.'s they 
 represent act just opposite to each other. If now inductance 
 and capacity be present in a circuit at the same time, the 
 electrical pressures required to overcome their effects would 
 tend to neutralize. When the effects of inductance and 
 capacity are equal, the two e.m.f.'s exactly neutralize, and the 
 only e.m.f. required would be that to overcome the resistance 
 of the circuit. The current and impressed e.m.f. in such a 
 circuit would be in phase. If, however, the e.m.f.'s required 
 to overcome the effects of inductance and capacity are not 
 equal, they will not exactly neutralize and there will be a 
 resultant e.m.f. in the circuit to overcome, which has a value 
 at any instant equal to the difference between the e.m.f.'s to 
 overcome the effects of inductance and capacity. The e.m.f.'s 
 required to overcome the effects of resistance, inductance, and 
 capacity, and thus produce the current (I), are shown in 
 Fig. 283. The e.m.f. required to overcome the effect of in- 
 ductance in this case is greater than that required to overcome 
 the effect of capacity, and they will not exactly neutralize 
 
THE ALTERNATING-CURRENT CIKCUIT 
 
 345 
 
 90 180" 
 
 Fig. 283 
 
 70 360 
 
 each other. The curve (R) represents their combined value. 
 This resultant pressure represented by the curve (R) must 
 now be combined with the e.m.f. to overcome the resistance 
 (Er) in order to obtain the impressed pressure required to 
 produce the current (I). These two curves can be combined 
 by adding their ordinates for 
 various points along the hori- 
 zontal line (AB),the algebraic 
 sum of their ordinates at any 
 point being the ordinate of 
 the resultant curve (E), which 
 represents the total pressure 
 that must be impressed upon 
 the circuit to produce the cur- 
 rent (I). When the pressure 
 required to overcome the ef- 
 fect of the inductance is o* 
 greater than the pressure re- 
 quired to overcome the effect 
 
 of the capacity, the current lags the impressed pressure, as 
 shown in Fig. 283. If the pressure required to overcome the 
 effect of the capacity is greater than that to overcome the 
 effect of the inductance, the current in the circuit will lead 
 the impressed pressure. 
 
 384. Numerical Values of E.M.F. Required to Overcome 
 Resistance, Inductance, and Capacity. If the current in a cir- 
 cuit changes in value according to the sine law, and (I) be 
 taken as the effective value of the current in the circuit, the 
 pressures required to overcome the effect of the inductance 
 and capacity can be determined by means of the equations 
 
 Ei=2X7rXfXLXl (131) 
 
 I 
 
 Ec = (132) 
 
 2 X TT X f X C 
 
 In the above equations (f ) represents the frequency in cycles 
 per second, TT = 3.1416, (L) is the inductance of the circuit in 1 
 henrys, (C) is the capacity in farads, and (I) is the effective 
 current in amperes. (Ei) and (E c ) represent the effective 
 e.m.f.'s required to overcome the effects of the inductance 
 and capacity, respectively. The e.m.f. required to overcome 
 the effect of inductance leads the current by 90 degrees, and 
 
346 PRACTICAL APPLIED ELECTRICITY 
 
 the e.m.f. required to overcome the effect of capacity lags the 
 current by 90 degrees. The e.m.f. required to overcome the 
 resistance is equal to (RI) and it is always in phase with the 
 current. These three e.m.f.'s can be represented by three 
 vectors, as shown in Fig. 284, the counter-clockwise direction 
 of rotation being taken as positive. 
 
 385. Total Electromotive Force Required to Produce a 
 Given Alternating Current. If the two quantities (2 X TT X f X 
 L X I) and (I-f-2X7rXfXC), Fig. 284, are equal in value, 
 the vectors representing them will be 
 equal in length. The resultant of these 
 
 2TrfLIk^\ NJ^* two vectors then will be zero, and the 
 v only e.m.f. required to produce the 
 * current (I) is that to overcome the re- 
 
 sistance, which is equal to (RI). 
 
 If, however, the e.m.f. required to 
 50 overcome the effect of the inductance 
 
 2frfr * is greater than that to overcome the 
 
 capacity, the vector (Ei), Fig. 285, will 
 Fig. 284 be greater in length than the vector 
 
 (E c ). The resultant of these two 
 
 e.m.f.'s will be equal to (Ei E c ), and its direction will corre- 
 spond to that of the larger vector, or (Bi). This resultant 
 must now be combined with (E,-) in order to obtain the total 
 e.m.f. required to produce the current (I), which can be done 
 graphically, as shown in the figure. The resultant (E) is 
 equal to the diagonal of a parallelogram whose sides are 
 (Ei Ec) and (E r ), and its value is equal to the square root of 
 the sum of the squares of the two sides, or 
 
 E= V E2 + (Et E c )2 (133) 
 
 Substituting in the above equation the values of (Ei) and 
 (Ec) as given in equations (131) and (132), and the value 
 of (Er), which is equal to (RI), gives the equation 
 
 -V 
 
 E = (RI)2+ 27rfLI (134) 
 
 27TfC * 
 
 By taking (I) from under the radical sign, this equation can 
 be changed to the form 
 
THE ALTERNATING-CURRENT CIRCUIT 
 
 347 
 
 R2 
 
 -\ 
 
 7TfC' 
 
 or 
 
 E 
 
 1 = 
 
 (135) 
 
 (136) 
 
 2 7T f L 
 
 2 TTfC 
 
 The above equation gives the value of 
 the current (I) in terms of the im- 
 pressed electromotive force (E), the 
 ohmic resistance of the circuit (R), 
 the inductance (L) in henrys, the 
 capacity (C) in farads, frequency (f) 
 in cycles per second, and the constant 
 (27r), which is equal to (2 X 3.1416) 
 or 6.2832. 
 
 386. Impedance and Reactance of a 
 Circuit. The impedance of a circuit in 
 which there is an alternating current is 
 
 the total opposition offered by the circuit to the flow of the 
 electricity through it. The letter (Z) is usually used to 'rep- 
 resent the impedance. It is, from equation (136), numerically 
 equal to 
 
 Fig. 285 
 
 ->! 
 
 = R2 
 
 27Tf L 
 
 (137) 
 
 27rf C ' 
 
 The impedance of a circuit is composed of two factors, the 
 resistance and the reactance. The reactance is the quantity 
 which, when multiplied ,by the current, gives the component 
 of the impressed e.m.f. that is at right angles to the current. 
 The resistance multiplied by the current gives the component 
 of the impressed e.m.f. in phase with the current. The re- 
 actance, which is usually represented by the letter (X), is 
 equal to 
 
 L 
 
 (138) 
 
 27Tf C 
 
 The above value of (X) is composed of two factors, (27rfL) and 
 (l~27rfC). The quantity (27rfL) is called the inductance re- 
 actance and is represented by the symbol (Xi), while the 
 
348 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 quantity (1 -5- 2?rfc) is called the capacity reactance and is 
 represented by the symbol (X c ). In general: 
 
 Z=VR2 + X2 (139) 
 
 or 
 
 Z = VR 2 + (X, X c )2 (140) 
 
 The inductance reactance (Xi) is considered as positive and 
 the capacity reactance (X c ) as negative, when they are being 
 combined. The impedance and the reactance of a circuit are 
 measured in ohms just as the resistance is measured in ohms. 
 
 387. Impedance Diagram. Since 
 the impedance of a circuit is equal 
 to the square root of the sum of the 
 X = (Xl~X(0 squares of two quantities, as given 
 in equation (139), a right-angle tri- 
 R angle can be drawn, as shown in 
 
 Fig. 286 Fig. 286, its three sides representing 
 
 the resistance, reactance, and im- 
 pedance. Such a figure is called an impedance diagram. 
 388. Impedances in Series. Any number of impedances in 
 series can be added by adding their resistances and reactances, 
 respectively, which gives the resistance and the reactance of 
 the resultant impedance. Thus two impedances, (Z x ) and 
 (Z 2 ) connected in series, may be added as shown in Fig. 287a, 
 both reactances being positive. If one of the reactances be 
 negative, the impedances are added as shown in Fig. 287b, 
 
 r (R.+R 
 
 Fig. 287 a 
 
 Fig. 287 b 
 
 the resultant reactance being negative; it may, however, 
 be positive, depending upon whether the negative react- 
 ance is greater or less than the positive reactance. If the 
 resultant reactance is positive, the current lags thee.m.f.; and 
 
THE ALTERNATING-CURRENT CIKCUIT 349 
 
 if the resultant reactance is negative, the current leads the 
 e.m.f. The impedance of a series circuit composed of a num- 
 ber of impedances (Z x ), (Z 2 ),(Z 3 ), etc., can be calculated by 
 substituting in the following general equation 
 Z = V (Ri + R 2 + R 3 + etc.) a + (X x + X 2 + X 3 + etc.)2 (141) 
 
 Example. Calculate the total impedance of a circuit com- 
 posed of two impedances in series having resistances of 10 and 
 5 ohms and reactances of 15 and 5 ohms, respectively. 
 
 Solution. The total resistance of the circuit is (10 + 5), or 
 15 ohms and the resultant reactance is [15+ ( 5)], or 10 
 ohms. Combining the total resistance and the resultant 
 reactance gives 
 
 Z = V (15)2+ (10)2= 18.03 
 
 Ans. 18.03 ohms. 
 
 389. Impedances in Parallel. In calculating the combined 
 impedance of a number of impedances in parallel, an equation 
 is used similar to equation (141), but instead of using the 
 separate resistances and reactances, the conductance and sus- 
 ceptance of the circuit are used. 
 
 The conductance of a circuit is the quantity by which the 
 e.m.f. must be multiplied to give the component of the current 
 parallel to the e.m.f. 
 
 The susceptance of a circuit is the quantity by which the 
 e.m.f. must be multiplied to give the component of the cur- 
 rent perpendicular to the e.m.f. 
 
 Admittance, conductance, and susceptance are all measured 
 in a unit called the mho. 
 
 The conductance is represented by the letter (G) and it is 
 numerically equal to 
 
 R R 
 
 G = = (142) 
 
 R2 + X2 Z2 
 
 The susceptance is represented by the letter (B) and it is 
 numerically equal to, 
 
 X X 
 
 B= (143) 
 
 R2 + X2 Z2 
 
 The reciprocal of the impedance of a circuit is called the 
 admittance and is represented by the letter (Y). 
 
350 PRACTICAL APPLIED ELECTRICITY 
 
 1 
 
 Y=- (144) 
 
 Z 
 
 Since 
 
 E 
 Z = - (145) 
 
 I 
 Then 
 
 Y = I-^E (146) 
 
 The admittance of a circuit bears the same relation to the 
 conductance and susceptance as exists between the impedance, 
 resistance, and reactance, or 
 
 Y= V G2 + B2 (147) 
 
 The total impedance of a number of devices connected in 
 parallel then is equal to the reciprocal of the admittance, 
 which can be determined by the equation 
 
 Y = V (G x + G 2 + etc.)> + (Bi + B 2 + etc.)2 (148) 
 
 Example. Calculate the total impedance of two impedances 
 in parallel having resistances of 8 and 6 ohms, and reactances 
 of 4 and 5 ohms, respectively. 
 
 Solution. Substituting in equation (142) gives the value of 
 the conductance of the first branch (Gi), equal to 
 
 8 81 
 
 GI = = .1 mho 
 
 82 -f 42 80 10 
 
 and the conductance of the second branch (G 2 ) equal to 
 
 6 6 
 
 G 2 = - = = .983 mho 
 
 62 4- 52 61 
 
 Substituting in equation (143) gives the value of the suscept- 
 ance of the first branch (B^, equal to 
 
 4 41 
 
 B! = = = =.05 mho 
 
 82 + 42 80 20 
 
 and the susceptance of the second branch (B 2 ), equal to 
 
 5 5 
 
 B 2 = = = .0819 mho 
 62 + 52 61 
 
 The total conductance (G) of the circuit is equal to (G x + G 2 ), 
 
THE ALTERNATING-CURRENT CIKCUIT 
 
 351 
 
 or 
 
 G=.l + .0983 = .1983 
 susceptance (B) of the circuit is equal to 
 
 and the total 
 (Bi + B 2 ), or 
 
 B = .05 + .0819 = .1319 
 
 The admittance may now be obtained by substituting in equa 
 tion (147), which gives 
 
 Y= V (.1983)2 + (.1319)2 
 = V .039 323 + .017 398 
 
 = V .056 72 
 = .238 mho 
 
 The impedance is equal to the reciprocal of the admittance, or 
 
 1 
 
 Z = =4.20 
 
 .238 
 
 Ans. 4.20 ohms. 
 
 390. Phase Relation of the Current and Potential Drops in 
 a Series Circuit. The series circuit shown in Fig. 288 is com- 
 posed of three parts, a resistance (R), an inductance (L), and 
 a condenser (C). The current is the same in all parts of such 
 
 Fig. 288 
 
 a circuit and an ammeter, that will operate on alternating 
 current, may be connected in the circuit at any point and it 
 will indicate the current that exists in the circuit. 
 
 A voltmeter (V) may be connected across the entire circuit, 
 as shown in the figure, and it will indicate the drop in poten- 
 tial over all three parts of the circuit combined. Three other 
 voltmeters (V r ), (Vi), and (V c ), may be connected across 
 
352 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 the resistance, inductance and capacity, respectively, as shown 
 in the figure, and their indications will be a measure of the 
 drop in potential over the three parts of the circuit. The sum 
 of the indications of the three voltmeters, (V r ), (Vi), and 
 (V c ), will be greater than the indications of the voltmeter 
 (V) for the following reason: The drop in potential over the 
 resistance is in phase with the current, the drop in potential 
 over the inductance leads the current, and the drop in potential 
 over the capacity lags the current. Since these three drops 
 in potential are not in phase, their resultant is not equal to 
 their numerical sum. The drops over the inductance and 
 capacity may neutralize each other, being opposite in 
 phase, in which case the voltmeter (V r ) would indicate the 
 same drop as the voltmeter (V). In 
 an alternating-current circuit the sum 
 of the drops over the various parts of 
 the circuit is not equal to the im- 
 pressed voltage except in a circuit con- 
 taining resistance alone. 
 
 391. Phase Relation of Currents and 
 Potential Drops in a Divided Circuit. 
 A divided circuit composed of three 
 branches is shown in Fig. 289. The 
 upper branch is a non-inductive resist- 
 ance, the middle branch is an induct- 
 ance, and the lower branch is a ca- 
 pacity. A voltmeter (V) connected 
 between the terminals (D) and (B) 
 indicates the drop in potential over 
 each of the three branches of the di- 
 vided circuit. The current in any one 
 of the branches is equal to the indica- 
 tion of the voltmeter (V) divided by 
 the branch. If the relation between 
 the resistance is the same in each 
 
 Fig. 2 
 
 the 
 
 the 
 
 impedance of 
 reactance and 
 
 branch, the current in the various branches will be dis- 
 placed in phase from the pressure indicated by the volt- 
 meter (V), the same amount, or the several branch currents 
 (Ir), (Ii), and (I c ) will be in phase. The current (I) indi- 
 cated on the ammeter (A) connected in the main line is the 
 numerical sum of the branch currents, when they are all in 
 
THE ALTERNATING-CURRENT CIRCUIT 
 
 353 
 
 phase, and the vector sum when the branch currents are not 
 in phase. 
 
 392. Instantaneous Power in an Alternating-Current Circuit. 
 The instantaneous power in a circuit at any time is equal to 
 the product of the current 
 and the e.m.f. at that par- 
 ticular instant. The two 
 curves (I) and (E), Fig. 
 290, represent the current 
 in a circuit and the e.m.f. 
 acting on the circuit. These 
 two curves are in phase 
 and the power in the cir- 
 cuit is represented by the 
 curve (P), its ordinates 
 being proportional to the 
 product of the ordinate of 
 
 180 i70 
 Fig. 290 
 
 360 
 
 the other two curves. This 
 product is positive in sign 
 at all times since the 
 
 sign of both the current and the e.m.f. changes at the same 
 time, and both loops of the curva (P) are drawn above the 
 horizontal line. If the current and the e.m.f. be displaced in 
 
 phase, as shown in Fig. 291, 
 the product of their in- 
 stantaneous values is not 
 positive throughout the 
 cycle, but it is negative in 
 sign fcr a portion of the 
 time and, as a result, part 
 of the curve (P) is below 
 the horizontal line. The 
 loops of the curve (P) above 
 the horizontal line represent 
 an output from the source 
 of energy and the loops be- 
 low the horizontal line rep- 
 resent an input into the 
 
 source of energy. The actual output then is proportional to 
 the difference in area of an equal number of upper and lower 
 loops. When the current and the e.m.f. are in phase, there 
 
354 PRACTICAL APPLIED ELECTRICITY 
 
 are no lower loops, and the power in the circuit might be 
 thought of as all being positive. If the current and the e.m.f. 
 be displaced in phase by 90 degrees, the upper and lower 
 loops are equal in area and the resultant power is zero. 
 
 The current in any case may be divided into two parts, one 
 part in phase with the e.m.f. and the other part making an 
 angle of 90 degrees with the e.m.f., or at right angles to it. 
 The power output due to the part of the total current at right 
 angles to the e.m.f. is zero, because the area of the upper and 
 the lower power loops are equal. The part of the total cur- 
 rent in phase with the e.m.f. is all effective as far as power 
 output is concerned, because the power loops will all be above 
 the horizontal line. 
 
 When the current and the e.m.f. are in phase, the power is 
 equal to the product of the effective e.m.f. and the current. 
 If the current and the e.m.f. are displaced in phase, the power 
 is not equal to the product of the effective e.m.f: and the 
 current, but the current must be resolved into two parts, one 
 part in phase with the e.m.f. and the other at right angles to 
 the e.m.f. The part of the current or component in phase 
 with the e.m.f. is equal to (I) times the cosine of the angle 
 (9) between the current and the e.m.f. This component of 
 the current times the e.m.f. gives the true power in the cir- 
 cuit, or 
 
 Power in watts = E I cos 9 (149) 
 
 in which (9) is the angle between the current and the e.m.f. 
 and cos 9 is called the power factor. 
 
 393. Determining the Value of the Power Factor. Since 
 the cosine of an angle such as (9)., Fig. 128, is equal to the 
 ratio of the line (c) to (b) or it is equal to (c-=-b), the power 
 factor of a circuit can be easily determined when the con- 
 stants of the circuit are known. The e.m.f. (E) and the cur- 
 rent (I), Fig. 285, are displaced in phase by the angle (9). 
 The line (RI) divided by the line (E) gives the cosine of (9), 
 or the power factor. Since (E) is equal to (ZI), and Z = 
 V R 2 4- X^ the value of the cosine of (9) may assume a 
 Dumber of different forms. 
 
 RI RI R R 
 Power factor = = = = (150) 
 
 E ZI Z V R2 4- X2 
 
THE ALTERNATING-CURRENT CIRCUIT 355 
 
 394. A Wattmeter Indicates the True Power in an Alter- 
 nating-Current Circuit. The indication of a wattmeter is pro- 
 portional to the strength of two magnetic fields, one of which 
 is produced by the load current and the other by the impressed 
 pressure. The direction of these two fields must bear a dif- 
 ferent relation to each other in order that the deflection of 
 the moving system of the wattmeter be in the proper direc- 
 tion. If one field reverses due to a reversal of the e.m.f. or 
 current, the moving system of the wattmeter will tend to move 
 over the scale in the opposite direction to what it did before 
 the one field reversed in direction. If both fields reverse at 
 the same time, the force tending to deflect the moving system 
 does not change in direction. A wattmeter would indicate 
 zero power if the force acting on the moving system acted for 
 the same time in opposite directions. This would be the case 
 when the e.m.f. and the current are displaced in phase by 90 
 degrees, the upper and the lower power loops being equal in 
 area. When the current and the e.m.f. are in or out of phase, 
 the indication of the wattmeter is proportional to the average 
 of all the values of the instantaneous power for a complete 
 cycle, or the instrument measures the true power. When the 
 e.m.f. and current are displaced in phase less than 90 degrees, 
 the upper and the lower loops of the power curve are not 
 equal. The force acting on the moving system corresponding 
 to the lower loop is opposite to the force corresponding to the 
 upper loop, and the resultant force is thus proportional to the 
 difference in these two forces, which causes an indication 
 corresponding to the true power. 
 
 The product of the voltmeter and the ammeter reading, 
 (E) and (I), does not give the true power in an alternating- 
 current circuit unless the current and the e.m.f. are in phase. 
 The product (E X I) is called the apparent power. In general, 
 the wattmeter reading (P), or true power, equals (E X I), or 
 apparent power multiplied by the power factor. 
 
 P = E X I X power factor (151) 
 
 Power factor = P -f- (E X I) (152) 
 
356 PRACTICAL APPLIED ELECTRICITY 
 
 PROBLEMS ON THE ALTERNATING-CURRENT CIRCUIT 
 
 1. A condenser of 132-microfarads capacity and an induct- 
 ance of .061 henry are connected in series and a 60-cycle 
 e.m.f. of 100 volts is impressed upon the circuit. Calculate 
 the inductance and the capacity reactances, respectively. 
 
 Ans. Inductance reactance (Xi) = 23.0 ohms. 
 Capacity reactance (X,-) = 20.0 ohms. 
 
 2. If a resistance of 4 ohms be connected in series with 
 the circuit given in problem 1, what will be the total impe- 
 dance of the circuit? What current will be produced by the 
 impressed pressure of 100 volts? 
 
 Ans. Impedance of entire circuit (Z) = 5 ohms. 
 
 Current (I) = 20 amperes. 
 
 3. Two impedances are connected in series and they each 
 are composed of resistances of 10 and 12 ohms, and react- 
 ances of ' 50 and 70 ohms. Calculate the total impedance of 
 the circuit. 
 
 Ans. 29.7 ohms. 
 
 4. Calculate the admittance of a circuit having a suscept- 
 ance and conductance of 3 and 5 mhos, respectively. What is 
 the impedance of the circuit? 
 
 Ans. Admittance (Y) = 5.83 mhos. 
 Impedance (Z) = .171 ohm. 
 
 5. The indication of a wattmeter connected to a certain 
 load is 10 000 watts. An ammeter connected in the line indi- 
 cates 125 amperes and a voltmeter connected across the load 
 indicates 100 volts. What is the impedance of the circuit and 
 the power factor? 
 
 Ans. Impedance (Z) = .8 ohm. 
 Power factor (PF) = .8 
 
 6. The effective value of a sine alternating current is 10 
 amperes, what are the average and maximum values? 
 
 AnSo Average current = 9.00 amperes. 
 Maximum current = 14.14 amperes. 
 
 7. A circuit having a resistance of 3 ohms and a resultant 
 reactance of 4 ohms is connected to a 100-volt line. Determine, 
 
THE ALTERNATING-CURRENT CIRCUIT 357 
 
 (a) the impedance of the circuit, (b) power factor, (c) cur- 
 rent, (d) apparent power, (e) true power. 
 
 (a) Impedance (Z) = 5 ohms 
 
 (b) Power factor = .6 
 
 Ans. (c) Current = 20 amperes 
 
 (d) Apparent power = 2000 watts 
 
 (e) True power =1200 watts 
 
CHAPTER XVIII 
 
 ALTERNATING-CURRENT MACHINERY 
 
 395. Alternators. An alternator is a machine for convert- 
 ing mechanical energy into electrical energy, which is delivered 
 as an alternating current to a circuit connected to the ter- 
 minals of the machine. The fundamental electrical principle 
 upon which the alternator operates is the same as that of the 
 direct-current generator, namely, electromagnetic induction. 
 Alternators, like direct-current machines, consist of two prin- 
 cipal parts, a magnetic field and an armature. The commu- 
 tator of the direct-current machine is replaced in alternators 
 by slip-rings which are connected to the terminals of the 
 armature winding, and with which brushes make continuous 
 contact and thus conduct the electricity to and from the 
 armature winding. 
 
 396. Types of Alternators. Alternators may be divided 
 into three types, depending upon the mechanical arrangement 
 of the magnetic field and armature, viz, 
 
 (A) Alternators with stationary fields and revolving arma- 
 tures. 
 
 (B) Alternators with stationary armatures and revolving 
 fields. 
 
 (C) Alternators with both armature and field stationary 
 and using a rotating part called the inductor. Such alterna- 
 tors are called inductor alternators. 
 
 Small machines are usually of the revolving armature type, 
 as the e.m.f. generated is usually comparatively low and the 
 current the brushes must carry is small and no difficulty is 
 experienced in properly collecting such a current. A direct- 
 current generator can be converted into a revolving-armature 
 alternator by placing two collector rings on one end of the 
 armature and connecting these two rings to points in the 
 armature winding that are 180 electrical degrees apart. Such 
 
 358 
 
ALTEENATING-CUKEENT MACHINERY 
 
 359 
 
 a connection for a two-pole, ring-wound armature is shown in 
 Fig. 292. The commutator is not shown in this figure. 
 
 The necessity of collecting the 
 armature current is overcome by mak- 
 ing the armature the stationary part 
 and revolving the field poles, the cir- 
 cuit of the field winding being con- 
 nected to the source of excitation by 
 means of collector rings and brushes. 
 In such machines the armature wind- 
 ing is placed in a laminated frame 
 
 that surrounds the revolving field. A revolving-field alterna- 
 tor is shown in Fig. 293. 
 
 The construction of the inductor alternator is such that 
 both the armature and the field are stationary. The reluctance 
 of the magnetic circuit in this type of machine is changed in 
 
 Fig. 292 
 
 Fig. 293 
 
 value by means of projecting arms, on a revolving mass of 
 iron called the inductor. The path of the magnetic circuit is 
 through the armature coils and as a result of the reluctance 
 
360 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 of this path changing, due to the rotation of the inductor, 
 there will be a varying magnetic flux through the armature 
 winding, which will result in an induced electromotive force 
 in the winding. This induced e.m.f. will be in one direction 
 for an increasing flux through the armature coils, and in the 
 opposite direction for a decreasing flux, resulting in an alter- 
 nating e.m.f. 
 
 Alternators may also be classified into the following groups: 
 
 (A) Single-phase Alternators. 
 
 (B) Polyphase Alternators. 
 
