IRLF 
 
 77 
 

 LIBRARY 
 
 UNIVERSITY OF CALIFORNIA. 
 Deceived ... 
 
ELECTRICAL 
 
 ENGINEERING LEAFLETS 
 
 BY 
 
 PROFESSOR E. J. HOUSTON, PH. D. 
 
 AND 
 
 PROFESSOR A. E. KENNELLY, F.R.A.S. 
 
 ADVANCED GRADE 
 
 UNIVERSITY 
 
 1895 
 
 THE ELECTRICAL ENGINEER 
 NEW YORK 
 
H ' 
 
 Engineering 
 Library 
 
^9$, 
 
 'UBI7BR3I.TT: 
 
 'T'HE Electrical Engineering Leaflets have been pre- 
 pared for the purpose of presenting, concisely 
 but accurately, some of the fundamental principles of 
 electrical science, as employed in engineering practice. 
 They have been arranged under three grades ; namely, 
 the Elementary, the Intermediate, and the Advanced. 
 
 The Elementary Grade is intended for those electrical 
 artisans, linemen, motormen, central station workmen, or 
 electrical mechanics generally, who may not have advanced 
 sufficiently far in their studies to warrant their undertak- 
 ing the other grades. Here the mathematical treatment 
 is limited to arithmetic, and the principles are illustrated 
 by examples taken from actual practice. 
 
 The Intermediate Grade is intended for students of 
 electricity in high schools and colleges. In this grade a 
 certain knowledge of the subjects of electricity and physics 
 generally is assumed, and a fuller mathematical treat- 
 ment is adopted. These leaflets, moreover, contain such 
 information concerning the science of electricity, as should 
 be acquired by those desiring general mental culture. 
 
 The Advanced Grade is designed for students taking 
 special courses in electrical engineering in colleges or 
 universities. Here the treatment is more condensed and 
 mathematical than in the other grades. 
 
 Although the three grades have been especially pre- 
 
iv 
 
 pared for the particular classes of students referred to, 
 yet it is believed that they will all prove of value to the 
 general reading public, as offering a ready means for ac- 
 quiring that knowledge, which the present extended use 
 and rapidly increasing commercial employment of elec- 
 tricity necessitates. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia, March, 1895. 
 
CONTENTS. 
 
 ADVANCED GRADE. 
 
 PAGE. 
 
 No. 1. ELECTRICAL EFFECTS 1 
 
 " 2. ELECTROMOTIVE FORCE 9 
 
 " 3. ELECTRIC RESISTANCE 17 
 
 " 4. ELECTRIC RESISTANCE 25 
 
 " 5. ELECTRIC RESISTANCE 33 
 
 " 6. ELECTRIC CURRENT 41 
 
 " 7. OHM'S LAW 49 
 
 " 8. ELECTRIC CIRCUITS 57 
 
 " 9. THE VOLTAIC CELL 65 
 
 " 10. THE VOLTAIC CELL 73 
 
 " 11. THE VOLTAIC CELL 81 
 
 " 12. MAGNETOMOTIVE FORCE 89 
 
 " 13. MAGNETIC RELUCTANCE. ... 97 
 
 " 14. MAGNETIC FLUX 105 
 
 " 15. ELECTROMAGNETS 113 
 
 " 16. INDUCED E. M. F 121 
 
 " 17. THE DYNAMO 129 
 
 " 18. THE DYNAMO 137 
 
 " 19. THE DYNAMO 145 
 
 " 20. THE REGULATION OF THE DYNAMO . . 153 
 
vl 
 
 PAGE. 
 
 No. 21. ELECTRODYNAMICS 161 
 
 " 22. THE ELECTRIC MOTOR, (CONTINUOUS CUR- 
 RENT TYPE) 169 
 
 u 23. THE ELECTRIC MOTOR, (CONTINUOUS CUR- 
 RENT TYPE) 177 
 
 " 24. THE ELECTRIC MOTOR, (CONTINUOUS CUR- 
 RENT TYPE) 184 
 
 " 25. ELECTRIC HEATING 193 
 
 " 26. INCANDESCENT LIGHTING 201 
 
 " 27. INCANDESCENT LIGHTING 209 
 
 " 28. ARC LIGHTING 217 
 
 " 29. ARC LIGHTING 225 
 
 " 30. ALTERNATING CURRENTS 233 
 
 " 31. ALTERNATING CURRENTS 241 
 
 " 32. ALTERNATING CURRENTS 249 
 
 " 33. ALTERNATORS 257 
 
 " 34. ALTERNATORS . . 265 
 
 " 35. ALTERNATING CURRENT TRANSFORMERS. . 273 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 T i -ICQA Price, - 10 Cents. 
 