 397. Single-phase and Two-phase Alternators. A single- 
 phase alternator is one that produces a single electromotive 
 force, and a polyphase alternator is one that produces two or 
 more electromotive forces, which may or may not produce 
 currents in circuits that are electrically independent. The 
 electromotive forces in a polyphase alternator are related to 
 each other only by the element of time, or they are said to 
 
 90" 180* 
 
 Fig. 294 
 
 \ 
 
 Eb 
 
 Fig. 295 
 
 differ in phase. Thus in a two-phase alternator, there are two 
 electromotive forces which are displaced in phase by 90 de- 
 grees, or they are said to be in quadrature. The armature 
 inductors in which these electromotive forces are induced 
 may or may not form independent windings on the armature. 
 When these windings are not independent, they must each be 
 connected to two independent collector rings. The e.m.f.'s 
 between these two sets of rings can be represented by two 
 curves (E a ) and (E b ), Fig. 294, which are displaced in 
 phase by 90 degrees, or they may be represented by the two 
 
ALTEENATING-CUEKENT MACHINEEY 
 
 361 
 
 vectors (E a ) and (E b ), Fig. 295, that are at right angles 
 to each other. The arrow (R) in Fig. 295 represents the 
 direction of rotation. The number of collector rings on 
 such a machine can, however, be reduced to three, when 
 they are independent windings on the armature, by using one 
 ring as a common connection for both armature windings. 
 Such an arrangement would constitute a two-phase three-wire 
 system and the one in the previous case would be a two-phase 
 four-wire system. In the two-phase three-wire system, the 
 current in the common lead is equal to the vector sum 
 of the currents in the two outside leads, Fig. 296. When 
 there is the same current in each outside lead and the same 
 phase relation exists between the currents and their e.m.f.'s, 
 the system is said to be balanced. The current in the common 
 lead is not zero for a balanced load, however, as shown in Fig. 
 296, it being the vector sum of (I a ) and (I b ), or it is equal 
 to (!). 
 
 398. Three-Phase Alternators. 
 If three single-phase windings be 
 placed upon an armature core and 
 displaced 120 electrical degrees 
 from each other, the electromotive 
 forces induced in these three wind- 
 ings will be displaced in phase 120 
 degrees, as shown by the curves 
 (Ea), (Ei,), and (E c ), in Fig. 297, 
 and by the vectors (A), (B) and 
 (C) in Fig. 298. Each of these 
 windings may be provided with two 
 slip-rings, there being six in all, 
 and connected to electrically inde- 
 pendent circuits. Such a system 
 would constitute a three-phase six- 
 wire system. The three circuits connected to the differ- 
 ent phases may be kept practically independent of each 
 other by using four leads and connecting three of the col- 
 lector rings together, as shown in Fig. 299. The lead (4) 
 serves as a common return to the other three. When the 
 three receiving circuits connected between the mains (1), (2), 
 (3), and (4) have the same resistance and reactance, the 
 system is said to be balanced and the current in the three 
 
 Fig. 296 
 
362 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 circuits are equal and displaced in phase from their electro- 
 motive forces by the same angle, the three currents are then 
 120 degrees apart and their vector sum, which is the current 
 in main (4), is zero. Hence, for a balance load, main (4) 
 carries no current, and this lead can be dispensed with and 
 only three collector rings need be used, the other three being 
 connected together, forming what is called the neutral point. 
 
 o*' 360 
 
 Fig. 297 
 
 This arrangement of connections is called the "Y" or "star" 
 scheme of connecting the three windings. Three of the six 
 rings can be dispensed with entirely, one terminal of each of 
 the windings being connected to the neutral point inside the 
 
 armature, as shown in the 
 symmetrical diagram in 
 Fig. 300. 
 
 Another method of con- 
 necting the three wind- 
 ings of a three-phase ma- 
 chine is shown in Fig. 301, 
 which js called the "A" 
 (delta) or "mesh" scheme. 
 399. Relation of E.M.F. 
 
 Fig. 299 
 
 and Current in "Y" and 
 
 "A" Connected Armatures. The currents in the mains (1), 
 (2), and (3), Fig. 300, are the same as the currents in the 
 three windings (A), (B), and (C). 
 
 If the positive direction of the electromotive forces and cur- 
 rents in the windings (A), (B), and (C) be taken in the direc- 
 tion indicated by the arrows in Figs. 300 and 301, then the 
 
ALTERNATING-CURRENT MACHINERY 
 
 363 
 
 e.m.f. between the mains (1) and (2) in Fig. 300 will be equal 
 to the vector difference between the e.m.f.'s in windings (A) 
 and (B). (It must be remembered that the direction of the 
 arrows does not represent the actual direction of the e.m.f.'s 
 and currents, but only the assumed positive direction.) The 
 vector difference between the two e.m.f.'s in the windings (A) 
 and (B), which are displaced in phase by 120 degrees, is ob- 
 
 Fig. 300 
 
 Fig. 301 
 
 tained by reversing the direction of the vector (B) and adding 
 it to the vector (A), giving the result (A B), Fig. 302. The 
 e.m.f.'s between leads (2) and (3), and (3) and (1) are ob- 
 tained in a similar manner. These resultant e.m.f.'s will be 
 equal to V~3~times the e.m.f. in any one of the windings, which 
 can be shown by reference to Fig. 303. (Ei) represents the 
 e.m.f. in winding (A) and ( Ei.) represents the e.m.f. in wind- 
 ing (B). Assuming (E a ) and (E b ) are each equal to 2 units 
 of e.m.f., then (a) will represent 1 unit and (d) will represent 
 VlTunits of e.m.f. Two (d), which is equal to (A B), will 
 be equal to (2 V 3) units of e.m.f. when (E a ) and (Eh) are 
 equal to 2 units of e.m.f. Hence (A B) is equal to the V~3 
 times the e.m.f. per winding. 
 
 The e.m.f. between leads (1) and (3), Fig. 301, is the same 
 as the e.m.f. in the winding (A), or the e.m.f. between leads 
 for the "A" connection is equal to the e.m.f. in the winding 
 connected to the two leads. The current in lead (1) is equal 
 to the vector difference between the currents in windings (A) 
 and (B). These two currents are displaced in phase 120 
 degrees and their difference is obtained by reversing (B) and 
 adding it to (A). The current in the other leads are obtained 
 
364 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 in a similar manner and for a balance load the current in any 
 lead will be equal to V~3~times the current in any winding. 
 
 400. Connecting Receiving Circuits to a Three-Phase System. 
 When the receiving circuits connected to the various phases 
 of a three-phase system are dissimilar or take unequal current, 
 resulting in an unbalanced load, four mains should be used, 
 
 Fig. 302 
 
 Fig, 303 
 
 as indicated in Fig. 299, each receiving circuit then takes cur- 
 rent from one of the windings (A), (B), or (C) over the main 
 (4) and one of the outside mains. It is always desirable, 
 however, in the operation of alternators to keep the loads on 
 the various phases as near equal as possible and in practice 
 the different receiving circuits are so distributed between the 
 three phases as to satisfy this condition as nearly as possible. 
 If three single-phase motors, all of the same capacity and 
 carrying the same load, be operated from the three phases of 
 a three-phase system, the system will be balanced and no cur- 
 rent will exist in the lead (4) when the connections are made 
 as shown in Fig. 299. Three lighting circuits taking equal 
 currents will result in the same condition. If, however, one 
 of the motors or one of the lighting circuits be disconnected, 
 there will then be a current in lead (4). 
 
 When the output of the three-phase alternator is used to 
 drive three-phase induction motors, synchronous motors, and 
 synchronous converters, the currents in each of the three 
 windings will be equal and will be displaced in phase from 
 their respective e.m.f.'s by the same angle, or the system is 
 balanced. For balanced load only three leads are required and 
 
ALTERNATING-CURRENT MACHINERY 
 
 365 
 
 either the "Y" connection without the neutral, as shown in 
 Fig. 300, or the "A"' connection, as shown in Fig. 301, may 
 be employed. 
 
 The current in each receiving circuit in Fig. 304 is equal to 
 the current in the lead connected to it, and the e.m.f. over any 
 one of the receiving circuits in Fig. 305 is equal to the e.m.f. 
 between the leads connected to that particular receiving cir- 
 cuit. The current in each receiving circuit in Fig. 305 is 
 equal to the current in each lead divided by the V"sTand the 
 e.m.f. over each receiving circuit in Fig. 304 is equal to the 
 e.m.f. between leads divided by the V 3. 
 
 401. Measurement of Power in Single-Phase System. The 
 connections for the measurement of power in a single-phase 
 
 Neutral 
 
 Fig. 304 
 
 Fig. 305 
 
 system are identical to those for the measurement of power 
 in a direct-current circuit. The connections of a Weston indi- 
 cating wattmeter are given in Fig. 306. The alternator (A) 
 is supplying energy to the lamps (L) as a load. 
 
 402. Measurement of Power in a Two-Phase System. In a 
 two-phase four-wire system, the power is measured in each of 
 the two phases by separate wattmeters as though they were 
 single-phase circuits and the total power is obtained by adding 
 the two wattmeter readings. 
 
 In a two-phase three-wire system, the power may be meas- 
 ured by two wattmeters, they being connected as shown in Fig. 
 307. When the connections are thus made, the upper watt- 
 meter indicates the power in phase (A) and the lower watt- 
 meter indicates the power in phase (B). The total power 
 
366 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 at any instant is equal to the sum of the indications on the 
 two wattmeters. 
 
 A single wattmeter may be used to measure the power in a 
 two-phase circuit by connecting its current coil in the common 
 lead, as shown in Fig. 308, and then noting its indication first, 
 when the pressure circuit is connected to one outside lead, 
 
 Current Coil 
 
 * /5 P] l . 
 
 r^sinnmr 6666 
 
 DT-^CO..^^ r~;\ 
 
 Pressure Coil 
 
 Load 
 
 Fig. 306 
 
 Current Coil 
 Fig. 307 
 
 as shown by the full line in the figure, and second, when the 
 pressure circuit is connected to the other outside lead, as 
 shown by the dotted line in the figure. If the load on the two 
 phases remain constant while these two readings are being 
 taken, the total power output of the two-phase machine will 
 be equal to the sum of the two wattmeter indications. 
 
 When the pressure circuit 
 
 _ _ is corrected as shown by 
 
 the dotted line, the watt- 
 meter will not indicate the 
 power delivered by phase 
 (A), nor will it indicate the 
 
 Common 
 
 Current Coil 
 
 555 
 
 power delivered by phase 
 (B) when the pressure con- 
 Fig. 308 nection is made as shown 
 by the full line, unless the 
 
 current in each phase is in phase with its e.m.f. The rea- 
 son for this can be shown by referring to Fig. 296, 
 in which (B a ) and (E b ) represent the e.m.f.'s of phases 
 (A) and (B), (I a ) and (I b ) represent the currents in 
 the two phases, and these currents are shown displaced 
 in phase from their e.m.f.'s by the angles (6^ and (9 2 ). 
 The current in the common lead, or in the current coil of the 
 wattmeter, is represented by the vector (I n ), which is the 
 
THE ALTEKNATING-CUEKENT CIKCUIT 367 
 
 resultant of (I a ) and (I b ). When the pressure coil is con- 
 nected across phase (A), the wattmeter indication is equal to 
 (E a X ! X sin 9 3 ). The product of (I n ) and (sin O 3 ) is equal 
 to the component of (I n ) that is in phase with (E a ). The 
 indication of the wattmeter when the pressure connection is 
 across phase (B) is equal to (Ei, X I n X cosB 3 ). The product 
 of (I n ) and (cos 0,) is equal to the component of (I n ) that 
 is in phase with (E b ). If the component of (I n ) in phase 
 with one of the e.m.f.'s, say (E a ), is equal to the current in 
 phase (A), then the wattmeter will indicate the power in 
 phase (A) when the pressure connection is made as shown by 
 the dotted line. The component of (I n ) in phase with (E a ) 
 will be equal to (L) only when the currents in the two 
 phases are in phase with their e.m.f.'s. 
 
 403. Measurement of Power in a Three-Phase System. The 
 power in a three-phase six-wire system can be measured as 
 though it were three single-phase circuits, which in reality 
 
 it is. The total power out- 
 
 I ./ooonoorv^ put of a macnine then is 
 
 ~~^? equal to the sum of the 
 wattmeter indications in the 
 three phases. In a three- 
 phase four-wire system the 
 
 power per P hase can be de ' 
 termined by connecting a 
 wattmeter in each of the 
 Fig. 309 leads (1), (2), and (3), and 
 
 connecting their pressure 
 
 circuits between these leads and the neutral lead (4), Fig. 299. 
 The total power output is equal to the sum of the three watt- 
 meter indications. In a three-phase three-wire system, the 
 power per phase can be determined by connecting three watt- 
 meters as shown in Fig. 309. The total power output of the 
 three phases is equal to the sum of the three wattmeter indi- 
 cations. The above connection will apply equally well when 
 the receiving circuit is connected "Y" or "A" provided the 
 series coils are connected in series with each load and the 
 pressure coils across the loads. 
 
 Two wattmeters may be used in measuring the power in a 
 three-phase three-wire system by connecting them as shown 
 in Fig. 310. 
 
368 PRACTICAL APPLIED ELECTRICITY 
 
 The sum of the two wattmeter readings is the total power 
 delivered to the three receiving circuits. When the power 
 factor is below .5, the reading of one wattmeter will be nega- 
 tive and the total power is then equal to the algebraic sum or 
 numerical difference of the two readings. 
 
 All of the above connections apply to either balanced or 
 unbalanced loads, making them applicable to any practical 
 case. 
 
 If the system is balanced, only one wattmeter need be used 
 in Fig. 309, and its indication multiplied by three will give the 
 total power, since on a balanced load each of the wattmeters 
 will indicate the same. The power in any balanced three- 
 phase three-wire system is equal to ( V~3~X E X I X cos 6), 
 (E) being the e.m.f. between leads, (I) the current in each 
 lead, and (cos 9) the power factor. 
 
 The power factor of a balanced three-phase circuit can be 
 determined from the two wattmeter readings, when they are 
 connected as indicated in Fig. 310, as follows: 
 
 _Pi-P 2 
 Tangent 6 = V 3 (153) 
 
 Pi + P 2 
 
 Substituting the values of (Pj), which is the larger reading 
 and will always be positive, and (P 2 ), which is the smaller 
 reading and may be positive or negative in the above equation, 
 
 gives the value of the tan- 
 Current Coil sent of (0). The angle 
 
 < e > can tnen be deter - 
 
 mined from the table of 
 trigonometric functions, 
 Chapter 20, and the cosine 
 of this angle is the power 
 factor. 
 
 Current Coil 404. The Synchronous 
 
 Fig. 310 Motor. In the operation of 
 
 an alternating-current gen- 
 erator, a mechanical force must be applied to rotate the 
 moving part of the machine, and when a given conductor 
 on the armature is under a north pole of the field, the 
 current in the conductor is in such a direction that the mag- 
 netic field exerts a force on it which opposes the movement of 
 the conductor or the rotation of the armature. If the conductor 
 
ALTERNATING-CURRENT MACHINERY 
 
 moves out of the field of a north pole and into the field 
 of a south pole, the current will be opposite in direc- 
 tion and, as a result, there is still a force acting on the con- 
 ductor which opposes the rotation of the armature. If the 
 current output of the generator increases, this opposing force 
 increases and more mechanical power must be supplied to 
 drive the machine. 
 
 If the field of an alternator be excited by a direct current, 
 and an alternating current from some external source be sent 
 through its armature, which is revolved by an engine or motor 
 at such a speed that a given inductor in the winding passes 
 from a certain position under a north pole to a corresponding 
 position under the next north pole during the time of one 
 cycle, the motion of the armature will be aided by the cur- 
 rent when the direction of the current is such that the force 
 exerted by the magnetic field upon the various conductors aids 
 the motion. Since the current reverses in direction when 
 the inductor passes from one pole to the adjacent pole, which 
 is of opposite polarity, the force exerted by the magnetic field 
 upon the conductor remains constant in direction. If the 
 speed of the alternator has been adjusted so that the above 
 conditions are fulfilled, the engine or motor may be discon- 
 nected and the alternator will continue to revolve at a con- 
 stant speed, which is determined by the frequency of the 
 supplied current and the number of poles comprising the mag- 
 netic field of the motor. When an alternator is operated in 
 the above manner it may deliver power to some load by means 
 of a belt or direct connection, and it is called a synchronous 
 motor. 
 
 Synchronous motors are designed to operate on single-phase 
 or polyphase circuits, their operation, however, is more satis- 
 factory on polyphase circuits. Motors of this kind are called 
 synchronous because they run in synchronism with the source 
 of supply. Their speed is not necessarily the same as that of 
 the generator driving them, it being the same only when the 
 motor and the generator have the same number of poles. The 
 Speed of a synchronous motor can be determined by the use 
 Of the equation 
 
 2 X f X 60 
 S = (154) 
 
370 PRACTICAL APPLIED ELECTRICITY 
 
 In the above equation (f) is the frequency of the impressed 
 voltage, (p) is the number of poles on the motor, and (S) is 
 the speed of the motor in revolutions per minute. 
 
 405. Operation of a Synchronous Motor. The synchronous 
 motor does not behave in the same way as a direct-current 
 motor. For example: If the field of a direct-current motor 
 be weakened, the motor will speed up in order that its counter- 
 electromotive force may reach the proper value. When the 
 field of a synchronous motor is weakened, there is no change 
 in its speed, since the motor must run in synchronism with 
 the impressed e.m.f. A change in load on a synchronous 
 motor Or a change in field strength will result in a change in 
 the phase displacement of the armature current and the im- 
 pressed voltage When the motor is operating without load, 
 the field current can be adjusted to such a value that the cur- 
 rent taken by the motor is very small and its counter e.m.f. 
 is practically in opposition to the impressed voltage. An 
 increase in field current will cause the armature current to 
 lead the impressed voltage, and a decrease in field current will 
 cause the armature current to lag the impressed voltage. If a 
 load be placed on a synchronous motor, its armature will lag 
 a small amount behind the alternator driving it, and this angle 
 will increase with an increase in the load. When the arma- 
 ture of the motor lags, the counter-electromotive force is no 
 longer in opposition to the impressed e.m.f. and a current will 
 be produced which is just sufficient to supply the required 
 torque to enable the motor to carry its load. By increasing 
 the load, the displacement of the armature will become suffi- 
 ciently great to cause the motor to be thrown out of synchron- 
 ism, or it will "break down" and stop. 
 
 406. Starting Synchronous Motors. A single-phase syn- 
 chronous motor cannot be started from rest by sending an 
 alternating current through its armature, the field being ex- 
 cited by a direct current, because the current in the armature 
 is rapidly reversing in direction and tends to cause the arma- 
 ture to rotate first in one direction and then in the other direc- 
 tion. Single-phase synchronous motors must always be 
 brought up to full speed by some outside source of power, such 
 as another motor or engine, before they can be connected to 
 the source of electrical power. 
 
 The polyphase synchronous motor may be started by con- 
 
THE ALTERNATING-CURRENT CIRCUIT 371 
 
 necting its armature directly to the line, the field circuit of 
 the machine being open. When the machine has reached 
 synchronous speed, the field circuit can be closed and the load 
 gradually thrown on. The motor is usually connected to its 
 load by means of a friction clutch. This method of starting 
 synchronous motors has the great disadvantage that the 
 machine takes an exceedingly large lagging current and this 
 causes an excessive drop in the supply lead 
 and a general disturbance of the distributing 
 system. The taking of a large current from the 
 line can be avoided by the use of an auto-starter 1 L, I i_ t IL 
 or compensator. The operation of an auto- 
 starter is described briefly in section (415). 
 
 Very large synchronous motors are usually 
 started by means of an induction motor that 
 can be operated from the same line the syn- c 
 chronous motor is operated from, or by means 
 of a small engine or direct-current motor, on 
 account of the very small torque exerted by the 
 armature when it is connected to the line. 
 
 407. Synchronizing. In order that an alter- Fig. 311 
 nator or a synchronous motor may be connected 
 to a line, it must be in synchronism. Synchronizing con- 
 sists in adjusting the frequency, the phase relation of two 
 e.m.f.'s and their magnitude so that they will coincide when 
 connected together. The general practice in synchronizing is 
 first to adjust the speed of the incoming machine until the 
 frequency of its e.m.f. corresponds to the frequency of the 
 line to which it is to be connected, then to adjust the field 
 current until the machine and the line voltage are the same. 
 Adjust the phase relation of the incoming machine until it is 
 in phase with the line, which can be determined by means of 
 lamps, a synchronoscope, or a voltmeter, and when they are 
 in phase, they may be connected directly together. 
 
 When lamps are used in synchronizing, they should be con- 
 nected as shown in Fig. 311, one in each phase. The switch 
 should be so arranged that it can be closed the instant the 
 machines are in phase and synchronism, viz, when the lamps 
 are dark. Two transformers may be used with their primaries 
 connected across the same leads but on opposite sides of the 
 paralleling switch. Their secondaries may be connected so 
 
372 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 that their e.m.f.'s are in series or in opposition when the two 
 machines are in phase and synchronism. When they are in 
 opposition and a lamp in circuit, the lamp will be dark when 
 the machines are in phase and synchronism, and if they are 
 connected in series the lamp will be light. 
 
 The synch ronoscope is an instrument that gives an indica- 
 tion of the phase relation of two e.m.f.'s, and the one of 
 higher frequency can be determined by noting the direction 
 in which the pointer on the instrument rotates. 
 
 In synchronizing machines it is always best to close the 
 main switch when the incoming machine is coming into 
 proper phase rather than going out of it, as the inertia of 
 the armature in one case assists and in the other retards 
 prompt synchronizing. 
 
 408. The Transformer. The 
 transformer in its simplest form 
 consists of two separate and elec- 
 trically independent coils of wire 
 that are wound upon a laminated 
 iron core that is common to both 
 of the windings. One of the 
 coils is connected to some source 
 of electrical energy which may 
 be high or low voltage, and re- 
 ceives an alternating current from it; and the other coil is 
 connected to a load to which it delivers alternating current at 
 a low or high voltage. The coil of the transformer that is 
 connected to the source of energy is called the primary coil, 
 and the one that is connected to the load is called the sec- 
 ondary coil, Fig. 312. When the transformer delivers energy 
 at a higher voltage than that impressed upon the primary 
 coil, it is called a step-up transformer; when it delivers energy 
 at a lower voltage than that impressed upon the primary coil, 
 it is called a step-down transformer. 
 
 409. Action of the Transformer without Load. A trans- 
 former is said to be operating on zero load when the sec- 
 ondary circuit is open and it is, of course, delivering no cur- 
 rent. When there is no current in the secondary winding, 
 there is a very small current in the primary winding for the 
 following reason: The current in the primary winding will 
 cause an alternating magnetic field to be set up through 
 
 Primary Secondary 
 Fig. 312 
 
THE ALTERNATING-CURRENT CIRCUIT 373 
 
 both the primary and the secondary windings, which induces 
 an electromotive force in both of them. This induced e.m.f. is 
 in the opposite direction to the e.m.f. impressed upon the 
 primary winding and very nearly equal to it. It is only this 
 difference in e.m.f. that is available for producing a current 
 in the primary winding, and since this difference is small, 
 there will be a small current in the primary winding when 
 there is no load on the transformer. This current is called 
 the no-load current of the transformer. The induced e.m.f. 
 In the secondary coil is in phase with the e.m.f. induced in 
 the primary, and it is in opposition to the impressed e.m.f. 
 on the primary, or the primary and the secondary e.m.f.'s are 
 displaced in phase by 180. 
 
 410. Action of the Transformer on Load. If the sec- 
 ondary coil of a transformer be connected to a receiving cir- 
 cuit and a delivering current, the transformer is said to be 
 loaded. Since the e.m.f. induced in the secondary coil is 
 180 from the impressed e.m.f. on the primary coil, the cur- 
 rent in the secondary coil will produce a magnetizing effect 
 which tends to lessen that produced by the small current 
 already in the primary coil and, as a result, the variations in 
 the magnetic flux passing through both of the coils is de- 
 creased, which results in a decrease in the induced e.m.f. 
 in the two coils. This decrease in counter e.m.f. in the 
 primary coil results in an increase in the difference between 
 the impressed e.m.f. and the counter e.m.f., which results in 
 an increase of current in the primary coil. If the load on the 
 secondary coil be increased or decreased there will be a pro- 
 portional increase or decrease of current in the primary coil. 
 
 411. Ideal Electromotive Force and Current Relations in 
 a Transformer. Neglecting all losses in the transformer, the 
 following relations will exist between the primary and the 
 secondary e.m.f.'s and the primary and the secondary currents. 
 Since it is assumed that the same magnetic flux passes 
 through both the coils, the ratio of the induced e.m.f.'s in the 
 two coils must be the same as the ratio between the number 
 of turns in the two windings. The induced e.m.f. in the 
 primary is equal to the impressed e.m.f. when all losses are 
 neglected, and then 
 
374 PRACTICAL APPLIED ELECTRICITY 
 
 E P Np 
 
 (155) 
 E s N S 
 
 Since the magnetizing action of the ampere-turns in the two 
 coils are equal and opposite, neglecting all losses, we have 
 
 NpIp = N s Is (156) 
 
 or 
 
 I P N s 
 
 (157) 
 
 Is Np 
 
 The above equation states that the primary and the second- 
 ary currents are to each other inversely as the number of 
 turns in the two coils. 
 
 412. Actual Electromotive Force and Current Relations in 
 a Transformer. In the previous section the relation of the 
 e.m.f.'s and the currents was based upon the assumption that 
 there were no losses in the transformer, which is not the 
 case in practice. The principal losses to consider in the 
 practice! operation of a transformer are: 
 
 (A) Loss due to no-load current. 
 
 (B) The I2R loss in the primary and the secondary coils. 
 
 (C) Loss due to magnetic leakage. 
 
 The part of the no-load current in phase with the impressed 
 e.m.f. on the primary coil represents a loss, and it is the no- 
 load current that affects the ideal relation between the pri- 
 mary and the secondary currents, as given in equation (157). 
 The resistance of the primary and the secondary coils and 
 magnetic leakage are, on the other hand, the only things that 
 affect to any extent the ideal relation between the primary 
 and the secondary voltages. If all of the magnetic flux created 
 by the current in either the primary or the secondary coils 
 passed through the other coil, there would be no magnetic 
 leakage, which would correspond to an ideal magnetic circuit. 
 Magnetic leakage in its effect is equivalent to an outside in- 
 ductance that is connected in series with the coils of the 
 transformer. If this inductance be represented by (L), then 
 the e.m.f. required to overcome it when there is a current of 
 (I) amperes in the circuit is equal to (27rfLI). The effect of 
 coil resistance and magnetic leakage upon the ideal relation 
 between the primary and the secondary voltages is shown by 
 means of a vector diagram. 
 
THE ALTERNATING-CURRENT CIRCUIT 
 
 375 
 
 413. Vector Diagram of a Transformer. The magnetic 
 flux that passes through both the primary and the secondary 
 coils is represented by the vector (<f>), as shown in Fig. 313, 
 and the no-load current by the vector (I ). The e.m.f. induced 
 in the primary and the secondary coils will lag the magnetic 
 flux (*) 90. 
 
 The e.m.f. impressed upon the 
 primary coil is used in overcom- 
 ing the resistance of the coil, the 
 counter e.m.f. induced in the coil 
 by the flux ($), which passes 
 through both coils, and the effect 
 of magnetic leakage. The e.m.f. 
 to overcome the resistance is in 
 phase with the primary current 
 (I P ), as shown in the figure, the 
 vector (E P ) represents the e.m.f. 
 required to overcome the e.m.f. 
 induced in the primary coil by 
 the flux ($), and the vector 
 (2irfL P Ip) represents the e.mf. 
 required to overcome the effect 
 of magnetic leakage in the pri- 
 mary, which is 90 degrees in 
 advance of the primary current. 
 The vector (E p ) represents the 
 
 voltage impressed upon the primary coil. The voltage induced in 
 the secondary winding is represented by the vector (E s ), which 
 bears the same relation to the e.m.f. induced in the primary 
 coil as exists between the primary and the secondary turns, 
 which has been assumed unity in this case. This vector will 
 represent the voltage at the terminals of the secondary coil 
 when there is no load on the transformer. When the sec- 
 ondary coil is supplying a current, the terminal voltage drops 
 on account of the (LRs) drop and magnetic leakage. These 
 drops must be subtracted from the total e.m.f. induced in 
 the secondary coil, which gives the terminal voltage equal to 
 (E s ). The drop (R S I S ) is parallel to (I s ), and the drop 
 (27rfL s Is) is perpendicular to (I s ). If the secondary coil is 
 supplying a current (I s ) there will be a current in the primary 
 
376 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 coil, which combines with the no-load current (I ), giving the 
 true primary current (I). 
 
 414. Types of Transformers. Transformers may be 
 divided into two types, depending upon the arrangement of 
 the coils and magnetic circuit, viz, 
 
 (A) Core-type transformers. 
 
 (B) Shell-type transformers. 
 
 In the core-type transformer the coils are placed outside of 
 the magnetic circuit, as shown in Fig. 314. In the shell-type 
 transformer the magnetic circuit surrounds the coils, as 
 shown in Fig. 315. 
 
 Transformers may be divided into two types, depending 
 upon the kind of circuit they are to be used on, viz, 
 
 (A) Single-phase transformers. 
 
 (B) Polyphase transformers. 
 
 Fig. 314 
 
 Fig. 315 
 
 In a single-phase transformer there is only one set of pri- 
 mary and secondary terminals, and the fluxes in the one or 
 more magnetic circuits are all in phase. In the polyphase 
 transformer there are a number of different sets of primary 
 and secondary connections. These various sets can be used in 
 the different phases of a polyphase system. In such a trans- 
 former there are two or more magnetic circuits through the 
 core, and the fluxes in the various circuits are displaced in 
 phase. It is not necessary to always use polyphase trans- 
 formers in polyphase circuits, as a number of single-phase 
 transformers may be used, one in each phase. 
 
 Transformers may be divided into three types, depending 
 upon the nature of their output, viz, 
 
THE ALTERNATING-CURRENT CIRCUIT 377 
 
 (A) Constant-potential transformers. 
 
 (B) Constant-current transformers. 
 
 (C) Current transformers. 
 
 The constant-potential transformer is one so constructed 
 that the relation of the primary and the secondary voltage 
 remains practically constant, regardless of the load on the 
 transformer. 
 
 The constant-current transformer is one so constructed that 
 the secondary current remains constant in value, and when 
 the load on the transformer changes, there is a change in the 
 e.m.f. induced in the secondary winding. 
 
 The current transformer is one so constructed that the 
 secondary current always bears a definite relation to the pri- 
 mary current. These transformers are used principally in 
 connection with instruments where it is desired to send a 
 definite fractional part of the total line current through the 
 instrument. They correspond to the shunt in the direct- 
 current circuit. 
 
 415. The Auto-Transformer. The auto-transformer con- 
 sists of an ordinary transformer with its primary and sec- 
 ondary coils so connected with respect to each other that 
 the e.m.f. induced in the secondary coils either aids or 
 opposes the e.m.f. impressed upon the primary coil. When 
 the e.m.f.'s of the two windings act in the same direction, 
 it is said to be an auto-step-up transformation, and when 
 they act in opposite directions it is said to be an auto-step- 
 down transformation. 
 
 416. Methods of Cooling Transformers. In small-capacity 
 transformers the radiating surface is ample to prevent an 
 excessive temperature rise when the transformer is in opera- 
 tion. With an increase in capacity of the transformer, there 
 is a proportional increase in the energy loss, and hence the 
 heat generated, but the radiating surface does not increase at 
 the same rate and, as a result, the temperature rise will, as 
 a rule, be greater in large transformers than it is in small 
 ones, unless some means be provided for cooling them. 
 Transformers may be classified according to the method em- 
 ployed in cooling them as follows: 
 
 (A) Dry-transformers, self-cooling. 
 
 (B) Oil-filled transformers, self-cooling. 
 
378 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 (C) Transformers cooled by a blast of air. 
 
 (D) Transformers cooled by a current of water. 
 
 (E) Transformers cooled by a combination of the above. 
 
 No special means is ever employed for cooling small trans- 
 formers, as they are dry. 
 
 Large transformers are cooled by filling the space sur- 
 rounding the coils and core with a good quality of oil, which 
 tends to equalize the temperature of the vari6us parts and 
 to conduct the heat to the containing case of the transformer, 
 where it is radiated. The containing case is often corrugated 
 or made with protruding ribs, which adds to its radiating sur- 
 face, as shown in Fig. 316. 
 
 Fig. 316 
 
 Fig. 317 
 
 Large transformers are often constructed so that they can 
 be cooled by forcing a blast of air through them. The coils 
 in such transformers are usually spread apart so as to form 
 ducts through which the air may circulate. 
 
 Large transformers are often cooled by circulating water 
 through a pipe which surrounds the coils and core. This 
 method of cooling, however, is usually used in combination 
 with the oil-cooled type. 
 
 417. Rotating Magnetic Field. Suppose the projecting 
 arms or poles on the field frame of a dynamo be divided into 
 
THE ALTERNATING-CURRENT CIRCUIT 379 
 
 three groups, and the poles belonging to one group marked 
 (Aj), (A 2 ), (A;,), etc., those of another group marked (Bj), 
 (B 2 ), (B 3 ), etc., and the third group (Ci), (C 2 ), (C 3 ), etc., 
 as shown in Fig. 317. If a winding be placed on the poles 
 belonging to any group, alternate ones being wound in op- 
 posite directions, and each of these windings then connected 
 to a source of direct e.m.f., the inner end of the poles will 
 be magnetized alternately north and south. If an alternating 
 e.m.f. be used, the polarity of the poles belonging to any 
 group will be reversed twice per cycle. By connecting the 
 three groups of windings to the different phases of a three- 
 phase circuit, any three poles that occur in succession 
 around the frame will not be magnetized to a maximum 
 polarity of the same time. The time required for the maximum 
 polarity to pass from one pole to the next is one-third of a 
 half cycle or one-sixth of a cycle. The maximum polarity is 
 passed from one pole to the next around the frame, which 
 results in what is termed a rotating magnetic field. The speed 
 at which this field rotates can be determined as follows: Let 
 (f) represent the frequency of the impressed voltage, (p) 
 the number of poles per phase, and since two poles corre- 
 spond to one cycle, the time per revolution of the field will 
 be equal to 
 
 2f 
 time per revolution = (158) 
 
 P 
 and 
 
 f 
 number of revolutions per second = (159) 
 
 2 P 
 
 418. Induction Motor. If a hollow metal cylinder b 
 mounted inside of a rotating field, there will be an e.m.f. in- 
 duced in it, due to the relative motion of the field and the 
 cylinder, and this e.m.f. will produce a current in the cylinder 
 which reacts upon the magnetic field and causes the cylinder 
 to rotate. The path taken by the induced current is not 
 very well defined in the case of a cylinder and, as a result, it 
 will not all be useful in producing a tangential force. This 
 difficulty is overcome by slotting the cylinder in a direction 
 parallel to the axis about which it rotates. The flux passing 
 between poles of opposite polarity can be greatly increased. 
 
380 PRACTICAL APPLIED ELECTRICITY 
 
 with the same current in the winding, by mounting the cyl- 
 inder upon an iron core, which should be laminated. This 
 increase in flux will result in a greater e.m.f. being induced 
 in the cylinder and a greater current would result, which 
 would increase the force tending to turn the cylinder. The 
 above principles are those upon which the induction motor 
 operates. 
 
 Fig. 318 
 
 The winding of an induction motor that is stationary is 
 called the stator, and the moving part is called the rotor. 
 The stator windings are usually placed in slots cut in what is 
 called the stator core, instead of being wound upon poles as 
 shown in Fig. 317. The stator core of a small induction motor 
 is shown in Fig. 318. The rotor in its simplest form consists 
 of copper conductors imbedded in slots in a laminated iron 
 core. These conductors are all connected in parallel by cop- 
 per collars, one being placed at each end. With this arrange- 
 ment the current due to the induced e.m.f. passes in a direc- 
 tion parallel to the axis about which the rotor rotates, and 
 its effect in producing rotation is a maximum. This simple 
 form of rotor is called the "squirrel-cage" type, Fig. 319. The 
 inductors may or may not be insulated from the core. 
 
THE ALTERNATING-CURRENT CIRCUIT 381 
 
 In some cases the rotor is provided with a regular wind- 
 ing, and this winding is connected to an external circuit by 
 means of slip-rings. 
 
 419. Operation of the Induction Motor. If the stator be 
 connected to a source of energy and the rotor is free to turn, 
 it will run at such a speed that the induced e.m.f. in the 
 rotor winding will produce the current required to drive the 
 rotor. The induced e.m.f. in the rotor depends upon the rela- 
 tive movement of the magnetic field and the rotor winding. 
 
 Fig. 319 
 
 If the rotor were to run at the same speed that the magnetic 
 field revolves, there would be no e.m.f. induced in its winding. 
 Then in order that there be an e.m.f. induced in its winding, 
 its speed must be less (in the case of a motor) than that of 
 the magnetic field. If (S f ) represents the speed of the field, 
 (S P ) the speed of the rotor, then the fifference in speed of 
 the rotor and the magnetic field is (S f S P ). This difference 
 in speed divided by (S P ) is called the slip, and it is usually 
 expressed as a per cent of the synchronous speed. When the 
 motor is loaded, the rotor speed decreases in order that the 
 current may increase in value, it depending upon the induced 
 e.m.f., which in turn depends upon the ratio of the speeds of 
 the rotor and the magnetic field. A three-phase induction 
 motor is shown in Fig. 320. 
 
 420. Speed Regulation of the Induction Motor. The speed 
 of induction motors may be regulated by changing the value of 
 the impressed voltage upon the stator, by changing the con- 
 nections of the stator winding so as to change the number 
 of poles, or by changing the resistance of the rotor winding. 
 
382 PRACTICAL APPLIED ELECTRICITY 
 
 With a decrease in impressed voltage, the stator flux is 
 lessened and the rotor current decreases if the speed re- 
 mains constant. If the torque the motor is to generate is to 
 remain constant, it being proportional to the product of the 
 flux and the rotor current, there must be an increase in rotor 
 current on account of the decrease in stator flux, in order 
 that the motor carry its load. The required increase in rotor 
 current is produced by a decrease in rotor speed. 
 
 If the stator winding be changed, so as to change the num- 
 ber of poles, there will be a corresponding change in rotor 
 speed, the slip remaining constant. 
 
 Fig. 320 
 
 If the resistance of the rotor be increased, the e.m.f. re- 
 quired to produce a given rotor current must increase, and 
 in order that there be an increase in rotor e.m.f. there must 
 be a decrease in rotor speed. 
 
 421. Methods of Starting the Induction Motor. Polyphase 
 induction motors may be started by connecting their stator 
 
THE ALTERNATING-CURRENT CIRCUIT 383 
 
 windings directly to the line. The current taken from the 
 line, however, is excessive, and an auto-starter or com- 
 pensator is usually used. 
 
 Single-phase induction motors will not start when their 
 stator windings are connected to. a single-phase circuit, unless 
 special provision is made for starting. There are four meth- 
 ods that are employed for starting single-phase motors, viz, 
 
 (A) Hand starting. 
 
 (B) Split-phase starting. 
 
 (C) Repulsion motor starting. 
 
 (D) "Shading-coil" starting. 
 
 Fig. 321 
 
 (A) Very small induction motors may be started by giv- 
 ing them a good start by hand. 
 
 (B) In split-phase starting there are two circuits through 
 the motor, and there is a phase difference between the cur- 
 rents in the two branches, if the ratio between the resistance 
 and reactance of the branches is different. This difference 
 in phase of the currents in the two circuits produces the 
 required rotating field to start the motor. The starting 
 
384 PRACTICAL APPLIED ELECTRICITY 
 
 torque, however, is very small when the current does not 
 exceed full-load current. 
 
 (C) If the field magnets of an ordinary direct-current 
 dynamo be laminated and excited by an alternating current, 
 there would be induced e.m.f.'s set up in the armature wind- 
 ing, provided the brushes were changed from their original 
 position. These induced e.m.f.'s would produce currents 
 which would react upon the alternating magnetic field and 
 produce a torque tending to cause rotation. A single-phase 
 alternating-current motor constructed to operate in the above 
 manner is called a repulsion motor. After the motor is up to 
 speed the brushes are automatically disconnected and it 
 operates as an induction motor. 
 
 (D) The "shading-coil" consists of a single turn of copper 
 about a part of each field-pole. The flux through the part 
 of the field-pole enclosed by this turn of wire does not 
 change in value as rapidly as the flux in the remaining por- 
 tion of the pole, due to the magnetic effect of the current in 
 the copper coil that is produced by the e.m.f. induced in it. 
 As a result of the above condition the flux travels across the 
 pole-face and there will be a torque exerted upon the rotor. 
 
 422. Induction Generator. An induction motor when 
 operating without load takes a very small current from the 
 supply leads and the speed of its rotor is very near that of 
 the magnetic field. If the rotor be connected to some source 
 of power and speeded up to the same speed as that of the 
 magnetic field, the electrical power intake of the stator will 
 be very small, it being equal to the iron loss in the stator. 
 By increasing the speed of the rotor until it is above syn- 
 chronism, the stator will deliver power to the alternating- 
 current leads, provided the alternating-current generator re- 
 mains connected to the leads to fix the frequency. When an 
 induction motor is so used it is called an induction generator. 
 
 423. Frequency Changer. An induction motor provided 
 with a rotor having a winding with terminals connected to 
 collector rings may be used as a frequency changer, that is, 
 it may be used to change the frequency. When the rotor of 
 the motor is held stationary, the magnetic flux of the stator 
 induces e.m.f.'s in the rotor winding that are of the same 
 frequency as the alternating e.m.f.'s applied to the stator. 
 If the rotor is run at one-half spe,ed, in the direction the mag- 
 
THE ALTEENATING-CUKRENT CIECUIT 385 
 
 netic field rotates, the e.m.f.'s induced in the rotor windings 
 will be one-half full frequency. By driving the rotor in the 
 opposite direction to the direction in which the magnetic 
 field revolves, the frequency is raised. Thus, if the rotor be 
 revolved backward at one-half speed, the induced e.m.f.'s in 
 the rotor windings -will be one and one-half times the fre- 
 quency of the e.m.f.'s impressed upon the stator windings. 
 
 424. Synchronous Converter. The synchronous converter 
 is a machine for converting- alternating-current to direct-cur- 
 rent, or vice versa, or it may be used as a double-current gen- 
 erator. The synchronous converter resembles a direct-cur- 
 rent generator in general appearance, the chief difference 
 being the addition of a number of collector rings at one end 
 of the armature, and the use of a larger commutator and 
 smaller magnetic circuit than is ordinarily used in a direct- 
 current generator. 
 
 When such a machine is driven by an engine or motor, it is 
 capable of supplying either direct or alternating current, or 
 both at the same time. It may be driven as a synchronous 
 motor from an alternating-current source of energy and de- 
 liver direct current, or it may be driven from a direct-current 
 source of energy and deliver alternating current. 
 
 The synchronous converter may be started as a synchronous 
 motor, as described in section (406), or it may be started from 
 the direct-current end. In starting from the direct-current 
 end, the machine is brought up to a speed a little above syn- 
 chronous speed and then disconnected from the direct-current 
 source, and when the speed has decreased to synchronous 
 speed the alternating-current end is connected to the alternat- 
 ing-current leads. A synchronous converter is shown in 
 Fig. 321. 
 
CHAPTEE XIX 
 
 RESUSCITATION FROM APPARENT DEATH FROM 
 ELECTRIC SHOCK 
 
 By Augustin H. Goelet, M. D. 
 
 Supplement to Electrical World and Engineer, September 6, 1902. 
 
 425. Resuscitation. The urgent necessity for prompt and 
 persistent efforts at resuscitation of victims of accidental 
 shocks by electricity is very well emphasized by the success- 
 ful results in the instances recorded. In order that the task 
 may not be undertaken in a half-hearted manner, it must be 
 appreciated that accidental shocks seldom result in absolute 
 death unless the victim is left unaided too long, or efforts at 
 resuscitation are stopped too early. 
 
 In the majority of instances the shock is only sufficient to 
 suspend animation temporarily, owing to the momentary and 
 imperfect contact of the conductors, and also on account of 
 the resistance of the body submitted to the influence of the 
 current. It must be appreciated also that the body under 
 the conditions of accidental shocks seldom receives the full 
 force of the current in the circuit, but only a shunt current, 
 which may represent a very insignificant part of the whole. 
 
 When an accident occurs the following rules should be 
 promptly executed with care and deliberation: 
 
 426. Rule (1) Remove the body at once from the circuit by 
 breaking contact with the conductors. This may be ac- 
 complished by using a dry stick of wood, which is a non- 
 conductor, to roll the body over to one side, or to brush aside 
 a wire, if that is conveying the current. When a stick is not 
 at hand, any dry piece of clothing may be utilized to protect 
 the hand in seizing the body of the victim, unless rubber 
 gloves are convenient. If the body is in contact with the 
 earth, the coat-tails of the victim, or any loose or detached 
 
RESUSCITATION 
 
 387 
 
 piece of clothing may be seized with impunity to draw it 
 away from the conductor. When this has been accomplished, 
 observe Rule (2). The object to be attained is to make the 
 subject breathe, and if this can be accomplished and con- 
 tinued he can be saved. 
 
 427. Rule (2) Turn the body upon the back, loosen the 
 collar and clothing about the neck, roll up a coat and place it 
 
 Fig. 322 
 
 under the shoulders, so as to throw the head back, and then 
 make efforts to establish respiration (in other words, make 
 him breathe), just as would be done in case of drowning. To 
 accomplish this, kneel at the subject's head, facing him as 
 shown in Fig. 322, and, seizing both arms, draw them forcibly 
 to their full length over the head, so as to bring them almost 
 together above it, and hold them there for two or three sec- 
 onds only. (This is to expand the chest and favor the en- 
 trance of air into the lungs.) Then carry the arms down to 
 the sides and front of the chest, firmly compressing the chest 
 walls, and expel the air from the lungs, as shown in Fig. 323. 
 Repeat this manoeuvre at least sixteen times per minute. 
 These efforts should bo continued unremittingly for at least 
 an hour, or until natural respiration is established. 
 
 428. Rule (3) At the same time that this is being done, 
 someone should grasp the tongue of the subject with a 
 handkerchief or piece of cloth, to prevent it slipping, and 
 
388 
 
 PRACTICAL APPLIED ELECTRICITY 
 
 draw it forcibly out when the arms are extended above the 
 head and allow it to recede when the chest is compressed. 
 This manoeuver should likewise be repeated at least sixteen 
 times per minute. This serves the double purpose of free- 
 ing the throat so as to permit air to enter the lungs, and 
 also, by exciting a reflex irritation from forcible contact of 
 the under part of the tongue against the lower teeth, fre- 
 quently stimulates an involuntary effort at respiration. To 
 secure the tongue if the teeth are clenched, force the jaws 
 
 Fig. 323 
 
 apart with a stick, a piece of wood, or the handle of a pocket 
 knife. 
 
 429. Rule (4) The dashing of cold water into the face 
 will sometimes produce a gasp and start breathing, which 
 should then be continued as directed above. If this is not 
 essential the spine may be rubbed vigorously with a piece of 
 ice. Alternate applications of heat and cold over the region 
 of the heart will accomplish the same object in some in- 
 stances. It is both useless and unwise to attempt to ad- 
 minister stimulants to the victim in the usual manner of 
 pouring it down his throat. 
 
 While the above directions are being carried out, a physi- 
 cian should be summoned, who, upon his arrival, can best put 
 into practice Rules (5), (6) and (7), in addition to the fore- 
 going, should it be necessary. 
 
RESUSCITATION 389 
 
 FOR THE PHYSICIAN SUMMONED 
 
 430. Rule (5) Forcible stretching of the sphincter muscle 
 controlling the lower bowel excites powerful refle:: irritation 
 and stimulates a gasp (inspiration) frequently when other 
 measures have failed. For this purpose the subject should be 
 turned on the side, the middle and index fingers inserted 
 into the rectum, and the muscle suddenly and forcibly drawn 
 backwards toward the spine. Or, if it is desirable to continue 
 efforts at artificial respiration at the same time, the knees 
 should be drawn up and the thumb inserted for the same 
 purpose, the subject retaining the position on the back. 
 
 431. Rule (6) Rhythmical traction of the tongue is some- 
 times effectual in establishing respiration when other meas- 
 ures have failed. The tongue is seized and drawn out quickly 
 and forcibly to the limit, then it is permitted to recede. This 
 is to be repeated 16 times per minute. 
 
 432. Rule (7) Oxygen gas, which may be readily obtained 
 at a drug store in cities or large towns, is a powerful stimu- 
 lant to the heart if it can be made to enter the lungs. A 
 cone may be improvised from a piece of stiff paper and at- 
 tached to the tube leading from the tank, and placed over the 
 mouth and nose while the gas is turned on during the efforts 
 at artificial respiration, 
 
CHAPTEE XX 
 
 LOGARITHMS 
 
 433. Definition of Logarithm. If (a) be any number, and 
 (x) and (n) two other numbers, such that ax = n, then (x) 
 is called the logarithm of (n) to the base (a) and is written 
 log a n. The logarithm of a number to a given base is the 
 index of the power to which the base must be raised that it 
 may be equal to the given number. Example: Since 102 = 
 100, therefore 2 =log 10 100. 
 
 434. Laws of Indices. In algebra the following laws, 
 known as the laws of indices, are found to be true; (m) and 
 (n) are to be any real quantities: 
 
 (A) amXan = am + n 
 
 (B) am -=- an = am n 
 
 (C) (am)n = a ra X n 
 
 There are three fundamental laws of logarithms correspond- 
 ing to the above. 
 
 (a) loga (m X n) = log a m + log a n 
 
 (b) loga (m -T- n) = log a m log a n 
 
 (c) log a m.n = n log a m. 
 These three laws expressed in words are: 
 
 (a) The logarithm of the product of two quantities is 
 equal to the sum of the logarithms of the quantities to the 
 same base. 
 
 (b) The logarithm of the quotient of two quantities is 
 equal to the difference in their logarithms to the same base. 
 
 (c) The logarithm of a quantity raised to any power is 
 equal to the logarithm of the quantity multiplied by the index 
 of the power. 
 
 435. Common System of Logarithms. In what is known 
 as the common system of logarithms the base is always 10, 
 so that if no base be expressed, the base 10 is always under- 
 stood. 
 
 390 
 
LOGARITHMS 391 
 
 436. Definition of Characteristic and Mantissa. If the 
 logarithm of any number be partly integral and partly frac- 
 tional, the integral portion is called its characteristic and the 
 decimal portion is called its mantissa. Thus, the logarithm 
 of 666 is 2.82347, in which 2 is the characteristic and 
 .82347 is the mantissa. 
 
 The characteristic of the logarithm of any whole number 
 will be one less than the number of digits in its integral part. 
 Thus, 2457.4 has four digits in its integral part and the char- 
 acteristic of its logarithm is 3. 
 
 The characteristic of the logarithm of any decimal frac- 
 tion will be negative and numerically greater by unity than 
 the number of ciphers following the decimal point. Thus, 
 .897 has no ciphers following the decimal point and the char- 
 acteristic will be numerically equal to (0 + 1) or 1, and it 
 will be negative. The fact that the characteristic is negative 
 can be indicated by drawing a horizontal line over it, thus 
 (1). The characteristic of .00434 is "3 since there are two 
 ciphers following the decimal point. 
 
 The mantissa of the logarithm of all numbers consisting 
 of the same digits are the same. 
 
 437. How to Obtain the Logarithm of a Number from 
 the Table. For example, if it is desired to obtain the 
 logarithm of the number 642, we proceed as follows: Run 
 the eye down the extreme left-hand column until it arrives 
 at the number 64. Then pass along the horizontal line of 
 figures until you are in the column vertically beneath the 
 number 2 at the top of the page, and you see the number 
 80754. This number just obtained is the mantissa of the 
 log of 642 and the characteristic is 2. 
 
 Then log 642 =* 2.807 54 
 
 and log 6420 = 3.807 54 
 
 log 6.42= .80754 
 
 log .00642 = 3.80754 
 
 438. To Find a Number Whose Logarithm Is Given. If the 
 
 logarithm be one tabulated in the table the number is easily 
 found, the procedure being just the reverse of that given in 
 the previous paragraph. Example: Find the number whose 
 logarithm is 68931. Referring to the table, we find the 
 
392 PRACTICAL APPLIED ELECTRICITY 
 
 mantissa 68931 corresponds to the digits 489, and the number 
 will be 4890, since the characteristic is 3. 
 