 > * JuNE 16 > l H ' Subscription, $8.00. 
 
 Electrical Engineering Leaflei 
 
 & 
 
 UHIVBRSITT; 
 
 BY 
 
 Prof. E. J. Houston, Ph. D. 
 
 . AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GRADE 
 
 ELECTRICAL 
 
 1. The development of electrical excitation by 
 friction, as is well known, is due to the contact of 
 dissimilar material surfaces. The discovery of the exist- 
 ence of an electric force is ascribed to Thales, B. C., 
 600. Not only is the exact mechanism whereby electrical 
 excitation is evoked by friction unknown, but even the 
 nature of the excitement itself yet remains to be dis- 
 covered. The electric force is, however, associated with a 
 stress in an all-pervading medium called the ether. When 
 two dissimilar substances are brought into contact, a 
 stress in the ether is produced at the contact surfaces, 
 and, on separating the bodies, a condition of deforma- 
 tion, or strain, pervades the ether in the surrounding 
 space. 
 
 Whatever the nature of the strain may be, it is cer- 
 tainly polarized as regards direction, as is evident from 
 the fact, that the condition of excitement, which appears 
 to exist at the surface of one of the bodies, is different 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 203 Broadway, New York, N. Y. 
 
 [Entered as second-class matter at the New York, N. Y., Post Office, June 14, 1894.] 
 
from, but supplementary to, the condition of excitement 
 at the surface of the other body, and this difference or 
 polarity is arbitrarily referred to as a positive and 
 negative charge respectively. 
 
 An electric charge is generally supposed to reside on 
 the surface only of the charged body, and, so far as 
 manifestations of force are concerned, one might readily 
 'believe this to be the case, but it has been clearly proved 
 that the active disturbance exists in the medium between 
 the two excited bodies, and that the so-called charge is 
 merely an effect of the discontinuity of this strain at 
 their surfaces. 
 
 2. Contact between dissimilar materials produces an 
 electromotive force in the ether between them, and 
 it is this electromotive force or stress, which establishes the 
 strain in the ether. The establishment of such a strain 
 is called an electro displacement and can only l)e main- 
 tained in non-conductors or dielectrics. Electric displace- 
 ment is of the nature of a flux^ and follows, in its 
 distribution, either the motion of displacement in an 
 incompressible fluid or the strain in a compressible iso- 
 tropic solid ; namely, that as much flux must issue from 
 any portion of space as enters it, provided no electric 
 (1 large exists within that space. This is only another 
 way of stating the fact that discontinuity of the flux 
 exists at the surfaces of the excited bodies or the boun- 
 daries of the E. M. F. 
 
 The passage of a displacement flux constitutes an 
 electric current ; a momentary electric current, therefore, 
 accompanies the charge and discharge of a dielectric, and 
 such current is oppositely directed on charge to what it 
 is on discharge. An electric current in a dielectric is 
 
accurately defined as the time-rate of change of the dis- 
 placement, as will be afterwards more fully explained. 
 
 3. The effects produced by an electric discharge or 
 current are extremely varied. Among the most 
 
 important are the following : 
 
 (1.) Radiant effects. 
 
 (0.) Thermal effects. 
 
 (3.) Magnetic effects. 
 
 (4.) Electrolytic effects. 
 
 (#.) Physiological effects. 
 
 All these effects are believed to be different 
 kinds of motions in the ether or in matter. To the 
 motion of the ether belong the effects of magnetism and 
 of radiant energy; i. e., heat and light; while in the 
 motion of the molecules of matter we have the purely 
 thermal phenomena connected with temperature, and in 
 the motions of the atoms and radicals, we have the 
 phenomena of electrolysis. 
 