 Often the logarithm is not tabulated and the number is 
 then found as follows: Example Find the number whose 
 logarithm is 3.44741. Referring to the table, we find that the 
 mantissa 44741 is not tabulated, but the nearest mantissae 
 are 44716 and 44871, between which the mantissa 44741 lies. 
 The difference between 44871 and 44716 is 155, and the differ- 
 ence between 44741 and 44716 is 75. 
 
 log 2800 = 3.447 16 
 
 log 2810 = 3.448 71 
 then 3.447 41 = log (2800 + X) 
 
 75 
 X = of 10 = 4.99 
 
 155 
 
 The required number then is (2800 + 4.99) = 2804.99. 
 
 EXAMPLES 
 
 (A) What is the value of the product of 24 and 19? 
 log 24 = 1.380 21 
 log 19 = 1.278 75 
 
 log (product) = 2.658 96 
 then (24 X 19) = 456 
 
 (B) What is the value of (27)2? 
 
 log (27)2 = 2 log 27 
 = 2.862 72 
 then (27)2 = 729 
 
 (C) What is the value of the product of .079 and .03? 
 
 log .079 = 27897 63 
 log .03 ==2L47712 
 
 log (product) = 3.374 75 (See note a, pa?e 
 then (.079 X .03) = .002 37 393) 
 
LOGARITHMS 393 
 
 (D) What is the value of the product of .65 and 48? 
 
 log.65=T.81291 
 log 48 = 1.681 24 
 
 log (product) = 1.494 15 
 then (.65 X 48) = 31.25 
 
 (E) What is the value of (.075)2? 
 
 log .075 = "2T875 06 
 
 2 log .075 = "3.750 12 
 
 then (.075)2= .005 625 
 
 (F) What is the value of (79.0)1-6? 
 
 log 79.0 = 1.897 63 
 log (79.0)1-6 = 1.6 X 1.89763 
 
 = 2.936 208 
 then (79.0)1-6 = 863.+ 
 
 (G) What is the value of V 656100 ? 
 
 log 656100 = 5.816 90 
 
 % log 656100 = 2.908 45 
 
 or log V 656100 = 2.908 45 
 
 then V 656100 = 810 
 
 Note (a) The characteristic is treated as a negative quan- 
 tity and the mantissa as a positive quantity. 
 
394 
 
 LOGABITHMS OF NUMBERS 
 
 No. 1 23456 
 
 7 
 
 8 9 
 
 
 
 
 00000 
 
 041 39 
 32222 
 49136 
 61278 
 70757 
 78533 
 85126 
 90849 
 95904 
 
 30103 
 
 07918 
 34242 
 505 15 
 62325 
 71600 
 79239 
 85733 
 91381 
 96379 
 
 47712 
 
 11394 
 361 73 
 51851 
 63347 
 72428 
 79934 
 86332 
 91908 
 96848 
 
 60206 
 
 14613 
 38021 
 53148 
 64345 
 73239 
 806 18 
 86923 
 92428 
 97313 
 
 69897 
 
 17609 
 39794 
 544 07 
 65321 
 74036 
 81291 
 87506 
 92942 
 97772 
 
 77815 
 
 84510 
 
 903 09 954 24 
 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 
 00000 
 30103 
 477 12 
 60206 
 69897 
 77815 
 845 10 
 90309 
 95424 
 
 20412 
 41497 
 55630 
 66276 
 74819 
 81954 
 88081 
 93450 
 98227 
 
 23045 
 43136 
 56820 
 67210 
 75587 
 82607 
 88649 
 93952 
 98677 
 
 25527 27875 
 447 16 462 40 
 579 78 591 06 
 681 24 690 20 
 763 43 770 85 
 832 51 818 85 
 892 09 897 63 
 944 48 949 39 
 991 23 | 995 64 
 
 10 
 
 00000 
 
 00432 
 
 00860 
 
 01284 
 
 01703 
 
 021 19 
 
 02531 
 
 02938 
 
 03342 03743 
 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 19 
 
 20 
 
 04139 
 07918 
 11394 
 14613 
 17609 
 204 12 
 23045 
 25527 
 27875 
 
 04532 
 08279 
 11727 
 14922 
 17898 
 20683 
 23300 
 25768 
 28103 
 
 04922 
 08636 
 12057 
 15229 
 18184 
 20952 
 23553 
 26007 
 28330 
 
 05308 
 08991 
 12385 
 15534 
 18469 
 21219 
 23805 
 26245 
 28556 
 
 05690 
 09342 
 127 10 
 15836 
 18752 
 21484 
 24055 
 26482 
 28780 
 
 06070 
 09691 
 13033 
 16137 
 19033 
 21748 
 24304 
 267 17 
 29003 
 
 06446 
 10037 
 13354 
 16435 
 193 12 
 22011 
 24551 
 26951 
 29226 
 
 06819 
 10380 
 13672 
 16732 
 195 90 
 22272 
 24797 
 271 84 
 29448 
 
 07188 
 10721 
 13988 
 17026 
 19866 
 22531 
 25042 
 27416 
 29667 
 
 07555 
 11059 
 14301 
 17319 
 20140 
 22789 
 25285 
 27646 
 29885 
 
 30103 
 
 30320 
 
 30535 
 
 307 50 
 
 30963 
 
 31175 
 
 31387 
 
 31597 
 
 31806 32015 
 
 21 
 22 
 
 23 
 24 
 25 
 26 
 
 27 
 28 
 29 
 
 32222 
 34242 
 361 73 
 38021 
 39794 
 41497 
 43136 
 44716 
 46240 
 
 47712 
 
 32428 
 34439 
 36361 
 38202 
 39967 
 41664 
 43297 
 44871 
 46389 
 
 32634 
 34635 
 36549 
 38382 
 40140 
 41830 
 43457 
 45035 
 46538 
 
 32838 
 34830 
 36736 
 38561 
 40312 
 41996 
 436 16 
 45179 
 46687 
 
 33041 
 35025 
 36922 
 38739 
 40483 
 42160 
 43775 
 45332 
 46835 
 
 33244 
 35218 
 37107 
 38917 
 40654 
 42325 
 43933 
 45484 
 46982 
 
 33445 
 354 11 
 37291 
 39094 
 40824 
 42488 
 44091 
 45637 
 47129 
 
 33646 
 35603 
 37475 
 39270 
 40993 
 42651 
 44248 
 45788 
 47276 
 
 33846 
 35793 
 37658 
 39445 
 41162 
 42813 
 44404 
 45939 
 47422 
 
 34044 
 35984 
 37840 
 39620 
 41330 
 42975 
 44560 
 46090 
 47567 
 
 30 
 
 47857 
 
 48001 
 
 48144 
 
 48287 
 
 48430 
 
 48572 
 
 48714 
 
 48855 
 
 48996 
 
 31 
 32 
 33 
 34 
 35 
 36 
 37 
 38 
 39 
 
 49136 
 505 15 
 51851 
 53148 
 54407 
 55630 
 56820 
 57978 
 59106 
 
 49276 
 50651 
 51983 
 53275 
 54531 
 55751 
 56937 
 58092 
 59218 
 
 49415 
 50786 
 521 14 
 53403 
 54654 
 55871 
 57054 
 58206 
 59329 
 
 49554 
 50920 
 52244 
 53529 
 54777 
 55991 
 57171 
 583 20 
 59439 
 
 49693 
 51055 
 52375 
 53656 
 54900 
 561 10 
 57287 
 58433 
 59550 
 
 60638 
 
 49831 
 51188 
 52504 
 537 82 
 55023 
 56229 
 57403 
 58546 
 59660 
 
 60746 
 
 49969 
 51322 
 52634 
 53908 
 551 45 
 56348 
 575 19 
 58659 
 59770 
 
 60853 
 
 50106 
 51455 
 52763 
 54033 
 55267 
 56467 
 57634 
 58771 
 59879 
 
 50243 
 51587 
 52892 
 54158 
 55388 
 56585 
 57749 
 58883 
 59988 
 
 50379 
 51720 
 53020 
 54283 
 55509 
 56703 
 57864 
 58995 
 60097 
 
 40 
 
 60206 
 
 603 14 604 23 
 
 60531 
 
 60959 
 
 61066 
 
 61172 
 
 41 
 42 
 43 
 44 
 45 
 46 
 47 
 48 
 49 
 
 61278 
 62325 
 63347 
 64345 
 65321 
 66276 
 67210 
 68124 
 69020 
 
 61384 
 624 28 , 
 63448 
 64444 
 65418 
 66370 
 67302 
 682 15 
 69108 
 
 61490 
 62531 
 63548 
 64542 
 65514 
 66464 
 67394 
 68305 
 69197 
 
 61595 
 62634 
 63649 
 64640 
 65610 
 66558 
 67486 
 68395 
 69285 
 
 61700 
 62737 
 63749 
 64738 
 65706 
 66652 
 67578 
 68485 
 69373 
 
 61805 
 62839 
 63849 
 64836 
 65801 
 66745 
 67669 
 68574 
 69461 
 
 70329 
 
 61909 
 62941 
 63949 
 64933 
 65896 
 66839 
 67761 
 68664 
 69548 
 
 62014 
 63043 
 64048 
 65031 
 65992 
 66932 
 67852 
 68753 
 69636 
 
 621 18 
 63144 
 64147 
 65128 
 66087 
 67025 
 67943 
 68842 
 69723 
 
 62221 
 63246 
 64246 
 65225 
 66181 
 67117 
 68034 
 68931 
 69810 
 
 50 
 
 69897 
 
 69984 
 
 70070 
 
 70157 
 
 70243 
 
 70415 
 
 70501 
 
 70586 
 
 70672 
 
LOGARITHMS OF NUMBERS 
 
 395 
 
 No. 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 51 
 52 
 53 
 54 
 55 
 56 
 57 
 58 
 59 
 
 70757 
 71600 
 72428 
 73239 
 74036 
 748 19 
 75587 
 76343 
 77085 
 
 70842 
 71684 
 72509 
 73320 
 741 15 
 74896 
 75664 
 76418 
 77159 
 
 70927 
 71767 
 72591 
 73400 
 74194 
 74974 
 75740 
 76492 
 77232 
 
 71012 
 71850 
 72673 
 73480 
 74273 
 75051 
 75815 
 76567 
 77305 
 
 71096 
 71933 
 72754 
 73560 
 74351 
 751 28 
 75891 
 76641 
 77379 
 
 71181 
 720 16 
 72835 
 73640 
 74429 
 75205 
 75967 
 76716 
 77452 
 
 71265 
 72099 
 72916 
 73719 
 74507 
 75282 
 76042 
 76790 
 77525 
 
 71249 
 72181 
 72997 
 73799 
 74586 
 75358 
 76118 
 76864 
 77597 
 
 71433 
 72263 
 730 .78 
 73878 
 74663 
 75435 
 76193 
 76938 
 77670 
 
 71517 
 723 46 
 73159 
 73957 
 74741 
 75511 
 76268 
 77012 
 77743 
 
 60 
 
 77815 
 
 77887 
 
 77960 
 
 78032 
 
 78104 
 
 78176 
 
 78247 
 
 78319 
 
 78390 
 
 78462 
 
 61 
 62 
 63 
 64 
 65 
 66 
 67 
 68 
 69 
 
 785 33 
 79239 
 79934 
 80618 
 81291 
 81954 
 82607 
 83251 
 83885 
 
 78604 
 79309 
 80003 
 80686 
 81358 
 82020 
 82372 
 833 15 
 83948 
 
 78675 
 79379 
 80072 
 80754 
 81425 
 82086 
 82737 
 83378 
 84011 
 
 78746 
 79449 
 80140 
 80821 
 81491 
 82151 
 82802 
 834 42 
 840 73 
 
 78817 
 795 18 
 80209 
 80889 
 81558 
 82217 
 82866 
 83506 
 841 36 
 
 78888 
 79588 
 80277 
 80956 
 81624 
 82282 
 82930 
 83569 
 841 98 
 
 78958 
 79657 
 80346 
 81023 
 81690 
 823 47 
 82995 
 83632 
 84261 
 
 79029 
 79727 
 80414 
 81090 
 81757 
 82413 
 83059 
 83696 
 84323 
 
 79099 
 79796 
 80482 
 81158 
 81823 
 82478 
 83123 
 83759 
 84386 
 
 79169 
 79865 
 80550 
 81224 
 81889 
 82543 
 83187 
 83822 
 84448 
 
 70 
 
 84510 
 
 84572 
 
 84634 
 
 84696 
 
 84757 
 
 848 19 
 
 84880 
 
 84942 
 
 85003 
 
 85065 
 
 71 
 72 
 73 
 74 
 75 
 76 
 77 
 78 
 79 
 
 85126 
 85733 
 863 32 
 86923 
 87506 
 88081 
 88649 
 89209 
 89763 
 
 85187 
 85794 
 863 92 
 86982 
 87364 
 88138 
 887 05 
 89263 
 89919 
 
 85248 
 85854 
 86451 
 87040 
 87622 
 88195 
 88762 
 89321 
 89873 
 
 85309 
 859 14 
 86510 
 87099 
 87679 
 88252 
 888 18 
 89376 
 89927 
 
 85370 
 85974 
 86570 
 87157 
 87737 
 88319 
 88874 
 89432 
 89982 
 
 85431 
 86034 
 86629 
 872 16 
 87795 
 88366 
 88930 
 89487 
 90037 
 
 85491 
 86094 
 86688 
 87274 
 87852 
 88423 
 88986 
 89542 
 90091 
 
 85552 
 86153 
 86747 
 87332 
 87910 
 88480 
 89042 
 89597 
 90146 
 
 85612 
 86213 
 86806 
 87390 
 87967 
 88536 
 89098 
 89653 
 90200 
 
 85673 
 86273 
 86864 
 87448 
 88024 
 88593 
 89154 
 89708 
 90255 
 
 80 
 
 90309 
 
 90363 
 
 90417 
 
 90472 
 
 90526 
 
 90580 
 
 906 34 
 
 90687 
 
 90741 
 
 90795 
 
 81 
 82 
 83 
 84 
 85 
 86 
 87 
 88 
 89 
 
 90849 
 91381 
 91908 
 92428 
 92942 
 93450 
 93952 
 94448 
 94939 
 
 90902 
 914 34 
 91960 
 92480 
 92993 
 935 00 
 94002 
 94498 
 94988 
 
 90956 
 91487 
 92012 
 92531 
 93044 
 93551 
 94052 
 94547 
 95036 
 
 91009 
 91540 
 92065 
 92583 
 93095 
 93601 
 94101 
 94596 
 95085 
 
 91062 
 91593 
 921 17 
 92634 
 93146 
 93651 
 94151 
 94645 
 95134 
 
 91116 
 91645 
 92169 
 92686 
 93197 
 93702 
 94201 
 94694 
 95182 
 
 91169 
 91698 
 92221 
 92737 
 93247 
 93752 
 94250 
 94743 
 95231 
 
 91222 
 91751 
 92273 
 92788 
 93298 
 93802 
 94300 
 94792 
 95279 
 
 91275 
 91803 
 92324 
 92840 
 93349 
 93852 
 94349 
 94841 
 95328 
 
 91328 
 91855 
 92376 
 92891 
 93399 
 93902 
 94399 
 94890 
 95376 
 
 90 
 
 95424 
 
 95472 
 
 955 21 
 
 95569 
 
 956 17 
 
 95665 
 
 95713 
 
 95761 
 
 95809 
 
 95856 
 
 91 
 92 
 93 
 94 
 95 
 96 
 97 
 98 
 99 
 
 95904 
 96379 
 96348 
 973 13 
 97772 
 98227 
 98677 
 99123 
 99564 
 
 95952 
 96426 
 96895 
 973 59 
 97814 
 98272 
 98722 
 99167 
 99607 
 
 95999 
 96473 
 96942 
 97405 
 97864 
 98318 
 98767 
 99211 
 99651 
 
 96047 
 96520 
 96988 
 97451 
 97909 
 98363 
 98811 
 99255 
 99695 
 
 96095 
 96567 
 97035 
 97497 
 979 55 
 98408 
 98856 
 99300 
 99739 
 
 961 42 
 96614 
 97081 
 97543 
 98000 
 98453 
 98900 
 99344 
 99782 
 
 96190 
 96661 
 97128 
 97589 
 98046 
 98498 
 989 45 
 99388 
 99826 
 
 96237 
 96708 
 97174 
 97635 
 98091 
 98543 
 98989 
 99432 
 99870 
 
 96284 
 96755 
 97220 
 97681 
 98137 
 98588 
 99034 
 994 76 
 99913 
 
 96332 
 96802 
 97267 
 97727 
 98182 
 98632 
 99078 
 99520 
 99957 
 
 100 
 
 00000 
 
 00043 
 
 00087 
 
 00130 
 
 00173 
 
 00217 
 
 00260 
 
 00303 
 
 00346 
 
 00389 
 
196 
 
 MENSUBATION EQUATIONS 
 
 TRIGONOMETRICAL FUNCTIONS 
 
 j2" xX ^ 
 
 a 5inee=-^- Cosinee=Y Tangent e=~t" 
 
 Base = b 
 
 Altitude = a 
 
 Hypothe_nuse=h 
 
 b^a 2 + b 2 
 
 MENSURATION 
 
 Diameter 
 
 Circumference 
 TT= 3.1416- 
 
 = TTxr 2 
 xn xd 2 
 
 Length =1 
 
 Breath -b 
 
 Depth = d 
 
 Volu7ne=lxbxd 
 
 Area surface= 
 
 Area Shaded 
 Portion^ (dj-dj) 
 
 l=b = d 
 Volume =lx b xd 
 
 Area Shaded 
 / 2 [lr- C (r-h)] 
 
 Surface 
 
TRIGONOMETRICAL FUNCTIONS 
 
 397 
 
 NATURAL SINES, COSINES, AND TANGENTS 
 
 An- 
 gle 
 
 Sines 
 
 Cosines 
 
 Tangents 
 
 An- 
 gle 
 
 Sines 
 
 Cosines 
 
 Tangents 
 
 
 
 .000000 
 
 1.000000 
 
 .000000 
 
 46 
 
 .719 340 
 
 .694658 
 
 .0355303 
 
 1 
 
 .017 452 
 
 .999 848 
 
 .017 455 
 
 47 
 
 .731 354 
 
 .681 998 
 
 .072 368 7 
 
 2 
 
 .034899 
 
 .999 391 
 
 .034921 
 
 48 
 
 .743 145 
 
 .669 131 
 
 .1106125 
 
 3 
 
 .052 336 
 
 .998 630 
 
 .02 408 
 
 49 
 
 .754 710 
 
 .656 059 
 
 .1503684 
 
 4 
 
 .069 756 
 
 .997 564 
 
 .069 927 
 
 50 
 
 .766044 
 
 .642788 
 
 1.1917536 
 
 5 
 
 .087 156 
 
 .996 165 
 
 .087 489 
 
 51 
 
 .777 146 
 
 .629 320 
 
 .234 897 2 
 
 6 
 
 .104528 
 
 .994522 
 
 .105 104 
 
 52 
 
 .788 Oil 
 
 .615 661 
 
 .279 941 6 
 
 7 
 
 .121869 
 
 .992 546 
 
 .122785 
 
 53 
 
 .798 636 
 
 .601 815 
 
 .3270448 
 
 8 
 
 .139173 
 
 .990268 
 
 .140541 
 
 54 
 
 .809017 
 
 .587785 
 
 1.3763810 
 
 9 
 
 .156434 
 
 .987 688 
 
 .158384 
 
 55 
 
 .819 152 
 
 .573 576 
 
 1.4281480 
 
 10 
 
 .173648 
 
 .984808 
 
 .176327 
 
 56 
 
 .829 038 
 
 .559 193 
 
 1.4825610 
 
 11 
 
 . 190 809 
 
 .981 627 
 
 .194380 
 
 57 
 
 .838 671 
 
 .544639 
 
 1.5398650 
 
 12 
 
 .207 912 
 
 .978 148 
 
 .212 557 
 
 58 
 
 .848048 
 
 .529919 
 
 1.6003345 
 
 13 
 
 .224951 
 
 .974370 
 
 .230 868 
 
 59 
 
 .857 167 
 
 .515038 
 
 1.6642795 
 
 14 
 
 .241 922 
 
 .970296 
 
 .249 328 
 
 60 
 
 .866 025 
 
 .500000 
 
 1.7320508 
 
 15 
 
 .258 819 
 
 .965 926 
 
 .267 949 
 
 61 
 
 .874 620 
 
 .484 810 
 
 1.8040478 
 
 16 
 
 .275 637 
 
 .961 262 
 
 .286 745 
 
 62 
 
 .882 948 
 
 .469472 
 
 1.8807265 
 
 17 
 
 .292372 
 
 .956 305 
 
 .305 731 
 
 63 
 
 .891 007 
 
 .453 990 
 
 1.9626105 
 
 18 
 
 .309 017 
 
 .951 057 
 
 .324 920 
 
 64 
 
 .898794 
 
 .438 371 
 
 2.0503038 
 
 19 
 
 .325 568 
 
 .945 519 
 
 .344 328 
 
 65 
 
 .906 308 
 
 .422618 
 
 2.1445069 
 
 20 
 
 .342020 
 
 .939693 
 
 .363 970 
 
 66 
 
 .913 545 
 
 .406737 
 
 2.2460368 
 
 21 
 
 .358368 
 
 .933 580 
 
 .383 864 
 
 67 
 
 .920 505 
 
 .390 731 
 
 2.3558524 
 
 22 
 
 .374607 
 
 .927 184 
 
 .404 026 
 
 68 
 
 .927 184 
 
 .374607 
 
 2.4750869 
 
 23 
 
 .390 731 
 
 .920 505 
 
 .424 475 
 
 69 
 
 .933 580 
 
 .358 369 
 
 2.6050891 
 
 24 
 
 .406 737 
 
 .913545 
 
 .445 229 
 
 70 
 
 .939 693 
 
 .342 020 
 
 2.7474774 
 
 25 
 
 .422 618 
 
 .906 308 
 
 .466 308 
 
 71 
 
 .945 519 
 
 .325 568 
 
 2.9042109 
 
 26 
 
 .438 371 
 
 .898794 
 
 .487 733 
 
 72 
 
 .951 057 
 
 .309 017 
 
 3.0776835 
 
 27 
 
 .453 990 
 
 .891 007 
 
 .509525 
 
 73 
 
 .956 305 
 
 .292 372 
 
 3.2708526 
 
 28 
 
 .469472 
 
 .882 948 
 
 .531 709 
 
 74 
 
 .961 262 
 
 .275 637 
 
 3.4874144 
 
 29 
 
 .484810 
 
 .874 620 
 
 .554 309 
 
 75 
 
 .965 926 
 
 .258 819 
 
 3.7320508 
 
 30 
 
 .500000 
 
 .866025 
 
 .577 350 
 
 76 
 
 .970 296 
 
 .241 922 
 
 4.0107809 
 
 31 
 
 .515 038 
 
 .857 167 
 
 .600861 
 
 77 
 
 .974 370 
 
 .224 951 
 
 4.3314759 
 
 32 
 
 .529 919 
 
 .848048 
 
 .624 869 
 
 78 
 
 .978 148 
 
 .207 912 
 
 4.7047301 
 
 33 
 
 .544 639 
 
 .838671 
 
 .649 408 
 
 79 
 
 .981 627 
 
 .190809 
 
 5.1445540 
 
 34 
 
 .559 193 
 
 .829 038 
 
 .674 509 
 
 80 
 
 .984 808 
 
 .173648 
 
 5.6712818 
 
 35 
 
 .573 576 
 
 .819 152 
 
 .700 208 
 
 81 
 
 .987 688 
 
 .156434 
 
 6.313 751 5 
 
 36 
 
 .587 785 
 
 .809017 
 
 .726 543 
 
 82 
 
 .990 268 
 
 .139173 
 
 7.1153697 
 
 37 
 
 .601 815 
 
 .798636 
 
 .753 554 
 
 83 
 
 .992 546 
 
 .121869 
 
 8.1443464 
 
 38 
 
 .615 661 
 
 .788011 
 
 .781 286 
 
 84 
 
 .994 522 
 
 .104528 
 
 9.5143645 
 
 39 
 
 .629320 
 
 .777 146 
 
 .809 784 
 
 85 
 
 .996 195 
 
 .087 156 
 
 11.430052 
 
 40 
 
 .642 788 
 
 .766044 
 
 .839 100 
 
 86 
 
 .997 564 
 
 .069756 
 
 14.300666 
 
 41 
 
 .656059 
 
 .754710 
 
 .869 287 
 
 87 
 
 .998 630 
 
 .052 336 
 
 19.081 137 
 
 42 
 
 .669 131 
 
 .743 145 
 
 .900 404 
 
 88 
 
 .999 391 
 
 .034899 
 
 28.636253 
 
 43 
 
 .681 998 
 
 .731 354 
 
 .932 515 
 
 89 
 
 .999 848 
 
 .017 452 
 
 57.289962 
 
 44 
 
 .694 658 
 
 .719340 
 
 .965 689 
 
 90 
 
 1.000000 
 
 .000000 
 
 infinite 
 
 45 
 
 .707 107 
 
 .707 170 
 
 1.000000 
 
 
 
 
 
398 
 
 SYMBOLS FOE ELECTEICAL APPAKATUS 
 
 Wire 
 
 Wires not 
 Connected 
 
 Wires 
 Connected 
 
 Ground 
 Connection 
 
 Fuse 
 
 -MA/W 
 
 Non-Inductive 
 Resistance 
 
 PrfmaryCell 
 
 Double-Pole Double 
 Throw Switch (Open) 
 
 Ammeter 
 
 V 
 
 Voltmeter 
 
 Galvanometer 
 
 Direct-Current 
 Generator 
 
 Direct-Current 
 Motor 
 
 Load 
 
 006 
 
 W 
 
 Wattmeter 
 
 Inductive 
 Resistance 
 
 WWVi - 
 
 Variable 
 
 Resistance or 
 
 Rheostat 
 
 Incandescent 
 Lamps in Series 
 
 X X X X 
 
 Arc Lamps 
 in Series 
 
 Alternating- 
 Current Generator 
 
 ' / ffTOW s 
 
 Simple Switch Transformer 
 
 Single-Pole Single 
 Throw Switch (Open) 
 
 Condenser 
 
 Single-Pole Double 
 
 'Throw Switch (Open) Deta Connection 
 
 Double-Pole Single- 
 
 Throw Switch (Open) Star Connection 
 
TABLE A 
 
 399 
 
 RELATION OF METRIC AND ENGLISH MEASURES 
 Equivalents of Linear Measures 
 
 Millimeter 
 Centimeter 
 Decimeter 
 Meter 
 Decameter 
 Hectometer 
 Kilometer 
 
 Meters 
 
 English Measures 
 
 Inches 
 
 Feet 
 
 Yards 
 
 Miles 
 
 .000621 
 .006214 
 .062 138 
 .621 382 
 
 .001 
 .01 
 .1 
 1. 
 10. 
 100. 
 1000. 
 
 .039 371 
 3.937079 
 .328089 
 39.370790 
 
 .003 281 
 .032 809 
 .328089 
 3.280899 
 32.80899 
 328.0899 
 3280.899 
 
 .001 094 
 .010936 
 . 109 363 
 1.093633 
 10.936 33 
 109.3633 
 1093.633 
 
 English Measures 
 
 Meters 
 
 Reciprocals 
 
 
 .02539954 
 
 39.37079 
 
 12 inches 1 foot 
 
 .3047945 
 
 3.280899 
 
 3 feet 1 vard 
 
 .9143835 
 
 1.093633 
 
 Equivalents of Surface Measures 
 
 
 Square 
 Meters 
 
 English Measures 
 
 Square 
 inches 
 
 Square 
 feet 
 
 Square 
 yards 
 
 Milliare 
 
 .1 
 1. 
 10. 
 100. 
 1000. 
 10000. 
 1000000. 
 
 155.01 
 1550.06 
 15500.59 
 155005.9 
 
 1.076 
 10.764 
 107.64 
 1076.4 
 10764.3 
 107643. 
 
 .119 
 1.196 
 11.960 
 119.6033 
 1096.033 
 11960.33 
 
 Diciare 
 
 
 Decare (not used) 
 Hectare 
 Square Kilometer 
 
 
 English Measures 
 
 Metric Measures 
 
 Reciprocals 
 
 
 6.451367 sq. cmt. 
 
 . 1550059 
 
 144 sq in 1 sq ft 
 
 09289968 sq. m. 
 
 10.7642996 
 
 9 sq. ft.=l sq. yd 
 
 .8360972 sq. m. 
 
 1.196033 
 
 Equivalents of Weights 
 
 
 Grams 
 
 English Weights 
 
 Oz. 
 avoir 
 
 Lbs. 
 avoir 
 
 Tons 
 2000 Ibs. 
 
 Tons 
 2240 Ibs. 
 
 Milligram 
 Centigram 
 Decigram 
 
 .001 
 .01 
 .1 
 1. 
 10. 
 100. 
 1000. 
 
 .0353 
 .3527 
 3.5274 
 35.2739 
 
 .0022 
 .02205 
 .22046 
 2.2046 
 
 .001102 
 
 .000984 
 
 Gram 
 
 Hectogram 
 Kilogram 
 
 English Weights "Avoirdupois" 
 
 Grams 
 
 Reciprocals 
 
 
 .06479895 
 
 15.43234875 
 
 
 1 771836 
 
 .564383 
 
 16 drams=l oz.=437 . 5 grains 
 16 oz.l rjound==7000 grains 
 
 28.349375 
 453.592652 
 
 .0352739 
 .00220462 
 
400 
 
 TABLE B 
 
 TABLE OF COMPARISON OF CENTIGRADE AND FAHRENHEIT 
 THERMOMETER SCALES 
 
 Cent, 
 
 Fahr. 
 
 Cent. 
 
 Fahr. 
 
 Cent. 
 
 Fahr. 
 
 Cent. 
 
 Fahr. 
 
 
 
 32.0 
 
 26 
 
 78.8 
 
 51 
 
 123.8 
 
 76 
 
 168.8 
 
 1 
 
 33.8 
 
 27 
 
 80.6 
 
 52 
 
 125.6 
 
 77 
 
 170.6 
 
 2 
 
 35.6 
 
 28 
 
 82.4 
 
 53 
 
 127.4 
 
 78 
 
 172.4 
 
 3 
 
 37.4 
 
 29 
 
 84.2 
 
 54 
 
 129 2 
 
 79 
 
 179.2 
 
 4 
 
 39.2 
 
 30 
 
 86.0 
 
 55 
 
 131.0 
 
 80 
 
 176.0 
 
 5 
 
 41.0 
 
 31 
 
 87.8 
 
 56 
 
 132.8 
 
 81 
 
 177.8 
 
 6 
 
 42.8 
 
 32 
 
 89.6 
 
 57 
 
 134.6 
 
 82 
 
 179.6 
 
 7 
 
 44.6 
 
 33 
 
 91.4 
 
 58 
 
 136.4 
 
 83 
 
 181.2 
 
 8 
 
 46.4 
 
 34 
 
 93.2 
 
 59 
 
 138.2 
 
 84 
 
 183.4 
 
 9 
 
 48.2 
 
 35 
 
 95.0 
 
 60 
 
 140.0 
 
 85 
 
 185.0 
 
 10 
 
 50.0 
 
 36 
 
 96.8 
 
 61 
 
 141.8 
 
 86 
 
 186.8 
 
 11 
 
 51.8 
 
 37 
 
 98.6 
 
 62 
 
 143.6 
 
 87 
 
 188.6 
 
 12 
 
 53.6 
 
 38 
 
 100.4 
 
 63 
 
 145.4 
 
 88 
 
 190.4 
 
 13 
 
 55.4 
 
 39 
 
 102.2 
 
 64 
 
 147.2 
 
 89 
 
 192.2 
 
 14 
 
 57.2 
 
 40 
 
 104.0 
 
 65 
 
 149.0 
 
 90 
 
 194.0 
 
 15 
 
 59.0 
 
 41 
 
 105.8 
 
 66 
 
 150.8 
 
 91 
 
 195.8 
 
 16 
 
 60.8 
 
 42 
 
 107.6 
 
 67 
 
 152.6 
 
 92 
 
 197.6 
 
 17 
 
 62.6 
 
 43 
 
 109.4 
 
 68 
 
 154.4 
 
 93 
 
 199.4 
 
 18 
 
 64.4 
 
 44 
 
 111.2 
 
 69 
 
 156.2 
 
 94 
 
 201.2 
 
 19 
 
 66.2 
 
 45 
 
 113.0 
 
 70 
 
 158.0 
 
 95 
 
 203.0 
 
 20 
 
 68.0 
 
 46 
 
 114.8 
 
 71 
 
 159.8 
 
 96 
 
 204.8 
 
 21 
 
 69.8 
 
 47 
 
 116.6 
 
 72 
 
 161.6 
 
 97 
 
 206.6 
 
 22 
 
 71.6 
 
 48 
 
 118.4 
 
 73 
 
 163.4 
 
 98 
 
 208.4 
 
 23 
 
 73.4 
 
 49 
 
 120.2 
 
 74 
 
 165.2 
 
 99 
 
 210 2 
 
 24 
 
 75.2 
 
 50 
 
 122.0 
 
 . 75 
 
 167.0 
 
 100 
 
 212.0 
 
 25 
 
 77.0 
 
 
 
 
 
 
 
 One deg. Fahr.=.5556 deg. centigrade. 
 One deg. centigrade=1.8 deg. Fahr. 
 
 To convert Fahr. to centigrade, subtract 32, multiply by 5 and divide by 9. 
 To convert centigrade to Fahr., multiply by 9, divide by 5 and add 32. 
 If temperature is below freezing, the above formula should read "subtract from 32" in place of 
 "subtract 32" and "add 32." 
 
 TABLE C 
 
 EQUIVALENT CROSS-SECTIONS OF DIFFERENT SIZE WIRES 
 (Brown and Sharpe Gauge) 
 
 Equiv. 
 section 
 
 Number of wires of various sizes 
 
 2 
 
 4 
 
 8 
 
 16 
 
 32 
 
 64 
 
 128 
 
 0000 
 
 
 
 3 
 
 6 
 
 9 
 
 12 
 
 15 
 
 18 
 
 000 
 
 1 
 
 4 
 
 7 
 
 10 
 
 13 
 
 16 
 
 One each 
 
 CO 
 
 2 
 
 5 
 
 8 
 
 11 
 
 14 
 
 17 
 
 Iand3 
 
 
 
 3 
 
 6 
 
 9 
 
 12 
 
 15 
 
 18 
 
 2 and 4 
 
 1 
 
 4 
 
 7 
 
 10 
 
 13 
 
 16 
 
 
 3 and 5 
 
 2 
 
 5 
 
 8 
 
 11 
 
 14 
 
 17 
 
 
 4 and 6 
 
 3 
 
 6 
 
 9 
 
 12 
 
 15 
 
 18 
 
 
 5 and 7 
 
 4 
 
 7 
 
 10 
 
 13 
 
 16 
 
 
 
 6 and 8 
 
 5 
 
 8 
 
 11 
 
 14 
 
 17 
 
 
 
 7 and 9 
 
 6 
 
 9 
 
 12 
 
 15 
 
 18 
 
 
 
 8 and 10 
 
 7 
 
 10 
 
 13 
 
 16 
 
 
 
 
 9 and 11 
 
 8 
 
 11 
 
 14 
 
 17 
 
 
 
 ] 
 
 10 and 12 
 
 9 
 
 12 
 
 15 
 
 18 
 
 
 
 
 11 and 13 
 
 10 
 
 13 
 
 16 
 
 
 
 
 
 12 and 14 
 
 11 
 
 14 
 
 17 
 
 
 
 
 
 13 and 15 
 
 12 
 
 15 
 
 18 
 
 
 
 
 
 14 and 16 
 
 13 
 
 16 
 
 
 
 
 
 
 
 15 and 17 
 
 14 
 
 17 
 
 
 
 
 
 
 16 and 18 
 
 15 
 
 18 
 
 
 
 
 
 
 
 
TABLE D 
 
 401 
 
 COMPARATIVE TABLE OF WIRE GAUGES 
 
 
 American Wire Gauge 
 (Brown & Shame) 
 
 Birmingham Wire Gauge 
 
 (Stubs) 
 
 Standard Wire Gauge 
 
 Gauge 
 No. 
 
 Diameter 
 
 Area 
 
 Diameter 
 
 Area 
 
 Diam'ter 
 
 4rea 
 
 
 Inches 
 
 Circular 
 Mills 
 
 Inches 
 
 Circular 
 Mills 
 
 Inches 
 
 Circular 
 Mills 
 
 7-0 
 
 
 
 
 
 0.500 
 
 250000. 
 
 6-0 
 
 
 
 
 
 0.404 
 
 2 15300. 
 
 5-0 
 
 
 
 
 
 0.432 
 
 1 86600. 
 
 4-0 
 
 0.4600 
 
 211 600. 
 
 0.451 
 
 208 100. 
 
 0.400 
 
 160000. 
 
 3-0 
 
 0.4096 
 
 167 800. 
 
 0.425 
 
 180600. 
 
 0.372 
 
 1 38400. 
 
 2-0 
 
 3648 
 
 133100. 
 
 0.380 
 
 144 400. 
 
 0.348 
 
 1 21100. 
 
 1-0 
 
 0.3249 
 
 105 500. 
 
 0.340 
 
 115600 
 
 0.324 
 
 105000. 
 
 1 
 
 2893 
 
 83690. 
 
 0.300 
 
 90000. 
 
 0.300 
 
 90000. 
 
 2 
 
 257 6 
 
 66 370. 
 
 0.284 
 
 80660. 
 
 276 
 
 76180. 
 
 3 
 
 0.2294 
 
 52630. 
 
 0.259 
 
 67080. 
 
 0.252 
 
 63500. 
 
 4 
 
 0.2043 
 
 41 740. 
 
 0.238 
 
 56640. 
 
 0.232 
 
 53820. 
 
 5 
 
 0.1819 
 
 33100 
 
 0.220 
 
 48400. 
 
 0.212 
 
 44940. 
 
 6 
 
 0.1620 
 
 26250. 
 
 0.203 
 
 41 210. 
 
 0.192 
 
 36860. 
 
 7 
 
 0.1443 
 
 20 820. 
 
 0.180 
 
 32400. 
 
 0.176 
 
 30980. 
 
 8 
 
 0.1285 
 
 16 510. 
 
 0.165 
 
 27230. 
 
 0.160 
 
 256oO. 
 
 9 
 
 0.1144 
 
 13090. 
 
 0.148 
 
 21900. 
 
 0.144 
 
 20740. 
 
 10 
 
 0.1019 
 
 10380. 
 
 0.134 
 
 17960. 
 
 0.128 
 
 16380. 
 
 11 
 
 009074 
 
 8234. 
 
 0.120 
 
 14400. 
 
 0.116 
 
 13460. 
 
 12 
 
 0.08081 
 
 6530. 
 
 0.109 
 
 11880. 
 
 0.104 
 
 10820. 
 
 13 
 
 0.071 96 
 
 5178. 
 
 0.0950 
 
 9025. 
 
 0.092 
 
 8464. 
 
 14 
 
 0.06408 
 
 4107. 
 
 0.083 
 
 6889. 
 
 0.080 
 
 6400. 
 
 15 
 
 0.05707 
 
 3257. 
 
 0.0720 
 
 5184. 
 
 0.072 
 
 5184. 
 
 16 
 
 0.05082 
 
 2583. 
 
 0.0650 
 
 4225. 
 
 0.064 
 
 4096. 
 
 17 
 
 0.04526 
 
 2048. 
 
 0.0580 
 
 3364. 
 
 0.056 
 
 3136. 
 
 18 
 
 0.04030 
 
 1624. 
 
 0.0490 
 
 2401. 
 
 0.048 
 
 2304. 
 
 19 
 
 0.03589 
 
 1288. 
 
 0.0420 
 
 1764. 
 
 0.040 
 
 1600. 
 
 20 
 
 0.03196 
 
 1022. 
 
 0.0350 
 
 1225. 
 
 0.036 
 
 1296. 
 
 21 
 
 0.02846 
 
 810.1 
 
 0.0320 
 
 1024. 
 
 0.032 
 
 1024. 
 
 22 
 
 0.025 35 
 
 642.4 
 
 0.0280 
 
 784. 
 
 0.028 
 
 784.0 
 
 23 
 
 0.02257 
 
 509.5 
 
 0.0250 
 
 625. 
 
 0.024 
 
 576.0 
 
 24 
 
 0.020 10 
 
 404.0 
 
 0.0220 
 
 484. 
 
 0.022 
 
 484.0 
 
 25 
 
 0.01790 
 
 320.4 
 
 0.0200 
 
 400. 
 
 0.020 
 
 400.0 
 
 26 
 
 0.01594 
 
 254.1 
 
 0.0180 
 
 324. 
 
 0.018 
 
 324.0 
 
 27 
 
 0.01420 
 
 201.5 
 
 0.0160 
 
 256. 
 
 0.016 4 
 
 269.0 
 
 28 
 
 0.01264 
 
 159.8 
 
 0.014.0 
 
 196. 
 
 0.014 8 
 
 219.0 
 
 29 
 
 0.01126 
 
 126.7 
 
 0.0130 
 
 169. 
 
 0.013 6 
 
 185.0 
 
 30 
 
 0.01o03 
 
 100.5 
 
 0.0120 
 
 144. 
 
 0.012 4 
 
 153.8 
 
 31 
 
 0.008928 
 
 79.70 
 
 0.0100 
 
 100. 
 
 0.0116 
 
 134.6 
 
 32 
 
 0.007950 
 
 63.21 
 
 0.0090 
 
 81. 
 
 0.0108 
 
 116.6 
 
 33 
 
 0.007080 
 
 50.13 
 
 0.0080 
 
 64. 
 
 0.0100 
 
 100.0 
 
 34 
 
 0.006305 
 
 39.75 
 
 0.0070 
 
 49. 
 
 0.0092 
 
 84.64 
 
 35 
 
 0.005615 
 
 31.52 
 
 0.0050 
 
 25. 
 
 0.0084 
 
 70.56 
 
 36 
 
 0.005000 
 
 25.00 
 
 0.0044 
 
 16. 
 
 0.0076 
 
 67.76 
 
 37 
 
 004 453 
 
 19.83 
 
 
 
 0068 
 
 46.24 
 
 38 
 
 0.003965 
 
 15.72 
 
 
 
 0.0060 
 
 36.00 
 
 39 
 
 003 531 
 
 12.47 
 
 
 
 0052 
 
 27 04 
 
 40 
 
 0.003145 
 
 9.888 
 
 
 
 0.0048 
 
 23.04 
 
 41 
 
 
 
 
 
 0.0044 
 
 19.36 
 
402 
 
 TABLE E 
 
 COPPER WIRE TABLE OF AMERICAN 
 Giving Weights and Lengths of cool, warm and hot wires, 
 
 B.&S. 
 or 
 A. W. G. 
 
 Diameter 
 
 Area 
 
 Lbs. Per 
 Foot 
 
 
 Inches 
 
 Circular 
 miles 
 
 Sq. in. 
 Sq. miles 
 
 
 68 F. 
 20 C. 
 
 0000 
 
 0.460 
 
 211600 
 
 166 190 
 
 0.6405 
 
 13090 
 
 000 
 
 0.4096 
 
 167800 
 
 131 790 
 
 0.5080 
 
 8232 
 
 00 
 
 0.3648 
 
 133100 
 
 104518 
 
 0.4028 
 
 5177 
 
 
 
 0.3249 
 
 105500 
 
 82887 
 
 0.3195 
 
 3256 
 
 1 
 
 0.289 3 
 
 83 690 
 
 65732 
 
 0.2533 
 
 2048 
 
 2 
 
 0.257 6 
 
 66370 
 
 52128 
 
 0.2009 
 
 1288. 
 
 3 
 
 0.2294 
 
 52630 
 
 41339 
 
 0. 159 3 
 
 810.0 
 
 4 
 
 0.2043 
 
 41 740 
 
 32784 
 
 0.1264 
 
 509.4 
 
 5 
 
 0.1819 
 
 33100 
 
 25999 
 
 0.1002 
 
 320.4 
 
 6 
 
 0.1620 
 
 26250 
 
 20 618 
 
 0.079 46 
 
 2015 
 
 7 
 
 0.1443 
 
 20820 
 
 16351 
 
 0.6302 
 
 126.7 
 
 8 
 
 0.1285 
 
 16 510 
 
 12967 
 
 0.04998 
 
 79.69 
 
 9 
 
 0.1144 
 
 13090 
 
 10283 
 
 0.03963 
 
 50.12 
 
 10 
 
 0.1019 
 
 10380 
 
 8155 
 
 0.03143 
 
 31.52 
 
 11 
 
 0.09074 
 
 8234 
 
 6467 
 
 0.024 93 
 
 19.82 
 
 12 
 
 0.08081 
 
 6530 
 
 5129 
 
 0.01977 
 
 12.47 
 
 13 
 
 0.071 96 
 
 5178 
 
 4067 
 
 0.01.568 
 
 7.840 
 
 14 
 
 0.06408 
 
 4107 
 
 3225 
 
 0.01243 
 
 4.931 
 
 15 
 
 0.05707 
 
 3257 
 
 2558 
 
 0.009 858 
 
 3.101 
 
 16 
 
 0.05082 
 
 2583 
 
 2029 
 
 0.007818 
 
 1.950 
 
 17 
 
 0.04526 
 
 2048 
 
 1609 
 
 0.006200 
 
 1.226 
 
 18 
 
 0.04030 
 
 1624 
 
 1276 
 
 0.004917 
 
 0.771 3 
 
 19 
 
 0.03589 
 
 1288 
 
 1012 
 
 0.003899 
 
 0.4851 
 
 20 
 
 0.031 96 
 
 1022 
 
 802 
 
 0.003092 
 
 0.3051 
 
 21 
 
 0.02846 
 
 810.1 
 
 632.3 
 
 0.002452 
 
 0.1919 
 
 22 
 
 0.025 35 
 
 642.4 
 
 504.6 
 
 0.001 945 
 
 1207 
 
 23 
 
 0.02257 
 
 509.5 
 
 400.2 
 
 0.001 542 
 
 0.07589 
 
 24 
 
 0.020 10 
 
 404.0 
 
 317.3 
 
 0.001 223 
 
 0.04773 
 
 25 
 
 0.01790 
 
 324.4 
 
 251.7 
 
 0.000 969 9 
 
 0.03002 
 
 26 
 
 0.015 94 
 
 254.1 
 
 199.6 
 
 0.0007692 
 
 0.01888 
 
 27 
 
 0.0142 
 
 201.5 
 
 158.3 
 
 0.0006100 
 
 0.011 87 
 
 28 
 
 0.01264 
 
 159.8 
 
 125.5 
 
 0.0004837 
 
 0.007466 
 
 29 
 
 0.01126 
 
 126.7 
 
 99.53 
 
 0.0003836 
 
 0.004 696 
 
 30 
 
 0.01003 
 
 100.5 
 
 78.94 
 
 0.0003042 
 
 0.002953 
 
 31 
 
 0.008928 
 
 79.70 
 
 62.60 
 
 0.0002413 
 
 0.001857 
 
 32 
 
 0.007 950 
 
 63.21 
 
 49.64 
 
 0.0001913 
 
 0.001 168 
 
 33 
 
 0.007080 
 
 50.13 
 
 39.37 
 
 0.000 1517 
 
 0000 734 6 
 
 34 
 
 0.006 305 
 
 39.75 
 
 31.22 
 
 0.0001203 
 
 0.0004620 
 
 35 
 
 0.005 615 
 
 31.52 
 
 24.76 
 
 0.00009543 
 
 0.0002905 
 
 36 
 
 0.0050 
 
 25.0 
 
 19.64 
 
 0.00007568 
 
 0.0001827 
 
 37 
 
 0.004 453 
 
 19.83 
 
 15.57 
 
 0.00006001 
 
 0.0001149 
 
 38 
 
 0.003965 
 
 15.72 
 
 12.35 
 
 0.00004759 
 
 0.00007210 
 
 39 
 
 0.003 531 
 
 12.47 
 
 9.79 
 
 0.00003774 
 
 0.00004545 
 
 40 
 
 0.003 145 
 
 9.888 
 
 7.77 
 
 0.00002993 
 
 0.00002858 
 
TABLE E 
 
 403 
 
 INSTITUTE OF ELECTRICAL ENGINEERS 
 of Matthiessen's standard of conductivity. 
 
 Ibs. per 
 Ohm. 
 
 Feet Tier 
 Pound 
 
 Feet Per 
 ohm 
 
 122 F. 
 50 C. 
 
 176 F. 
 
 80 C. 
 
 
 68 F. 
 20 C. 
 
 122 F. 
 50 C. 
 
 176 F. 
 80 C. 
 
 11720 
 
 10570 
 
 1.561 
 
 20440 
 
 18290 
 
 16510 
 
 7369 
 
 6647 
 
 1.969 
 
 16210 
 
 14510 
 
 13090 
 
 4634 
 
 4 182 
 
 2.482 
 
 12850 
 
 11500 
 
 10380 
 
 2914 
 
 2630 
 
 3 130 
 
 10190 
 
 9 123 
 
 8232 
 
 1833 
 
 1654 
 
 3.947 
 
 8083 
 
 7235 
 
 6528 
 
 1153 
 
 1040 
 
 4.977 
 
 6410 
 
 5738 
 
 5177 
 
 725.0 
 
 654.2 
 
 6.276 
 
 5084 
 
 4550 
 
 4106 
 
 455.9 
 
 411.4 
 
 7.914 
 
 4031 
 
 3608 
 
 3256 
 
 286.7 
 
 258.7 
 
 9.980 
 
 3 1<V7 
 
 2862 
 
 2582 
 
 180.3 
 
 162.7 
 
 12.58 
 
 2535 
 
 2269 
 
 2048 
 
 113.4 
 
 102.3 
 
 15.87 
 
 2011 
 
 1800 
 
 1624 
 
 71.33 
 
 64.36 
 
 20.01 
 
 1595 
 
 1427 
 
 1288 
 
 44.86 
 
 40.48 
 
 25.23 
 
 1265 
 
 1 132 
 
 1021 
 
 28.21 
 
 25.46 
 
 31.82 
 
 1003 
 
 897.6 
 
 809.9 
 
 17.74 
 
 16.01 
 
 40.12 
 
 795.3 
 
 711.8 
 
 642.3 
 
 11.16 
 
 10.07 
 
 50.59 
 
 603.7 
 
 564.5 
 
 509.4 
 
 7.017 
 
 6.332 
 
 63.79 
 
 500.1 
 
 447.7 
 
 404.0 
 
 4.413 
 
 3.982 
 
 80.44 
 
 396.6 
 
 355.0 
 
 320.3 
 
 2.776 
 
 2.504 
 
 101.4 
 
 314.5 
 
 281.5 
 
 254.0 
 
 1.746 
 
 1.575 
 
 127.9 
 
 249.4 
 
 223.3 
 
 201.5 
 
 1.098 
 
 0.990 6 
 
 161.3 
 
 197.8 
 
 177.1 
 
 159.8 
 
 0.6904 
 
 0.6230 
 
 203.4 
 
 156.9 
 
 140.4 
 
 126.7 
 
 0.434 2 
 
 0.3918 
 
 256.5 
 
 124.4 
 
 111.4 
 
 100.5 
 
 0.273 1 
 
 0.2464 
 
 323.4 
 
 98.66 
 
 88.31 
 
 98.68 
 
 0.1717 
 
 0.1550 
 
 407.8 
 
 78.24 
 
 70.03 
 
 63.19 
 
 0.1080 
 
 0.09746 
 
 514.2 
 
 62.05 
 
 55.. 54 
 
 50.11 
 
 0.06793 
 
 0.061 29 
 
 648.4 
 
 49.21 
 
 44.04 
 
 39.74 
 
 0.042 72 
 
 0.038 55 
 
 817.6 
 
 39.02 
 
 34.93 
 
 31.52 
 
 0.02887 
 
 0.02424 
 
 1 031 
 
 30.95 
 
 27.70 
 
 24.99 
 
 0.01690 
 
 0.015 25 
 
 1300 
 
 24.54 
 
 21.97 
 
 19.82 
 
 0.01063 
 
 0.009 588 
 
 1639 
 
 19.46 
 
 17.42 
 
 15.72 
 
 0.006683 
 
 0.006030 
 
 0067 
 
 15.43 
 
 13.82 
 
 12.47 
 
 0.004203 
 
 0.003792 
 
 2607 
 
 12.24 
 
 10.96 
 
 9.886 
 
 0.002643 
 
 0.002 385 
 
 3287 
 
 9.707 
 
 8.688 
 
 7.840 
 
 0.001 662 
 
 0.001 500 
 
 4 145 
 
 7.698 
 
 6.890 
 
 6.217 
 
 0.001 045 
 
 0.000 943 6 
 
 5227 
 
 6.105 
 
 5.464 
 
 4.930 
 
 0.0006575 
 
 000 593 3 
 
 6591 
 
 4.841 
 
 4.333 
 
 3.910 
 
 0.0004135 
 
 0.000373 1 
 
 8311 
 
 3.839 
 
 3.436 
 
 3.101 
 
 0.0002601 
 
 0.0002347 
 
 10480 
 
 3 045 
 
 2.725 
 
 2.459 
 
 0.0001636 
 
 0.0001476 
 
 13210 
 
 2.414 
 
 2.161 
 
 1.950 
 
 0.0001029 
 
 0.00009281 
 
 16660 
 
 1.915 
 
 1.714 
 
 1.547 
 
 0.00006454 
 
 0.00005824 
 
 21010 
 
 1.519 
 
 1.359 
 
 1.226 
 
 0.00004068 
 
 0.00003671 
 
 26500 
 
 1.204 
 
 1.078 
 
 0.9726 
 
 0.00002559 
 
 000 023 09 
 
 33 410 
 
 9550 
 
 0.8548 
 
 0.771 3 
 
404 
 
 TABLE F 
 
 COPPER WIRE TABLE OF AMERICAN 
 Giving Resistances of cool, warm and hot wires, 
 
 B. & S. 
 or 
 A. W. G. 
 
 Ohms per Pound. 
 