 4. It is necessary to distinguish between the terms 
 force, work, and energy. 
 
 Force is that which sets a body in motion, arrests its 
 motion, or changes the direction or velocity of its motion ; 
 i. <?., briefly that which alters the motion of matter. 
 Force manifests itself in a great variety of forms, viz : 
 muscular force, gravitational force, magnetic force, elec- 
 tric force, mechanical force and the forces of elasticity. 
 
 Work is done when force moves matter through a dis- 
 tance, and no work can be done unless the force or 
 forces applied do produce such motion. 
 
 Energy is the capability of doing work and is of two 
 kinds, namely, kinetic and potential. Kinetic energy is 
 
 UFI7BRSIT7 
 
either the energy in moving bodies, or energy actually 
 doing work ; i.e., the energy of motion. Potential 
 energy is the energy of bodies at rest, or energy not 
 actually displayed in motion, but connected with the 
 potentiality of doing work. 
 
 5. It is possible that potential energy is only an 
 unrecognized form of kinetic energy, just as the 
 
 heat energy in a body, which measures its temperature, 
 was at one time considered to be potential energy, but is 
 now admitted to be a form of molecular kinetic energy. 
 As knowledge advances it is probable that other forms 
 of energy now regarded as potential may prove in real- 
 ity to be due to motion, either in matter or in the ether; 
 i.e., kinetic energy. 
 
 6. The doctrine of the conservation of energy un- 
 derlies all the phenomena in the physical sciences, 
 
 and the appreciation of this doctrine underlies all engin- 
 eering. This doctrine may be stated as follows : 
 
 The sum of the energy in the whole universe, as 
 known to us^ is constant. 
 
 When energy disappears in one form, an equal amount 
 invariably appears in some other form ; and force is 
 manifested whenever energy changes form or changes 
 magnitude. 
 
 All natural phenomena are evidences of energy, and 
 are brought about by forces acting on matter. 
 
 7. For ready expression and calculation it is con- 
 venient to refer the magnitudes of force, work 
 
 and energy to certain fundamental scientific units, based 
 upon the centimetre as the unit of length, the gramme 
 
as the unit of mass, and the second as the unit of time. 
 These are, therefore, called the centimetre-gramme- 
 second units, or the c. G. s. units. 
 
 8. The c. G. s. unit of force is the dyne, and is that 
 force which, after acting for one second on a mass 
 of one gramme, imparts to it a velocity of one centi- 
 metre-per-second. The force of gravitation is com- 
 monly expressed by the formula, 
 
 g = 980.6056 2.5028 cos 2 I 0.000003 A, 
 
 J ! 
 
 5 CMS. 
 
 AL. WIRE g ^0.01 CM. DIAM, 
 SP.G. 2. 565, AT WASHINGTON . . j 
 DYNAMOMETER 
 
 FIGS. 1 AND 2. 
 
 / 
 
 II 
 
 I 
 1C,*. 
 
 4 
 i 
 \ 
 
 WORK. I ERG. 
 
 where 1 9 is the latitude of the station, and A, its height in 
 centimetres above the sea level, and, consequently, the 
 weight of a body in dynes, i.e., the force with which the 
 earth attracts the body, is the product of the body's 
 mass in grammes and this force, or 
 F mg 
 
 The dyne is approximately equal to the weight of one 
 milligramme (1.0203 mg.) at Washington. (See Fig. 1.) 
 
 Since the dyne is often an inconveniently small unit 
 
of force, the megadyne (one million dynes) is frequently 
 employed in ordinary applications. 
 
 The megadyne is approximately equal to the earth's 
 gravitational force on one kilogramme of matter, i.e., 
 to the weight of one kilogramme (1.0203 kgrn. at 
 Washington.) A column of mercury, Y60 cms. high, at 
 C., which represents one atmosphere, presses upon its 
 base with a force of approximately one megadyne per 
 square centimetre. (1.0126 megadyne at Washington.) 
 
 I- 
 
 ACTIVITY OR RATE OF WORKING 
 
 1 JOULE PER SECOND 
 
 <=A WATT 
 
 1 LB. LIFTED 0.738 FOOT 8.84" 
 
 PERFORMANCE OF 1 JOULE OF WORK AT WASHINGTON 
 *=10 MEGALERGS 
 
 FIG. 3. 
 