 68 F. 
 20 C. 
 
 122 F. 176 F. 
 50 C. ; 80 C. 
 
 0000 
 
 0.00007639 
 
 0.00008535 
 
 0.00009459 
 
 000 
 
 0.0001215 
 
 0.0001357 
 
 0.0001504 
 
 00 
 
 0.000 193 1 
 
 0.0002158 
 
 0.000239 1 
 
 
 
 0.0003071 
 
 0.0003431 
 
 0.0003803 
 
 1 
 
 0.0004883 
 
 0.0005456 
 
 0.0006040 
 
 2 
 
 0.0007765 
 
 0.000 867 5 
 
 0.0009614 
 
 3 
 
 0.001 235 
 
 0.001 379 
 
 0.001529 
 
 4 
 
 0.001 963 
 
 0.002 193 
 
 0.002431 
 
 5 
 
 0.003 122 
 
 0.003487 
 
 0.003865 
 
 6 
 
 0.004 963 
 
 0.005 545 
 
 0.006 145 
 
 7 
 
 0.007892 
 
 0.008 817 
 
 0.009772 
 
 8 
 
 0.012 55 
 
 0.014 02 
 
 0.01554 
 
 9 
 
 0.019 95 
 
 0.022 29 
 
 0.024 71 
 
 10 
 
 0.031 73 
 
 0.0345 
 
 0.03928 
 
 11 
 
 0.05045 
 
 0.056 36 
 
 0.06246 
 
 12 
 
 0.08022 
 
 0.08962 
 
 0.09932 
 
 13 
 
 0.1276 
 
 0.1425 
 
 0.1579 
 
 14 
 
 0.2028 
 
 0.226 6 
 
 0.251 1 
 
 15 
 
 0.3225 
 
 0.3603 
 
 0.3993 
 
 16 
 
 0.5128 
 
 0.5729 
 
 0.6349 
 
 17 
 
 0.815 3 
 
 0.9109 
 
 1.010 
 
 18 
 
 1.296 
 
 1.448 
 
 1.605 
 
 19 
 
 2.061 
 
 2.303 
 
 2.552 
 
 20 
 
 3.278 
 
 3.662 
 
 4.058 
 
 21 
 
 5.212 
 
 5.823 
 
 6.453 
 
 22 
 
 8.287 
 
 9.259 
 
 10.26 
 
 23 
 
 13.18 
 
 14.72 
 
 16.32 
 
 24 
 
 20.95 
 
 23.41 
 
 25.94 
 
 25 
 
 33.32 
 
 37.22 
 
 41.25 
 
 26 
 
 52.97 
 
 59.18 
 
 65.59 
 
 27 
 
 84.23 
 
 94.11 
 
 104.3 
 
 28 
 
 133.9 
 
 149.6 
 
 165.8 
 
 29 
 
 213.0 
 
 237.9 
 
 263.7 
 
 30 
 
 338.6 
 
 378.3 
 
 419.3 
 
 31 
 
 538.4 
 
 601.6 
 
 666.7 
 
 32 
 
 856.2 
 
 956.5 
 
 1060 
 
 33 
 
 1361 
 
 1521 
 
 1685 
 
 34 
 
 2165 
 
 2418 
 
 2680 
 
 35 
 
 3441 
 
 3845 
 
 4262 
 
 36 
 
 5473 
 
 6114 
 
 6776 
 
 37 
 
 8702 
 
 9722 
 
 10770 
 
 38 
 
 13870 
 
 15490 
 
 17170 
 
 39 
 
 22000 
 
 24580 
 
 27240 
 
 40 
 
 34980 
 
 39080 
 
 43320 
 
TABLE F 
 
 405 
 
 INSTITUTE OF ELECTRICAL ENGINEERS 
 of Matthiessen's standard of conductivity. 
 
 Ohms per foot. 
 
 B. &S. 
 or 
 A. W. G. 
 
 68 F. 
 20 C. 
 
 122 F. 
 50 C. 
 
 176 F. 
 80 C. 
 
 0.00004893 
 
 0.000 054 67 
 
 0.00006058 
 
 0000 
 
 0.00006170 
 
 0.00006893 
 
 0.00007640 
 
 000 
 
 0.00007780 
 
 0.00008692 
 
 0.00009633 
 
 00 
 
 0.00009811 
 
 0,000 1096 
 
 0.0001215 
 
 
 
 0.0001237 
 
 0.0001382 
 
 0.0001532 
 
 1 
 
 0.0001560 
 
 0.0001743 
 
 0.0001932 
 
 2 
 
 0.0001967 
 
 0.0002198 
 
 0.0002435 
 
 3 
 
 0.0002480 
 
 0.0002771 
 
 0.0003071 
 
 4 
 
 0.0003123 
 
 0.0003495 
 
 0.0003873 
 
 5 
 
 0.0003944 
 
 0.0004406 
 
 0.0004883 
 
 6 
 
 0.0004973 
 
 0.0005556 
 
 0.0006158 
 
 7 
 
 0.0006271 
 
 0.0007007 
 
 0.0007765 
 
 8 
 
 0.0007908 
 
 0.0008835 
 
 0.0009791 
 
 9 
 
 0.0009972 
 
 0.001 114 
 
 0.001 235 
 
 10 
 
 0.001257 
 
 O.OOJ 405 
 
 0.001 557 
 
 11 
 
 001 586 
 
 001771 
 
 0.001963 
 
 12 
 
 0.001999 
 
 0.002234 
 
 0.002 476 
 
 13 
 
 0.002521 
 
 0.002817 
 
 0.003 122 
 
 14 
 
 003 179 
 
 0.003552 
 
 0.003936 
 
 15 
 
 0.004009 
 
 0.004479 
 
 0.004964 
 
 16 
 
 0.005055 
 
 0.005 648 
 
 0.006 259 
 
 17 
 
 0.006374 
 
 0.007 122 
 
 0.007 892 
 
 18 
 
 0.008038 
 
 0.008980 
 
 0.009952 
 
 19 
 
 0.01014 
 
 0.011 32 
 
 0.012 55 
 
 20 
 
 0.01278 
 
 0.01428 
 
 0.01583 
 
 21 
 
 0.016 12 
 
 0.01801 
 
 0.01096 
 
 22 
 
 0.02032 
 
 0.02271 
 
 0.025 16 
 
 23 
 
 0.02563 
 
 0.02863 
 
 0.031 73 
 
 24 
 
 0.032 31 
 
 0.036 10 
 
 0.041 10 
 
 25 
 
 0.04075 
 
 0.04552 
 
 0.05045 
 
 26 
 
 0.051 38 
 
 0.05740 
 
 0.06362 
 
 27 
 
 0.06479 
 
 0.07239 
 
 0.08022 
 
 28 
 
 0.081 70 
 
 0.09128 
 
 0.1012 
 
 29 
 
 0.1030 
 
 0.115 1 
 
 0.1276 
 
 30 
 
 0.1299. 
 
 0.1451 
 
 0.1608 
 
 31 
 
 0.1638 
 
 0.1830 
 
 0.2028 
 
 32 
 
 0.2066 
 
 0.2308 
 
 0.2558 
 
 33 
 
 0.2605 
 
 0.2910 
 
 0.3225 
 
 34 
 
 0.3284 
 
 0.3669 
 
 0.4067 
 
 35 
 
 0.4142 
 
 0.4627 
 
 0.5129 
 
 36 
 
 0.5222 
 
 0.5835 
 
 0.6466 
 
 37 
 
 0.6585 
 
 0.7357 
 
 0.8154 
 
 38 
 
 0.8304 
 
 0.927 7 
 
 1.028 
 
 39 
 
 1.047 
 
 1.170 
 
 1.296 
 
 40 
 
406 
 
 TABLE G 
 
 TABLE OF CARRYING CAPACITY OF WIRE AS ESTABLISHED BY THE 
 NATIONAL BOARD OF UNDERWRITERS 
 
 Copper 
 B. & S. G. 
 
 Circular 
 Mils. 
 
 Rubber Cover- 
 ed Wires, 
 Amperes 
 
 Other 
 Insulations 
 Amperes 
 
 18 
 
 1 624 
 
 3 
 
 5 
 
 16 
 
 2583 
 
 6 
 
 8 
 
 14 
 
 4 107 
 
 12 
 
 16 - 
 
 12 
 
 6530 
 
 17 
 
 23 
 
 10 
 
 10380 
 
 24 
 
 32 
 
 8 
 
 16 510 
 
 33 
 
 46 
 
 6 
 
 26250 
 
 46 
 
 65 
 
 5 
 
 33 100 
 
 54 
 
 77 
 
 4 
 
 41 740 
 
 65 
 
 92 
 
 3 
 
 52630 
 
 76 
 
 110 
 
 2 
 
 66370 
 
 90 
 
 131 
 
 1 
 
 83690 
 
 107 
 
 156 
 
 
 
 105 500 
 
 127 
 
 185 
 
 00 
 
 133 100 
 
 150 
 
 220 
 
 000 
 
 167 800 
 
 177 
 
 265 
 
 0000 
 
 211 600 
 
 210 
 
 312 
 
 
 200 000 
 
 200 
 
 300 
 
 
 300 000 
 
 270 
 
 400 
 
 
 400 000 
 
 330 
 
 500 
 
 
 500 000 
 
 390 
 
 590 
 
 
 600 000 
 
 450 
 
 680 
 
 
 700 000 
 
 500 
 
 760 
 
 
 800 000 
 
 550 
 
 840 
 
 
 900 000 
 
 600 
 
 920 
 
 
 1 000 000 
 
 650 
 
 1 000 
 
 
 1 100 000 
 
 690 
 
 1080 
 
 
 1 200 000 
 
 730 
 
 1 150 
 
 
 1 300 000 
 
 770 
 
 1220 
 
 
 1 400 000 
 
 810 
 
 1290 
 
 
 1 500 000 
 
 850 
 
 1360 
 
 
 1 600 000 
 
 890 
 
 1 430 
 
 
 1 700 000 
 
 930 
 
 1 490 
 
 
 1 800 000 
 
 970 
 
 1 550 
 
 
 1 900 000 
 
 1010 
 
 1 610 
 
 
 2 000 000 
 
 1050 
 
 1670 
 
 The question of drop is not taken into consideration in the 
 above table. 
 
TABLE H 
 
 407 
 
 DIAMETER OF WIRE WHICH WILL FUSE WITH GIVEN CURRENT 
 (W. H. Preece.) 
 
 
 Diameter in Mils 
 
 Amp. 
 
 Copper 
 
 Alum- 
 
 Plat- 
 
 German 
 
 Plat- 
 
 Iron 
 
 Tin 
 
 Tin lead 
 
 Lead 
 
 
 
 inium 
 
 inium 
 
 silver 
 
 inoid 
 
 
 
 alloy 
 
 
 1 
 
 2 
 
 2.1 
 3.4 
 
 2.6 
 4.1 
 
 3.3 
 5.3 
 
 3.3 
 5.3 
 
 3.5 
 
 5.6 
 
 4.7 
 
 7.4 
 
 7.2 
 11.3 
 
 8.3 
 13.2 
 
 8.1 
 12.8 
 
 3 
 
 4.4 
 
 5.4 
 
 7.0 
 
 6.9 
 
 7.4 
 
 9.7 
 
 14.9 
 
 17.3 
 
 16.8 
 
 4 
 
 5.3 
 
 6.5 
 
 8.4 
 
 8.4 
 
 8.9 
 
 11.7 
 
 18.1 
 
 21.0 
 
 20.3 
 
 5 
 
 6.2 
 
 7.6 
 
 9.8 
 
 9.7 
 
 10.4 
 
 13.6 
 
 21.0 
 
 24.3 
 
 23.6 
 
 10 
 
 9.8 
 
 12.0 
 
 15.5 
 
 15.4 
 
 16.4 
 
 21.6 
 
 33.4 
 
 38.6 
 
 37.5 
 
 15 
 
 12.9 
 
 15.8 
 
 20.3 
 
 20.2 
 
 21.5 
 
 28.3 
 
 43.7 
 
 50.6 
 
 49.1 
 
 20 
 
 15.6 
 
 19.1 
 
 24.6 
 
 24.5 
 
 26.1 
 
 34.3 
 
 52.9 
 
 61.3 
 
 59.5 
 
 25 
 
 18.1 
 
 22.2 
 
 28.6 
 
 28.4 
 
 30.3 
 
 39.8 
 
 61.4 
 
 71.1 
 
 69.0 
 
 30 
 
 20.5 
 
 25.0 
 
 32.3 
 
 32.0 
 
 34.2 
 
 45.0 
 
 69.4 
 
 80.3 
 
 77.9 
 
 35 
 
 22.7 
 
 27.7 
 
 35.8 
 
 35.6 
 
 37.9 
 
 49.8 
 
 76.9 
 
 89.0 
 
 86.4 
 
 40 
 
 24.8 
 
 30.3 
 
 39.1 
 
 38.8 
 
 41.4 
 
 54.5 
 
 84.0 
 
 97.3 
 
 94.4 
 
 45 
 
 26.8 
 
 32.8 
 
 42.3 
 
 42.0 
 
 44.8 
 
 58.9 
 
 90.9 
 
 105.2 
 
 102.1 
 
 50 
 
 28.8 
 
 35.2 
 
 45.4 
 
 45.0 
 
 48.0 
 
 63.2 
 
 97.5 
 
 112.9 
 
 109.5 
 
 60 
 
 32.5 
 
 39.7 
 
 51.3 
 
 50.9 
 
 54.2 
 
 71.4 
 
 110.1 
 
 127.5 
 
 123.7 
 
 70 
 
 36.0 
 
 44.0 
 
 56.8 
 
 56.4 
 
 60.1 
 
 79.1 
 
 122.0 
 
 141.3 
 
 137.1 
 
 80 
 
 39.4 
 
 48.1 
 
 62.1 
 
 61.6 
 
 65.7 
 
 86.4 
 
 133.4 
 
 154.4 
 
 149.9 
 
 90 
 
 42.6 
 
 52.0 
 
 67.2 
 
 66.7 
 
 71.1 
 
 93.5 
 
 144.3 
 
 167.1 
 
 162.1 
 
 100 
 
 45.7 
 
 55.8 
 
 72.0 
 
 71.5 
 
 76.2 
 
 100.3 
 
 154.8 
 
 179.2 
 
 173.9 
 
 120 
 
 51.6 
 
 63.0 
 
 81.4 
 
 80.8 
 
 86.1 
 
 113.3 
 
 174.8 
 
 202.4 
 
 196.4 
 
 140 
 
 57.2 
 
 69.8 
 
 90.2 
 
 89.5 
 
 95.4 
 
 125.5 
 
 193.7 
 
 224.3 
 
 217.6 
 
 160 
 
 62.5 
 
 76.3 
 
 98.6 
 
 97.8 
 
 104.3 
 
 137.2 
 
 211.8 
 
 245.2 
 
 237.9 
 
 180 
 
 67.6 
 
 82.6 
 
 105.6 
 
 105.8 
 
 112.8 
 
 148.4 
 
 229.1 
 
 265.2 
 
 257.3 
 
 200 
 
 72.5 
 
 88.6 
 
 114.4 
 
 113.5 
 
 121.0 
 
 159.2 
 
 245.7 
 
 284.5 
 
 276.0 
 
 225 
 
 78.4 
 
 95.8 
 
 123.7 
 
 122.8 
 
 130.9 
 
 172.2 
 
 265.8 
 
 307.7 
 
 298.6 
 
 250 
 
 84.1 
 
 102.8 
 
 132.7 
 
 131.7 
 
 140.4 
 
 184.8 
 
 285.1 
 
 330.1 
 
 320.3 
 
 275 
 
 89.7 
 
 109.5 
 
 141.4 
 
 140.4 
 
 149.7 
 
 196.9 
 
 303.8 
 
 351.8 
 
 341.3 
 
 300 
 
 95.0 
 
 116.1 
 
 149.8 
 
 148.7 
 
 158.6 
 
 208.6 
 
 322.0 
 
 372.8 
 
 361.7 
 
408 
 
 * TABLE I 
 
 RING ARMATURE WINDINGS 
 
 J 
 
 TH <N 
 
 CO 
 
 ?!! 
 
 OH 
 
 jb 
 
 CO 
 CO 
 
 ft 
 1 
 
 o 
 O 
 
 CO 
 CO 
 
 ft 
 W 
 
 CS3 
 
 K 
 
 93 
 
 <M 
 
 H- 
 
 
 -H 
 
 H 
 
 M 
 
 
 n ii 
 
 -H 
 
 ^ 
 fl 
 (N 
 -f| 
 
 | 
 
 bC 
 
 M 
 
 X! 
 
 Iflffll 
 
 2g|^ 
 
 10 sadAr 
 
* TABLE J 
 
 WAVE-WOUND DRUM ARMATURE WINDINGS 
 
 409 
 
 |SS& 
 
 H 
 
 (N 
 
 CO 
 
 ^ 
 
 ll 
 
 *|| 
 
 o 
 
 _0 
 
 1 
 
 i! 
 
 L*&1 
 
 co <3 s 
 
 ^5 
 
 ^ 
 
 
 1 
 
 CO 
 
 
 
 
 1 
 
 * 
 
 P 
 
 o 
 
 3 
 
 ^ Q) 
 
 s s 
 
 4d 
 
 
 
 QQ 
 
 
 T3 
 
 l"rt 
 
 TJ 
 
 O 
 
 ^^ ^^ 
 
 
 
 
 fe 
 
 
 
 
 
 1.1 
 II 
 
 <N 
 
 1- 
 
 - 
 
 * 
 
 J. 
 
 Us 
 
 CS3 
 
 CS3 
 
 N 
 
 CS3 
 
 If 
 
 03 
 
 d 
 
 ^ 
 
 ^ 
 
 3 II 
 
 drf 
 
 ~L| ^T 1 
 
 QJ 
 
 1^1 J* 
 
 S.rj 
 
 k^f 
 
 .j ri 
 
 ky( 
 
 li ^"s 
 
 B 
 
 <N 
 
 s 
 
 (N 
 
 S 
 
 
 ^ O N 
 
 IT" 
 
 
 
 _ 
 
 '^ CH /-( 
 
 > *** > fl3 
 
 
 
 (X 
 
 ^ o .-*5 
 
 x ^ >"B i 
 
 ^2 
 
 ^0*1 
 
 i 
 
 -H a^^ | J 
 
 
 -H A 
 
 4i n 
 
 
 Il S | 
 
 N 11 1+^ 
 
 
 SI 
 
 UI = 
 
 da}g ppi^ 
 
 1-1 
 
 i i 
 
 TH 
 
 TH 
 
 Number of In- 
 ductors = Z 
 
 5 
 
 <N 
 
 -H 
 ^ 
 
 _-H 
 
 S 
 
 -H 
 
 i 
 
 A^jfi 
 
 
 
 .5 3 p a 
 
 
 :S< 
 
 CO 
 
 cl 
 
 ^g^ 
 
 ,a 
 XI 
 
 
 
 
 * SC OJJ2 O 
 
 
 6||| f 
 
 N 
 
 <N 
 
 00 "o B j^ c3 
 
 X3 d 
 
 (Q S-3 gpO 
 
 ls|g 
 
 
 
 a * S v 
 
 -t< s a;^ a> 
 
 "l^ 
 
 ll 
 
 
 (H (H 
 
 
 !H f-i 
 
 oil 
 
 rH 
 
 5fii 
 
 TH 
 
 CO >^ ^ p 
 
 Smpui^ 1 j _ | 
 
 <N 
 
 CO 
 
 ^ 
 
410 
 
 p 
 
 * TABLE K 
 
 LAP-WOUND DRUM ARMATURE WINDINGS 
 
 F-H <N CO 
 
 *JM 
 
 1 
 
 JSi 
 
 tS3 
 
 fc 
 
 I 1 
 
 P5 
 
 Q 
 
 - 
 
 X! 
 
 -H 
 
 -fl 
 
 -H 
 
 ?: 
 
 -H 
 
 UI = 
 
 da^g pptj 
 
 
 O 
 
 X! 
 ft 
 
 -f: 
 
 N 
 
 li 
 
 . 
 
 CN 
 
TABLE M 
 
 411 
 
 WIRING TABLE FOR TWO PER CENT LOSS ON A 50-VOLT CIRCUIT 
 Table for 1 Volt Loss 
 
 
 i 
 
 M -H cs oo co o us T* cocoiMCN^HOOQQOgg 
 
 
 
 
 i 
 
 CO (M O O5 1-- tO fO 5-<l<Tt<C<3CO<>Ji-H^HOOOO o O 
 
 
 
 
 
 -*C^~HC500t^cOO "3 ^" * W C^l (M 1-1 I-H O O g ^ Q O 
 00 
 
 S5 
 
 
 H 
 
 
 
 Tt<CO-HOOOI>.l>-! lOtOTjlTjtcOC^iM'-HOO QOOO O 
 
 00 
 
 
 
 53 
 
 &<?> 
 
 
 
 O IcC OJ O OJ OO t>- t OOiOTt^<COC^<M-HOOgOgOOO 
 
 5 ^8SS 
 
 1 oo 
 
 B| 
 
 g^ 
 
 
 
 o|^j co I-H o 01 oo r- o-totouo^^ccccc^^H ooooooo QQ o 
 ooo 
 
 1 
 I" 
 
 8 
 
 CO O CO (M O O3 OS OO t^t^OcOiC'*i^irOiMiM-HOOOOOOOOO 
 
 1-H ^H rt 1-H i-H OOOggOSl 
 
 
 
 S 'l 
 
 ^ '! 
 
 8 
 
 I O <*( (M T-H O O5 OO 00 t^ !> <O "3 "5 - 1 * 1 Tt< COIM i-c i-H O O g g OggOg g 
 
 : oo 
 
 gs 
 
 
 
 I-H jj^H I-I,-H^HT-( OOOoSj 
 
 
 8 
 
 lOfCO <M -H O O OJOOOO !>-^-!O"5OTficOC^ (Mr-ti-H OO O OO OOO 
 
 1-1 I-H -H i-H r-t i 1 
 
 g 
 
 S 
 
 CO * CO (M ^H O OO5O5OO^-l>'OCOiO^COCO(MC^'^'-^r-iOOOg55 
 
 1 
 
 s 
 
 <O "5|2 (N IM ^ O O OS OS 00 t O- CO 1C >O Tfi CO CO C<l (M <M -H r-^ TH O O O 
 
 i 
 
 9 
 
 
 Q 
 
 5 
 
 : : : ^T - " - -"-*-"- 1 
 
 
 3 
 
 . . . SSpS2 S 2^32" 
 
 
 8 
 
 IO tQygj CO CO (M <M -H O O O> O5 00 t^ CO CO >O 1C Tf Tfl Tfi CO CO CO W N 
 
 
 S 
 
 : : : : s s S F 2222^2^ 
 
 
 8 
 
 
 o| 
 
 4 
 
 
 ^^CNCO^^cOt^ OOO.OCN^COOOO^OJO^.nOJggJgOJOggg 
 
412 
 
 TABLE N 
 
 WIRING TABLE FOR TWO PER CENT LOSS OX A 110- VOLT CIRCUIT 
 Table for 2.2 Volts Loss 
 
 DISTANCE IN FEET TO CENTER OF DISTRIBUTION 
 (Wire sizes in B. & S. Gauge) 
 
 
 
 r s= ^ 
 
 00 
 
 
 
 
 00 
 
 i 
 
 S | SSS 
 
 o o 
 
 i 
 
 i!i: 
 
 00 
 
 1 
 
 T 
 
 " H 83g 5 Sg 
 
 00 
 
 1 
 
 T 
 
 oo 
 
 1 
 
 1 oo 
 
 S 
 
 s t s= 
 
 
 
 i 
 
 SIS S S 
 
 
 1 
 
 2|S 2 S S 3S >> r *.*.oe, oggg 
 
 8 
 
 sis 2 
 
 CM * ' * OO O> OO OO t*~ t^ to 1C ^ ^ CO CO CM '-H I-H O O O 
 
 g ... ^i^, ^ 
 
 2 22 S3 2 oooo^tooo^^coc.^^^0 
 
 tO 2 -H 
 
 g^g-gS-^o-5-oor.^.o-s^^eo-. 
 
 ..... to 
 
 2133 22 232 SS * 001 ^ 500 " 5 "* 
 
 ^ : : 2 i22I^S 222 2 3 S ^ "" ^ l ' l '" u " 
 
 g :::::: 
 
 : 22 S2ISS2 SSSSS 030 - 
 
 en 
 
 21 
 
 10 
 
 
 
 
TABLE 
 
 413 
 
 WIRING TABLE FOR TWO PER CENT LOSS ON A 220-VOLT CIRCUIT 
 Table for 4.4 Volts Loss 
 
 
 DISTANCE IN FEET TO CENTER OF DISTRIBUTION 
 (Wire sizes in B. & S. Gauge) 
 
 No. of 
 amperes 
 
 Si 
 
 3 
 
 -=- 
 
 3 
 
 3 
 
 S 
 
 8 
 
 B 
 
 8 
 
 
 
 fj 
 
 1 
 
 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 16 
 
 1.5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 16 
 
 15 
 
 M 
 
 2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 16 
 
 15 
 
 15 
 
 "" TT-TT 
 
 3 
 
 
 
 
 
 
 
 
 
 
 
 
 16 
 
 15 
 
 15 
 
 "IT 
 
 "IT 
 
 T3 
 
 12 15! 
 
 4 
 
 
 
 
 
 
 
 
 
 
 16 
 
 15 
 
 15 
 
 13 
 
 13 
 
 13 
 
 12 
 
 12 
 
 11 
 
 11 
 
 5 
 
 
 
 
 
 
 
 
 
 16 
 
 15 
 
 T4 
 
 13 
 
 13 
 
 13 
 
 12 
 
 11 
 
 11 
 
 10 10 
 
 6 
 
 
 
 
 
 
 
 16 
 
 15 
 
 15 
 
 13 
 
 14 
 
 13 
 
 12 
 
 12 
 
 11 
 
 11 
 
 10 
 
 9 
 
 9 
 
 7 
 
 
 
 
 
 
 16 
 
 15 
 
 T4 
 
 T4 
 
 14 
 
 13 
 
 12 
 
 12 
 
 11 
 
 11 
 
 10 
 
 9 
 
 9 
 
 8 
 
 8 
 
 
 
 
 
 16 
 
 15 
 
 15 
 
 14 
 
 14 
 
 13 
 
 12 
 
 12 
 
 11 
 
 11 
 
 10 
 
 9 
 
 9 
 
 8 
 
 8 
 
 9 
 
 
 
 
 
 15 
 
 15 
 
 13 
 
 14 
 
 13 
 
 12 
 
 12 
 
 11 
 
 11 
 
 10 
 
 9 
 
 9 
 
 8 
 
 8 
 
 7 
 
 10 
 
 
 
 
 16 
 
 15 
 
 14 
 
 14 
 
 13 
 
 13 
 
 12 
 
 11 
 
 11 
 
 10 
 
 10 
 
 9 
 
 8 
 
 8 
 
 7 
 
 7 
 
 12 
 
 
 
 16 
 
 15 
 
 14 
 
 14 
 
 13 
 
 12 
 
 12 
 
 11 
 
 11 
 
 10 
 
 9 
 
 9 
 
 8 
 
 8 
 
 7 
 
 7 
 
 6 
 
 14 
 
 
 16 
 
 15 
 
 14 
 
 14 
 
 13 
 
 12 
 
 12 
 
 11 
 
 11 
 
 10 
 
 9 
 
 9 
 
 8 
 
 7 
 
 7 
 
 6 
 
 6 
 
 5 
 
 16 
 
 
 16 
 
 15 
 
 14 
 
 13 
 
 12 
 
 12 
 
 11 
 
 11 
 
 10 
 
 9 
 
 9 
 
 8 
 
 8 
 
 7 
 
 7 
 
 6 
 
 6 
 
 5 
 
 18 
 
 
 15 
 
 14 
 
 13 
 
 
 12 
 
 11 
 
 11 
 
 10 
 
 9 
 
 9 
 
 8 
 
 8 
 
 7 
 
 7 
 
 6 
 
 5 
 
 5 
 
 4 
 
 20 
 
 16 
 
 15 
 
 14 
 
 13 
 
 12 
 
 11 
 
 11 
 
 10 
 
 10 
 
 9 
 
 8 
 
 8 
 
 7 
 
 7 
 
 6 
 
 5 
 
 5 
 
 4 
 
 4 
 
 25 
 
 16 
 
 14 
 
 13 
 
 12 
 
 [1 
 
 10 
 
 10 
 
 9 
 
 9 
 
 8 
 
 7 
 
 7 
 
 6 
 
 6 
 
 5 
 
 4 
 
 4 
 
 3 
 
 3 
 
 30 
 
 15 
 
 13 
 
 [2 
 
 11 
 
 10 
 
 10 
 
 9 
 
 9 
 
 8 
 
 7 
 
 7 
 
 6 
 
 6 
 
 5 
 
 4 
 
 4 
 
 3 
 
 3 
 
 2 
 
 35 
 
 1 
 
 13 
 
 [j 
 
 10 
 
 10 
 
 9 
 
 8 
 
 8 
 
 7 
 
 7 
 
 6 
 
 5 
 
 5 
 
 4 
 
 4 
 
 3 
 
 2 
 
 2 
 
 1 
 
 40 
 
 14 
 
 12 
 
 [j 
 
 10 
 
 9 
 
 8 
 
 8 
 
 7 
 
 7 
 
 6 
 
 5 
 
 5 
 
 4 
 
 4 
 
 3 
 
 2 
 
 2 
 
 1 
 
 1 
 
 45 
 
 13 
 
 12 
 
 10 
 
 9 
 
 9 
 
 8 
 
 7 
 
 7 
 
 6 
 
 6 
 
 5 
 
 4 
 
 4 
 
 3 
 
 3 
 
 2 
 
 1 
 
 1 
 
 
 
 50 
 
 13 
 
 
 10 
 
 9 
 
 8 
 
 7 
 
 7 
 
 6 
 
 6 
 
 5 
 
 4 
 
 4 
 
 3 
 
 3 
 
 2 
 
 1 
 
 1 
 
 
 
 
 
 60 
 
 12 
 
 [0 
 
 9 
 
 8 
 
 
 7 
 
 6 
 
 6 
 
 5 
 
 4 
 
 4 
 
 3 
 
 3 
 
 2 
 
 1 
 
 1 
 
 
 
 
 
 00 
 
 70 
 
 11 
 
 10 
 
 8 
 
 7 
 
 
 
 6 
 
 5 
 
 5 
 
 4 
 
 4 
 
 3 
 
 2 
 
 2 
 
 1 
 
 1 
 
 
 
 00 
 
 00 
 
 000 
 
 80 
 
 11 
 
 9 
 
 8 
 
 7 
 
 6 
 
 5 
 
 5 
 
 4 
 
 4 
 
 3 
 
 2 
 
 2 
 
 1 
 
 1 
 
 
 
 00 
 
 00 
 
 000 
 
 000 
 
 90 
 
 10 
 
 9 
 
 7 
 
 6 
 
 6 
 
 5 
 
 4 
 
 4 
 
 3 
 
 3 
 
 2 
 
 1 
 
 1 
 
 
 
 00 
 
 00 
 
 000 
 
 000 
 
 0000 
 
 100 
 
 10 
 
 8 
 
 j 
 
 6 
 
 5 
 
 4 
 
 4 
 
 3 
 
 3 
 
 2 
 
 1 
 
 1 
 
 
 
 
 
 00 
 
 000 
 
 000 
 
 0000 
 
 0000 
 
 120 
 
 9 
 
 7 
 
 6 
 
 5 
 
 4 
 
 4 
 
 31 3 
 
 2 
 
 1 
 
 1 
 
 
 
 
 
 00 
 
 000 
 
 000 
 
 0000 
 
 0000 
 
 
414 
 
 SYMBOLS FOR WIRING PLANS 
 
 STANDARD SYMBOLS FOR WIRING PLANS 
 IU1101UI OKTUCAl COXTtACTORS ASSOCIATION OF THE IWITED STATEs"a* THE AMERICAN INSTITUTE OF ARCHITECTS, 
 
 {4} Ceilint Outlet; Electric only. Humeral in center indicates numoer of Standard 16 C. P. Incandescent Lasps. 
 
 3J Ceiling Outlet; Combination. } indicate! 4-16 C. P. Standard Incandeicent Lampi and 2 Oai Buraen. If gai i 
 
 -@ Bracket Outlet; Electric only. Humeral in center indicate! number of Sta ndard 16 C. P. Incandeicent Lam; 
 
 ?HXJ f Bracket Outlet; Combination, j indicate! 4-16 C. P. Standard Incandeicent Lamp, and 2 Oai Burnen. If ga: 
 
 ^-{5 Wall or Baseboard Beceptacle Outlet. Humeral in center indicates number of Standard 16 C. P. Incandeicen 
 
 ^ Floor Outlet. Humeral in center indicates number of Standard 16 C. P Incandeicent Lamps. 
 
 JJ 6 Outlet for Outdoor Standard or Pedestal; Electric only. Humeral indicates number of Stand 16 C P. Lamps 
 
 0| Outlet for Outdoor Standard or Pedestal; Combination, f indicates 6-16 C. P. Stand. Incan. Lamp: 6 Oai B 
 
 J{ Drop Cord Outlet 
 
 One Light Outlet, for Lamp Eeccptaele. 
 
 3 Arc Lamp Outlet 
 
 Q Special Outlet, for Lighting, Heating and Power Current, as described in Specification!. 
 
 CQo CeUil * Fan " Uet - 
 
 Show ai many Symbols as there are Switches. Or in case of a very large group 
 of Switches, indicate number of Switchei by a Roman numeral, thai: S> XII. 
 meaning 12 Single Pole Switchei. 
 
 Describe Type of Switch in Specification!, that is, 
 
 Flush or Surface, Push Button or Snap, 
 
 8. P. Switch Outlet. 
 D. P. Switch Outlet. 
 8-Wey Switch Outlet. 
 4- Way Switch Outlet 
 automatic Door Switch Outlet 
 Electrolier Switch Outlet 
 
 a 
 
 Diitribution Panel 
 
 Junction or Pull Box. 
 
 Motor Outlet; Numeral in center Indicate! Rone Power. 
 
 Motor Control Outlet 
 
 Main or Feeder ran concealed under Floor. 
 
 Feeder ran concealed under Floor above. 
 
 Branch Circuit run concealed under Floor. 
 
 Branch Circuit ran concealed under Floor then. 
 
 - 
 
 4 
 
 HD 
 
 fJJ 
 
 Telephone Outlet; Public Sen-ice. 
 
 Bell Outlet 
 
 Butter Outlet. 
 
 Push Button Outlet ; Humeral indicates number of Pushes, 
 
 Annunciator; Humeral indicates aaaate rf Pointa. 
 
 Speaking Tube. 
 
 Watchman Clock Outlet. 
 
 Watchman Station Outlet. 
 
 Matter Time Clock Outlet. 
 
 Secondary Time Clock Outlet 
 
 Door Opener. 
 
 Special Outlet ; Tor Signal Systems, as described In Specttettlont. 
 
 SUCCESTIONS IN 
 
 DARD SYMBOLS FOR 
 
 PLANS 
 
 It la Important that ample- apace be 
 allowed for the initallatlon of main*, feed- 
 en, branches and distribution panels. 
 
 It li desirable that a key to the symbols 
 used accompany all plans 
 
 If mains, feeders, branches and die- 
 tribution panels are shown on the plena, 
 it la desirable that they be designated by 
 letters or numbers. 
 
 Hdf hts of Centre ol Wall Outlets (uolcai 
 otherwise specified) 
 
 LlTinj Rooms 5' 8" 
 
 Chambers ' 0" 
 
 Offices ' 0' 
 
 Corridor! 6' 3' 
 
 Height of Switchei (unless otherwise spcc- 
 
 Uied) ' 4' 0- 
 
 Copyrighted 
 
 I Circuit for Clock, Telephone, Bell or other Serrice, ran under Floor, concealed 
 (Kind of Service wanted ascertained by Symbol to which line connects. 
 ( Omit for Clock, Telephone, Bell or ether Serrlce. ran under Poor abore, concealed. 
 \ Kind of Serrioe wanted ascertained by Symbol to which line connect!. 
 
 ROTX If ether than Standard 18 C. P. Incandescent lamps an 
 Bpecdnoatloni should describe capacity of Lamp to be uted. 
 
PRACTICAL APPLIED ELECTRICITY 
 
 415 
 
 SUMMARY OF 
 
 DIRECT- AND ALTERNATING-CURRENT 
 RELATIONS 
 
 SYNOPSIS OF UNITS AND SYMBOLS IN GENERAL USE 
 
 Unit 
 
 Name 
 
 Symbols 
 
 DEFINING EQUATIONS 
 
 Direct 
 Current 
 
 Alternating 
 Current 
 
 Electromotive 
 Force 
 Current 
 Resistance 
 Power 
 Impedance 
 Reactance 
 Inductance 
 Capacity 
 Quantity 
 Admittance 
 Conductance 
 Susceptance 
 
 Volt 
 Ampere 
 Ohm 
 Watt 
 Ohm 
 Ohm 
 Henry 
 Farad 
 Coulomb 
 Mho 
 Mho 
 Mho 
 
 E, e 
 I, i 
 R. r 
 P 
 
 Z, z 
 X, x 
 
 L, 1 
 C, c 
 Q, Q 
 Y, y 
 G, g 
 B, b 
 
 IR 
 E-^-R 
 
 El 
 
 Q X -M: 
 
 IXtime 
 I-^R 
 
 IZ 
 E+Z 
 
 VZ 2 X 2 
 ElXp.f. 
 
 VR 2 -f-X 2 
 
 VZ 2 R 2 
 
 Q-^E 
 IXtime 
 
 R-=-Z 2 =VY 2 B 2 
 
 X+Z^VY'-G 2 
 
 * Linkage=turnsXmagnetic flux. 
 
 DIRECT-CURRENT RELATIONS 
 
 Electromotive Force, represented by E or e. 
 
 Current times resistance I X R. 
 
 Watts divided by current P -f- 1. 
 Current, represented by I or i. 
 
 E.m.f. divided by resistance E -=- R. 
 
 Watts divided by e.m.f. P-=-E.. 
 Resistance, represented by R or r. 
 
 E.m.f. divided by current E -=- I. 
 
 Watts divided by square of current P -f- 12. 
 Watts, represented by P. 
 
 E.m.f. times current E X I. 
 
 Square of current times resistance I 2 X R. 
 
 Square of e.m.f. divided by resistance ES R. 
 Resistances in Series. 
 
 The total resistance of a number of resistances in series is 
 equal to the sum of all of them. R = R x + R., + R 3 +. . . 
 
416 PRACTICAL APPLIED ELECTRICITY 
 
 Resistances in Parallel. 
 The joint resistance of two resistances in parallel is equal 
 
 to their product divided by their sum. R = (Ri X R?) 
 
 (Ri + Ro). 
 The joint resistance of a number of resistances connected 
 
 in parallel is the reciprocal of the sum of the reciprocals. 
 
 R! R 2 R 3 ' ' ' ' 
 
 If conductance is used in place of resistance, the joint 
 resistance is the reciprocal of the sum of the conduct- 
 ances. 
 
 
 G, + G, + 
 
 ALTERNATING-CURRENT RELATIONS 
 
 Impressed e.m.f., represented by E. 
 
 Current times impedance I X Z. 
 
 Current divided by admittance I -r- Y. 
 
 Inductive e.m.f. divided by sine of lag or lead angle (re- 
 active factor) E! -r- r.f. 
 
 Effective e.m.f. divided by cosine of lag or lead angle 
 (power factor) E r -*- p.f. 
 
 The square root of the sum of the squares of the resultant 
 reactive e.m.f. and the effective e.m.f. 
 
 E = VEr2 -f- (Ei EC) 2. 
 
 Inductive e.m.f., represented by Ej. 
 
 6.28 times frequency times inductance reactance = 27rfLI. 
 Current times inductance reactance. 
 Impressed e.m.f. times sine of lag angle (reactive factor) 
 
 if there is no capacity E X r.f. 
 
 The square root of the square of impressed, minus the 
 square of effective e.m.f. if the current lags and there is 
 no capacity. ______ 
 
 Ei = VE2 E r 2. 
 
 Condensive e.m.f., represented by E c . 
 Current times one divided by 6.28 times the frequency 
 
 times the capacity I X (1 H- 2irfC). 
 Current times capacity reactance I X X... 
 Impressed e.m.f. times sine of lead angle (reactive factor) 
 
 if there is no inductance E X r.f. 
 The square root of the square of the impressed minus the 
 
 square of the effective e.m.f. if the current leads and 
 
 there is no inductance. 
 
PRACTICAL APPLIED ELECTRICITY 417 
 
 Effective e.m.f., represented by E r . 
 
 Current times resistance I X R. 
 
 Current divided by conductance I -=- G. 
 
 True watts divided by current P -j- I. 
 
 Impressed e.m.f. times cosine of lag or lead angle (power 
 factor) E X p.f. 
 
 The square root of the. square of the impressed e.m.f. 
 
 minus the square of the reactive e.m.f. 
 Current, represented by I or i. 
 
 Effective e.m.f. divided by resistance E -*- R. 
 
 Effective e.m.f. multiplied by conductance E X G. 
 
 Impressed e.m.f. divided by impedance E -=- Z. 
 
 Impresed e.m.f. multiplied by admittance E X Y. 
 
 True watts divided by impressed e.m.f. times power factor 
 (cosine angle of lag or lead) P -4- (E X p.f.). 
 
 Reactive e.m.f. divided by reactance. 
 
 The square root of true watts divided by resistance 
 
 1= VP-i-R. 
 
 Impedance, represented by Z or z. 
 Impressed e.m.f. divided by current E -*- Z. 
 Resistance divided by power factor (cosine of lag or lead 
 
 angle) R -=- p.f. 
 Reactance divided by reactive factor (sine of lag or lead 
 
 angle) X -r- r.f. 
 The square root of the sum of the squares of resistance 
 
 and reactance VR 2 + X^. 
 Resistance, represented by R or r. 
 Impedance times power factor (cosine of lag or lead angle) 
 
 Z X p.f. 
 
 The square of effective e.m.f. divided by true watts E,,2 -=- p. 
 Effective e.m.f. divided by current Er -*- I. 
 True watts divided by square of current P -=- 12. 
 The square root of impedance squared minus square of 
 
 reactance VZ^ X-V 
 
 Reactance (inductive), represented by X x . 
 6.28 times inductance times frequency 2?rLf. 
 Impedance times reactive factor (sine of lag angle) Z X r.f. 
 Reactance (condensive), represented by X c . 
 1 divided by 6.28 times frequency, times capacity 
 
 6.28 f C 
 
 Impedance times reactive factor (sine of lead angle) Z X r.f. 
 
 Condensive e.m.f. divided by current. 
 Admittance, represented by Y or y. 
 
 One divided by impedance 1 -f- Z. 
 
 Current divided by e.m.f. I -f- E. 
 
418 PRACTICAL APPLIED ELECTRICITY 
 
 The square root of the sum of the squares of conductance 
 
 and susceptance, Y = VG 2 + B2. 
 Susceptance, represented by B or b. 
 Admittance times sine of lag or lead angle (reactive factor) 
 
 Y X r.f. 
 
 Sine of lag or lead angle divided by impedance, r.f. -r- Z. 
 The square root of the square of admittance minus the 
 
 square of conductance, B = VY2 G2. 
 One divided by reactance if there is no resistance 1 H- X. 
 Conductance, represented by G or g. 
 Admittance times cosine of lag or lead angle (power factor) 
 
 Y X p.f. 
 
 Cosine of lag or lead angle divided by impedance p.f. -=- Z. 
 The square root of the square of admittance minus the 
 
 square of susceptance, G = VY^ B2. 
 One divided by resistance (for direct current) 1 -r- R. 
 Power (true watts), represented by P. 
 Effective e.m.f. times current E r X I. 
 Impressed e.m.f. times current times power factor E X 
 
 I X p.f. 
 
 Square of current times resistance 12 x R. 
 Square of current divided by conductance (no reactance) 
 
 12 --G. 
 Impedance times current squared times power factor 
 
 Z X I 2 X p.f. 
 
 Apparent Watts, represented by P. 
 Impressed e.m.f. times current E X I. 
 Square of current times impedance 12 X Z. 
 Square of current divided by admittance 12 -5- Y. 
 Power Factor. 
 
 True watts divided by apparent watts P -=- (E X I). 
 Resistance divided by impedance R -f- Z. 
 Effective e.m.f. divided by impressed e.m.f. E r -f- E. 
 Reactance Factor. 
 
 Reactance divided by the resistance X H- R. 
 Reactive Factor. 
 Wattles volt-amperes divided by the total volt-amperes 
 
 XXl-^-ZXl = X^-Z = sine of the angle of lag or lead. 
 
INDEX 
 
 A 
 
 PAGE 
 
 Admittance of a circuit 349 
 
 Alternating-current circuit 332 
 
 addition and subtraction of vectors 338 
 
 alternation 333 
 
 chemical and heating effects of 334 
 
 cycle 333 
 
 definition of alternating current 332 
 
 determining value of power factor 354 
 
 electromotive force required to overcome resistance 339 
 electromotive force required to overcome resistance, 
 
 inductance, and capacity 344 
 
 factors determining value of a. c 338 
 
 frequency 333 
 
 hydraulic analogy of alternating current 332 
 
 hydraulic analogy of capacity 342 
 
 hydraulic analogy of inductance 339 
 
 impedance of a circuit 347 
 
 impedance diagram 348 
 
 impedances in parallel 349 
 
 impedances in series 348 
 
 instantaneous power in 353 
 
 maximum, average and effective values of e.m.f.... 336 
 
 period 333 
 
 phase 333 
 
 phase relation of current and potential drops in a 
 
 divided circuit 352 
 
 phase relation of current and potential drops in a 
 
 series circuit 351 
 
 phase relation of e.m.f. to overcome inductance, etc. 341 
 
 problems on 356 
 
 reactance of a circuit. . 347 
 
INDEX 
 
 Alternating-current circuit continued PAGE 
 
 sine wave e.m.f 335 
 
 synchronism 333 
 
 total e.m.f. required to produce a given alternating 
 
 current 346 
 
 vector representation of alternating e.m.f.'s and 
 
 currents 338 
 
 wattmeter indicates true power in 355 
 
 Alternating current machinery 358 
 
 alternators 358 
 
 connecting receiving circuits to a three-phase system 364 
 
 induction generator 384 
 
 induction motor 379 
 
 measurement of power in single-phase system 365 
 
 measurement of power in three-phase system 367 
 
 measurement of power in two-phase system 365 
 
 relation of e.m.f. and current in "Y" and "A" con- 
 nected armatures 362 
 
 rotating magnetic field 378 
 
 synchronizing 371 
 
 synchronous converter 385 
 
 synchronous motor 368 
 
 transformer 372 
 
 Alternation, definition of 333 
 
 Alternators 358 
 
 inductor' 358 
 
 single-phase 360 
 
 with stationary armatures 358 
 
 with stationary fields 358 
 
 three-phase 361 
 
 Amalgamation 60 
 
 Ammeter 122-132 
 
 Ammeter, calibration of 163 
 
 Ammeter shunts 124 
 
 Ampere, definition of 6-10 
 
 Ampere-hour meters 159 
 
 Ampere-turns, definition of 94 
 
 Angle of lag, definition of 182 
 
 Angle of lead, definition of 182 
 
 Armature coil 227 
 
 Armature inductor 226 
 
INDEX 
 
 PAGE 
 
 Armature reaction 180 
 
 Armature reaction, means of reducing 183 
 
 Armatures 219 
 
 armature core 219 
 
 armature-core stampings 220 
 
 ventilation 221 
 
 armature windings 224 
 
 armature coil 227 
 
 armature inductor 226 
 
 drum windings 230 
 
 element of 227 
 
 equipotential connections 235 
 
 front and back pitch, choice of 234 
 
 multiplex windings 232 
 
 number of commutator segments 227 
 
 number of paths through 233 
 
 pitch of winding and field step 228 
 
 re-entrancy 232 
 
 ring windings 229 
 
 table 335 
 
 brushes and brush holders 223 
 
 commutator 222 
 
 commutator risers 222 
 
 construction of 223 
 
 Anode, definition of 126 
 
 Artificial magnets 77 
 
 Automobile motors 212 
 
 Auto-transformer 377 
 
 B 
 
 Balanced load 261 
 
 Bichromate cell 65 
 
 Bonding, definition of 129 
 
 Boosters 267 
 
 Bremer flaming-arc lamp 304 
 
 British thermal heat unit, definition of 142 
 
 Brushes and brush holders 223 
 
 Bunsen photometer 308 
 
 Bus-bars 270 
 
INDEX 
 C 
 
 PAGE 
 
 Calculation of illumination 310 
 
 Calculation of resistance of conductor 318 
 
 Calculation of size of conductor when allowable drop 
 
 and current are given 319 
 
 Calibration of instruments 161 
 
 ammeters 163 
 
 voltmeters 161 
 
 wattmeter 163 
 
 Carbon arc lamp 294 
 
 Carbon-filament lamp . . 299 
 
 Cathion, definition of 126 
 
 Cathode, definition of 126 
 
 Chemical depolarization 65 
 
 Fuller cell 66 
 
 Grenet cell 65 
 
 Leclanche cell 67 
 
 Chemicals used in cells and their symbols 65 
 
 Choice of material to use as conductor 317 
 
 Circuit breakers 273 
 
 Circular mil, definition of 28 
 
 Closed-coil windings 225 
 
 Commercial wheatstone bridge 54 
 
 Commutation of generator 185 
 
 Commutator pitch 229 
 
 Compensated wattmeter 155 
 
 Compound generators in parallel *. . 271 
 
 Compound motor 194 
 
 Compound motor, characteristics of 208 
 
 Compound-wound generator 179 
 
 Concealed "knob and tube" work 325 
 
 Condenser 145 
 
 capacity of 145 
 
 connection of in series and parallel 147 
 
 dielectric 145 
 
 problems on 149 
 
 relation of impressed voltage, quantity and con- 
 denser capacity 148 
 
 Conductance of a circuit 349 
 
 Conductance of a conductor 18 
 
INDEX 
 
 PAGE 
 
 Conductors 6 
 
 Conductors, area of circular 20 
 
 Constant-current distribution 258 
 
 Constant-voltage distribution 257 
 
 Coulomb, definition of 6-9 
 
 Counter electromotive force 199 
 
 Cumulative compound motor 195 
 
 Current, definition of 4 
 
 Current of electricity 6 
 
 Current, uniformity of in series circuit 35 
 
 Cycle, definition of 333 
 
 D 
 
 Daniell cell 64 
 
 Daniell cells, electro-chemical depolarization of 67 
 
 D'Arsonval ammeters 134 
 
 D'Arsonval galvanometer 133 
 
 D'Arsonval voltmeters 134 
 
 Dead-line release 205 
 
 Diamagnetic, definition of 82 
 
 Dielectric 145 
 
 Differential compound motor 195 
 
 Differential shunt. . . ., 298 
 
 Direct-current dynamos, diseases of . . ' 280 
 
 Direct-current generator 166 
 
 adaptability of 189 
 
 armature of a dynamo 173 
 
 armature reaction 180 
 
 back turns 182 
 
 building up of 187 
 
 capacity of 186 
 
 commercial rating of 191 
 
 commutation of 185 
 
 compound-wound 179 
 
 cross-turns 182 
 
 efficiency of 190 
 
 external characteristics of 187 
 
 losses in 189 
 
 magnetic field of a dynamo 173 
 
INDEX 
 
 Direct-current generator continued PAGE 
 
 magnetic leakage 17* 
 
 multiple-coil armatures 171 
 
 problems on 191 
 
 reducing armature reaction 183 
 
 self-excitation of 177 
 
 separate excitation of 177 
 
 series-wound 178 
 
 simple alternator. 168 
 
 simple direct-current dynamo 170 
 
 simple dynamo 166 
 
 shunt-wound 178 
 
 values of induced e.m.f. in armature winding 176 
 
 Direct-deflection method of measuring resistance 50 
 
 Direct-current motors 193 
 
 adaptability of 208 
 
 armature reaction in 196 
 
 automobile 212 
 
 characteristics of 207 
 
 combined starting and field-regulating rheostats... 206 
 
 compound 194 
 
 construction of 209 
 
 counter electromotive force 199 
 
 dead-line release 205 
 
 efficiency of 215 
 
 elevator and crane 214 
 
 Fleming's left-hand rule 193 
 
 fundamental principle of 193 
 
 interchangeability of motor and generator 193 
 
 interpole motor 203 
 
 mechanical output of 198 
 
 normal speed of 199 
 
 overload release 206 
 
 position of brushes on 197 
 
 problems on 217 
 
 railway 210 
 
 regulating speed of 200 
 
 series 194 
 
 shunt 194 
 
 speed regulation 206 
 
 starting 204 
 
INDEX 
 
 Direct-current motors continued PAGE 
 
 starting boxes 205 
 
 torque exerted on 198 
 
 Ward Leonard system of speed control 203 
 
 Diseases of direct-current dynamos 280 
 
 dynamo fails to generate 290 
 
 heating of armature 284 
 
 heating of bearings 285 
 
 heating of field coils 284 
 
 motor runs backward or against the brushes 290 
 
 motor stops 289 
 
 noise 287 
 
 sparking at brushes caused by excessive current in 
 
 armature due to overload 282 
 
 sparking at brushes due to fault of armature 283 
 
 sparking at brushes due to fault of brushes 280 
 
 sparking at brushes due to fault of commutator 
 
 or magnetic field 281 
 
 speed too high 288 
 
 speed too low 289 
 
 suggestions and precautions 292 
 
 Disk windings 224 
 
 Distribution curves : 310 
 
 Distribution and operation 257 
 
 boosters 267 
 
 circuit breakers 273 
 
 constant-current distribution 258 
 
 compound generators in parallel 271 
 
 constant-voltage distribution 257 
 
 drop in potential in the neutral wire 261 
 
 dynamotors 265 
 
 Edison three-wire system of distribution 259 
 
 ground detectors 275 
 
 instructions for starting a generator or motor 276 
 
 motor generators, or balar cers 267 
 
 operation of compound motors 273 
 
 operation of generators and motors for combined 
 
 output 269 
 
 operation of series motors in series and parallel.... 272 
 
 operation of shunt motors in series and parallel 272 
 
 rheostat 274 
 
INDEX 
 
 Distribution and operation continued PAGI) 
 
 series generators connected for combined output. ... 27( j 
 
 series-parallel system of distribution 25i 
 
 shunt generators connected for combined output 26i 
 
 starting and stopping compound generators that are 
 
 operating in parallel 27 
 
 switchboard 27 
 
 switches 27J 
 
 three-wire generators 26; 
 
 Drop in potential in the neutral wire 261 
 
 Drum windings 224 
 
 lap 23( 
 
 progressive 231 
 
 retrogressive 231 
 
 wave 231 
 
 Dry cells 6 
 
 Dynamic brake 21E 
 
 Dynamotor as an equalizer 26 
 
 Dynamotors 26!; 
 
 E 
 
 Eddy currents Ill 
 
 Eddy-current loss 11 
 
 Edison chemical meter 15J 
 
 Edison storage battery 241 
 
 care of 25( 
 
 chemistry of 24J 
 
 Edison three-wire system of distribution 25i 
 
 Effect different colored walls have upon general illumi- 
 nation 3: 
 
 Electric heaters 32< 
 
 Electric generators and motors 33( 
 
 Electric lamp 29' 
 
 Electric lighting 29- 
 
 Bremer flaming-arc lamp 30^ 
 
 Bunsen photometer 30* 
 
 calculation of illumination 31( 
 
 carbon arc lamp 29^ 
 
 carbon-filament lamp 291 
 
 distribution curves . 31( 
 
INDEX 
 
 ilectric lighting continued PAGE 
 effect different colored walls have upon general illu- 
 mination 315 
 
 electric lamp 294 
 
 flaming arc 304 
 
 glow lamp - 299 
 
 heftier lamp 307 
 
 mercury vapor lamp 304 
 
 metalized carbon-filament or gem lamp 300 
 
 Moore tube 300 
 
 multiple arc lamps 296 
 
 Nernst lamp 303 
 
 photometry 307 
 
 regulation of arc lamps on constant-voltage and con- 
 stant-current circuit 295 
 
 series arc lamps 297 
 
 shades, reflectors, and diffusers 314 
 
 specific consumption of lamps 309 
 
 tantalum lamp 300 
 
 tungsten lamp 301 
 
 units of illumination 307 
 
 vapor lamp 303 
 
 Electric wiring 316 
 
 calculation of resistance of conductor 318 
 
 calculation of size of conductor when allowable drop 
 
 and current are given 319 
 
 choice of material to use as conductor 317 
 
 concealed "knob and tube" work 325 
 
 electric generators and motors 330 
 
 electric heaters 329 
 
 electrical inspection 330 
 
 factors determining size of conductors 316 
 
 installing arc lamps and fixtures 329 
 
 interior conduit and armored cable work 326 
 
 location of outlets, switches, and distributing board. 328 
 
 methods of wiring and rules governing s?me 322 
 
 motor wiring formula 321 
 
 moulding work 324 
 
 open, or exposed, work 323 
 
 service wires 327 
 
 wiring in general 316 
 
INDEX 
 
 PAGE 
 
 Electrical circuit 1 
 
 compared with hydraulic circuit 5 
 
 conductors 6 
 
 coulomb, ampere, ohm, and volt 9 
 
 current of electricity 6 
 
 derived units 15 
 
 electrical force 11 
 
 electrical power 13 
 
 electrical quantities , 6 
 
 electrical work or energy 12 
 
 electromotive force 7 
 
 fundamental units 15 
 
 hydraulic analogy of 2 
 
 insulators 7 
 
 Joule, unit of electrical work 12 
 
 kilowatt 14 
 
 kilowatt-hour 15 
 
 mechanical horse-power 14 
 
 * Ohm's Law 8 
 
 resistance 6 
 
 watt-hour 15 
 
 Electrical force, definition of 11 
 
 Electrical inspection 330 
 
 Electrical instruments 121 
 
 ammeter 122 
 
 ammeter shunts 124 
 
 calibration of instruments 161 
 
 galvanometer 122 
 
 measurement of power 151 
 
 operation depending on electro-chemical effect 125 
 
 electrolysis 125 
 
 electroplating 127 
 
 electrotyping 128 
 
 polarity indicator 128 
 
 weight voltameter 129 
 
 operation depending on electrostatic effect 145 
 
 electrostatic voltmeter 150 
 
 condenser 145 
 
 operation depending on heating effect 141 
 
 hot-wire instruments . 143 
 
INDEX 
 
 Electrical instruments continued PAGE 
 
 operation depending on magnetic effect 132 
 
 electro-dynamometer 139 
 
 magnetic vane ammeter or voltmeter 138 
 
 plunger type ammeter or voltmeter 137 
 
 tangent galvanometer 132 
 
 Thomsen inclined-coil instruments 138 
 
 voltmeter 122 
 
 Electrical power, unit of 13 
 
 Electrical quantities 6 
 
 Electrical units .' 12-16 
 
 derived units 15 
 
 fundamental units 15 
 
 horse-power 14 
 
 Joule 12 
 
 kilowatt 14 
 
 kilowatt-hour 15 
 
 systems of units 16 
 
 watt 13 
 
 watt-hour 15 
 
 Electrical work or energy 12 
 
 Electricity, definition of 1 
 
 Electro-chemical depolarization 67 
 
 Electrodynamometer 139 
 
 Electrodes, definition of 125 
 
 Electrolysis 125-127 
 
 of copper sulphate 127 
 
 definition of 125 
 
 Electrolyte 241 
 
 Electrolytic action, prevention of 128 
 
 Electrolytic cell, definition of 125 
 
 Electromagnet 98 
 
 Electromagnetic induction 102 
 
 currents induced in coil. .- 105 
 
 .currents induced in conductor 102 
 
 eddy currents 117 
 
 induced pressures, rules for 116 
 
 inductance 114 
 
 Lentz's law 115 
 
 magnitude of induced e.m.f 106 
 
 mutual induction 113 
 
INDEX 
 
 Electromagnetic induction continued PAGE 
 
 non-inductive circuit 119 
 
 primary coils 109 
 
 secondary coil 109 
 
 self-induction 113 
 
 Electromagnetism 86 
 
 direction of an electromagnetic field 86 
 
 electromagnet 98 
 
 law of traction 101 
 
 magnetic field around conductor carrying current... 86 
 
 magnetomotive force 93 
 
 permeability 92 
 
 problems on 97 
 
 reluctance 95 
 
 rules for determining direction of field 88 
 
 solenoid 89 
 
 strength of magnetic field 89 
 
 toroid 92 
 
 Electromotive force 7 
 
 Electromotive force in a circuit, effective 38 
 
 Electromotive force of a cell, factors determining 62 
 
 Electromotive force and potential difference 7 
 
 Electroplating 127 
 
 Electrostatic voltmeter 150 
 
 Electrotyping 128 
 
 Elevator and crane motors 214 
 
 Equalizer 271 
 
 Evershed ohmmeter, principle of 56 
 
 F 
 
 Factors determining size of conductors 316 
 
 Feeder valve 306 
 
 Field rheostat 178 
 
 Flaming arc ; 304 
 
 Flashing 300 
 
 Fleming's motor rule 193 
 
 Foot-candle 307 
 
 Frequency, definition of 333 
 
 frequency changer 384 
 
 Friction brake 214 
 
 Fuller cell . 64 
 
INDEX 
 G 
 
 PAGE 
 
 Galvanometer 122 
 
 Gauss, definition of 94 
 
 Generator panels and feeder panels 273 
 
 Gilbert, definition of 94 
 
 Glow lamp 299 
 
 Grenet cell 63-65 
 
 Ground detectors 275 
 
 H 
 
 Heating effect of a current, commercial applications of. . 142 
 
 Hefner lamp 307 
 
 Hefner unit 307 
 
 Henry, unit of inductance 115 
 
 Horse-power 14 
 
 electrical 14 
 
 mechanical 14 
 
 Horseshoe magnet 85 
 
 Hot-wire instruments 143 
 
 Hydraulic analogy of electrical circuit 2 
 
 Hydraulic circuit compared with electrical : 5 
 
 Hydrometer 242 
 
 Hysteresis 98 
 
 definition of 83 
 
 loss 99 
 
 I 
 
 Induced electromotive force ,V 102 
 
 direction of 107 
 
 magnitude of ' 106 
 
 rules for determining 109 
 
 in secondary coil 109 
 
 Induced pressures, rules for 116 
 
 Inductor alternators 358 
 
 Inductance 114 
 
 Induction generator 384 
 
 Induction motor 379 
 
 methods of starting 382 
 
INDEX 
 
 Indication motor continued PAGE 
 
 operation of 381 
 
 rotor 380 
 
 speed regulation of 381 
 
 "squirrel-cage" type 380 
 
 stator 380 
 
 Installing arc lamps and fixtures 329 
 
 Instructions for starting a generator or motor 276 
 
 Insulators 7 
 
 Integrating wattmeters 159 
 
 Interior conduit and armored cable work 326 
 
 Internal resistance 62 
 
 International ohm, definition of 10 
 
 Interpole motor 203 
 
 Ions, definition of , 126 
 
 J 
 
 Joule, unit of electrical work and energy 12 
 
 K 
 
 Kicking box 325 
 
 Kilovolt, definition of 10 
 
 L 
 
 Lalande cell 64 
 
 Lead storage cells 237 
 
 action of, while charging 238 
 
 action of, while discharging 238 
 
 Leakage coefficient 176 
 
 Leclanche cell 63 
 
 Lentz's law 115 
 
 Location of outlets, switches, 'and distributing board. . . . 328 
 
 Logarithms 390 
 
 characteristic, definition of 391 
 
 common system of 390 
 
 definition of 390 
 
 to find a number whose log is given 391 
 
 how to obtain log of a number from table 391 
 
 laws of indices 390 
 
 mantissa, definition of 391 
 
INDEX 
 M 
 
 PAGE 
 
 Magnet '. 77 
 
 artificial 77 
 
 permanent 84 
 
 poles of 78 
 
 currents induced in a conductor by 102 
 
 Magnetic attraction 78 
 
 Magnetic circuit, materials used in construction of 175 
 
 Magnetic field of a dynamo 173 
 
 air gap 174 
 
 armature core 174 
 
 field cores 173 
 
 pole face 174 
 
 pole pieces 174 
 
 yoke 173 
 
 Magnetic field of force 80 
 
 distortion of 81 
 
 making of 81 
 
 Magnetic field, strength of 89 
 
 Magnetic force 79 
 
 Magnetic flux 94 
 
 Magnetic induction , 82 
 
 Magnetic leakage 176 
 
 Magnetic lines of force 80 
 
 Magnetic meridian 78 
 
 Magnetic needle 78 
 
 Magnetic repulsion 78 
 
 Magnetism 77 
 
 magnet 77 
 
 magnetic attraction 78 
 
 magnetic field 80 
 
 magnetic force . 79 
 
 magnetic lines of force 80 
 
 magnetic induction 82 
 
 magnetic needle 78 
 
 magnetic repulsion 78 
 
 magnetizable metals 79 
 
 molecular theory of 83 
 
 retention of magnetization 82 
 
 Magnetizable metals 79 
 
INDEX 
 
 PAGE 
 
 Magnetization curve 187 
 
 Magnetization, retention of 82 
 
 Magnetomotive force 93 
 
 Maximum demand meters. 160 
 
 Maxwell, definition of. 94 
 
 Mean horizontal candle-power 307 
 
 Mechanical depolarization 65 
 
 Megohm, definition of 10 
 
 Mercury vapor lamp 304 
 
 Metalized carbon-filament or gem lamp 300 
 
 Methods of wiring and rules governing same 322 
 
 Microhm, definition of 10 
 
 Mil-foot resistance 29 
 
 Millivolt, definition of 10 
 
 Molecular theory of magnetism 83 
 
 Moore tuhe 306 
 
 Motor-generators, or balancers 267 
 
 Motor wiring formula 321 
 
 Moulding work 324 
 
 Multiple arc lamps 296 
 
 Multipliers 136 
 
 Multiplex windings 232 
 
 Mutual induction 113 
 
 N 
 
 Negative booster 268 
 
 Negative grid 238 
 
 Nernst lamp 303 
 
 Neutral wire 260 
 
 No-load current 373 
 
 Non-lead storage cells 246 
 
 Non-inductive circuit 119 
 
 O 
 
 Ohmmeter 56 
 
 Ohm's law 8 
 
 problems on 10 
 
 Open-coil windings 226 
 
 Open, or exposed, work 323 
 
INDEX 
 
 PAGE 
 
 Operation of compound motors 273 
 
 Operation of generators and motors for combined output. 269 
 
 Operation of series motors in series and parallel 272 
 
 Operation of shunt motors in series and parallel 272 
 
 Overload release 206 
 
 Oversulphation 243 
 
 P 
 
 Panels 273 
 
 Paramagnetic, definition of 82 
 
 Period of an e.m.f., definition of 333 
 
 Permanent magnets, application of 84 
 
 Permeability 92 
 
 Phase, definition of 333 
 
 Photometer 307 
 
 Photometer bench 309 
 
 Photometry 307 
 
 Polarity, definition of 78 
 
 Polarity indicator 128 
 
 Polarity of solenoids 91 
 
 Polarization 60 
 
 chemical means of prevention 61 
 
 electro-chemical means of prevention 62 
 
 mechanical means of prevention 61 
 
 Poles of a magnet 78 
 
 Portable storage batteries 251 
 
 Positive grid 238 
 
 Potential difference, relation of, to resistance 36 
 
 Power, measurement of 151 
 
 Power and energy calculations, problems on 16 
 
 Power factor 354 
 
 Pressure, definition of 
 
 Primary batteries 58 
 
 amalgamation 60 
 
 cell requirements 70 
 
 chemical action in battery 59 
 
 chemical depolarization 65 
 
 chemicals used in cells 65 
 
 closed-circuit cell 63 
 
INDEX 
 
 Primary batteries continued PAGE 
 
 double-fluid cell 64 
 
 dry cells 68 
 
 electro-chemical depolarization 67 
 
 electromotive force of a cell 62 
 
 grouping of cells, problems on 74 
 
 internal resistance 62 
 
 local action in battery 60 
 
 mechanical depolarization 65 
 
 open-circuit cell 63 
 
 parallel connection of cells 72 
 
 polarization 60 
 
 primary cell 63 
 
 secondary cell 63 
 
 series connections of cells 70 
 
 series and parallel combinations of cells 73 
 
 single-fluid cell 64 
 
 standard cells 69 
 
 voltaic cells 58 
 
 Primary cells, forms of 64 
 
 Prony brake 216 
 
 R 
 
 Railway motors and their control 210 
 
 Reactance coil 296 
 
 Re-entrant windings 232 
 
 Regulation of arc lamps on constant-voltage and con- 
 stant-current circuit 295 
 
 Relative conductivity of a material 30 
 
 Relative resistance of a material 30 
 
 Reluctance of magnetic circuit 95 
 
 Resistance, calculation of 18 
 
 area of circular conductors 20 
 
 changes with temperature 21 
 
 from dimensions and specific resistance 31 
 
 due to change in temperature 24 
 
 meaning of (K) 28 
 
 mil-foot resistance 29 
 
 relation to physical dimensions 27 
 
 relation between square and circular-mil measure. .. 30 
 
INDEX 
 
 Resistance, calculation of continued PAGE 
 
 relative conductivity 30 
 
 relative resistance 30 
 
 specific resistance 28 
 
 temperature coefficient 21 
 
 varies inversely as cross-section of conductor 19 
 
 varies directly as the length of conductor 18 
 
 Resistance, definition of 4 
 
 Resistance, measurement of 44 
 
 commercial Wheatstone bridge 54 
 
 by comparison 47 
 
 direct-deflection method 50 
 
 drop in potential method 44 
 
 ohmmeter 56 
 
 series voltmeter method 48 
 
 slide-wire Wheatstone bridge 52 
 
 Resuscitation from apparent death from electric shock.. 386 
 
 Reverse-current 274 
 
 Rheostats 205, 274 
 
 Right-hand screw rule 88 
 
 Ring windings 224 
 
 series-connected' wave-wound 230 
 
 spirally-wound 229 
 
 S 
 
 Screen 308 
 
 Self-excitation of generator 177 
 
 Self-induction 113 
 
 Separate excitation of generator 177 
 
 Series arc lamps 297 
 
 Series and divided circuits 34 
 
 effective e.m.f. in a circuit 38 
 
 parallel or multiple grouping 39 
 
 problems on 43 
 
 relation of p.d. to resistance 36 
 
 resistance* of 37 
 
 series grouping , 34 
 
 series and parallel combinations 42 
 
 uniformity of current 35 
 
 Series generators connected for combined output 270 
 
INDEX 
 
 PAGE 
 
 Series motor 194 
 
 characteristics of 207 
 
 Series-parallel system of distribution 259 
 
 Series voltmeter method of measuring resistance 48 
 
 Series-wound generator 178 
 
 Service wires 327 
 
 Shades, reflectors, and diff users 314 
 
 Shunt generators connected for combined output 269 
 
 Shunt motor 194 
 
 characteristics of 207 
 
 Shunt-wound generator 178 
 
 Single-phase alternator 360 
 
 Slide-wire Wheatstone bridge, principle of 52 
 
 Solenoid 89 
 
 permeability 92 
 
 polarity of 91 
 
 toroid 92 
 
 Specific consumption of lamps 309 
 
 Specific inductive capacity 145 
 
 Speed regulation of a motor 206 
 
 Specific resistance 28 
 
 Square and circular-mil measure, relation between 30 
 
 Standard cells 69 
 
 Starting and stopping compound generators that are op- 
 erating in parallel 278 
 
 Storage batteries 237 
 
 to aid generators in carrying maximum load 253 
 
 capacity of 241 
 
 commercial application of 250 
 
 containing vessel and separators 242 
 
 Edison 247 
 
 in electrical laboratories 251 
 
 electrolyte 241 
 
 hydrometer 242 
 
 lead cell 237 
 
 management of 245 
 
 non-lead cell 246 
 
 portable 251 
 
 to put out of service 246 
 
 sulphation 243 
 
INDEX 
 
 Storage batteries continued PAGE 
 
 to supply energy during certain hours 253 
 
 to supply energy for electrically driven vehicles 
 
 and boats 255 
 
 storage battery grids 239 
 
 storage cell 237 
 
 in telephone and telegraph work 252 
 
 for train lighting 252 
 
 troubles and their remedies 244 
 
 buckling of plates 245 
 
 corrosion of plates 245 
 
 loss of capacity 244 
 
 loss of voltage 245 
 
 shedding of active material 245 
 
 used in changing voltage 254 
 
 used in subdividing voltage of a generator 255 
 
 Storage battery grids 239 
 
 comparison of Plante and Faure 240 
 
 example of 239 
 
 Faure process 239 
 
 Plante process 239 
 
 Sulphation 243 
 
 Susceptance of a circuit 349 
 
 Switchboard 273 
 
 Switches 275 
 
 Synchronism, definition of 333 
 
 Synchronizing 371 
 
 Synchronoscope 372 
 
 Synchronous converter 385 
 
 Synchronous motor 368 
 
 operation of 370 
 
 starting 370 
 
 synchronizing 371 
 
 T 
 
 Table 
 
 approximate specific consumption of different type 
 
 lamps 310 
 
 capacity of storage battery, percentage variation of. 241 
 centigrade and Fahrenheit thermometer scales, com- 
 
INDEX 
 
 Table continued PAGE 
 
 parison of 400 
 
 constants to be used in calculating illumination on 
 
 horizontal plane below lamp 312 
 
 copper wire table of American Institute of Electrical 
 
 Engineers 402-405 
 
 electro-chemical equivalents 130 
 
 factors for obtaining effective illumination 315 
 
 hysteretic constant, value of, for different materials. 100 
 
 lap-wound drum armature windings 410 
 
 logarithms of numbers 394, 395 
 
 mensuration equations 396 
 
 metric and English measures, relation of 399 
 
 primary cells / 64 
 
 required illumination for various classes of service. 313 
 
 ring armature windings 408 
 
 specific inductive capacities '. 146 
 
 specific resistance data 29 
 
 symbols for electrical apparatus 398 
 
 symbols for wiring plans 414 
 
 temperature coefficients 22 
 
 temperature coefficient of copper 23 
 
 trigonometrical functions 397 
 
 units in English and metric systems, relation of 16 
 
 v/ave- wound drum armature windings 409 
 
 wire, carrying capacity of 406 
 
 wires, equivalent cross-section of different size 400 
 
 wire gauzes 401 
 
 wiring table for 2 per cent loss on a 50-volt circuit. . 411 
 
 wiring table for 2 per cent loss on a 110-volt circuit. 412 
 
 wiring table for 2 per cent loss on a 220-volt circuit. 413 
 
 wire which will fuse with given current, diameter of. 407 
 
 Tangent galvanometer 132 
 
 Tantalum lamp 300 
 
 Temperature coefficient, definition of 21 
 
 Thomson watt-hour meter 158 
 
 Three-phase alternator 361 
 
 Three-wire generators 263 
 
 Toroid 92 
 
 Traction, law of 101 
 
 Transformer 372 
 
INDEX 
 
 Transformer continued PAGE 
 
 action of, on load 373 
 
 action of, without load 372 
 
 actual e.m.f. and current relations in 374 
 
 auto-transformer 377 
 
 constant-current 377 
 
 constant-potential 377 
 
 core type 376 
 
 current 377 
 
 ideal e.m.f. and current relations in 373 
 
 methods of cooling 377 
 
 polyphase 376 
 
 shell type 376 
 
 single-phase 376 
 
 vector diagram of 375 
 
 Transposition, definition of 113 
 
 Tungsten lamp 301 
 
 U 
 
 Unbalanced load 261 
 
 Under-load , 274 
 
 Units of illumination 307 
 
 V 
 
 Vapor lamp 303 
 
 Voltaic battery 59 
 
 amalgamation 60 
 
 chemical action in 59 
 
 local action , 60 
 
 polarization 60 
 
 Voltaic cell 58 
 
 Volt, definition of 10 
 
 Voltameter 
 
 adaptability of 131 
 
 definition of 126 
 
 Voltmeter 122 
 
 calibration of . 161 
 
INDEX 
 W 
 
 PAGE 
 
 Watt-hour meters 156 
 
 Wattmeter 153 
 
 adaptability of .* 156 
 
 calibration of 163 
 
 compensated 155 
 
 principle of 153 
 
 Weston 155 
 
 Whitney 154 
 
 Weight voltameter 129 
 
 Weston portable voltmeter 137 
 
 Weston wattmeter 155 
 
 Wheatstone bridge 
 
 commercial 54 
 
 slide-wire 52 
 
 Whitney wattmeter 1 54 
 
 Wire gauges 32 
 
 Wiring in general 316 
 
 Wright demand meter 160 
 
 Zero load 372 
 
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