 1). The erg, or the unit of work, is the work done 
 when the force of one dyne acts through the dis- 
 tance of one centimetre. (See Fig. 2.) The erg is, there- 
 fore, the dyne-centimetre. Since the erg is too small a 
 unit of work for practical purposes (so small a unit as one 
 foot-pound, or the work done when a pound of matter is 
 raised through the vertical distance of one foot, being 
 about 13,550,000 ergs at Washington), the megerg, or one 
 million ergs is more commonly employed. 
 
One foot Ib. = 13.55 mesrerffs. ) , -m r i 
 
 ? r at Washington, 
 One megerg = 0.0738 foot Ib. ) 
 
 It may be remarked that the total amount of energy 
 aggregated in the sun by the concentration from infinite 
 diffusion to his apparent bulk under the influence of 
 gravitation would be 2.6 X 10* s ergs, or 2.6 X 10* 1 
 joules. 
 
 In the measurement of electrical energy, the joule, 
 which is 10 megergs (10,000,000 ergs), is the unit gener- 
 ally employed. 
 
 A joule is, therefore, = 0.738 foot pounds at Wash- 
 ington, or 1 foot pound = 1.355 joules at Washington. 
 
 10. When work is done, say, in lifting a weight 
 against gravitational force, the same amount of 
 energy is obviously expended (disregarding air resist- 
 ance), whether the weight is lifted in one minute or in one 
 second ; but in the latter case it is evident that energy is 
 expended sixty times more rapidly than in the former. 
 This rate of expending energy, or of doing work, is 
 called activity, as is diagram matically shown in Fig. 3. 
 
 The c. G. s. unit of activity is the dyne-centimetre per 
 second, i.e., the erg per second; but the practical unit 
 usually employed in engineering is the watt, which is 
 one joule per second. 
 
 The average activity of a laborer, working with pick 
 and shovel, is about 50 joules per second, or 50 watts. 
 The average activity of the standard horse introduced 
 by Watt into engineering, i.e., 550 foot pounds per 
 second is 746 watts. The activity in a nominal 2,000 
 candle power arc light is rated at 450 watts or 0,225 
 watts per candle, and in a 16 candle power incandescent 
 lamp is about 50 watts or 3J- watts per candle. 
 
8 
 
 For many engineering purposes the kilowatt (1,000 
 watts) is the unit of activity employed. Dynamos, for 
 example, are commonly rated in kilowatts. 
 
 11. The amount of energy absorbed by a machine 
 is called its intake. Since energy is never de- 
 stroyed, the amount of work done by the machine must 
 be rigorously equal to the intake. Since, however, some 
 energy is always expended in the machine uselessly, 
 the useful amount of work delivered by the machine, 
 called the output, must always be less than the intake. 
 The output divided by the intake is called the efficiency 
 of the machine. Yery large, well constructed dynamos 
 of, say, 1,000 kilowatts capacity have an efficiency at 
 full load of 0.96. 
 
 SYLLABUS. 
 
 Contact between dissimilar materials establishes a stress 
 in the ether called electromotive force (E. M. r.) 
 
 The stress produces a strain flux in the ether called 
 electric displacement. The strain accompanying an elec- 
 tric charge resides in the dielectric medium. The time 
 rate of change of this flux is an electric current, flowing 
 in the positive direction when increasing, in the negative 
 direction when diminishing, the direction of the displace- 
 ment being taken as positive. 
 
 All electrical effects are believed to be referable to 
 different kinds of motion either in the ether or in matter. 
 
 All energy is either kinetic or potential. At any in- 
 stant the sum of the kinetic and potential energies in the 
 known universe is believed to be constant. 
 
 Electrical energy is conveniently measured in joules. 
 
 The rate of exchange or development of energy is 
 termed activity and is measured in watts. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER/] 
 WEEKLY. 
 
 9 TTT-KTT? 9^ 1 KM-L Price, - 10 Cents. 
 
 JUNE 2d, 1 Subscription, $3.00. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED G F? A D E . 
 
 ELECTROMOTIVE KORCE 
 
 12. By the term electromotive force is meant the 
 unknown cause or force which produces or tends 
 to produce an electric current. Although but little is 
 known concerning the exact nature of electromotive 
 force, (abbreviated E. M. F.), it is believed to be associated 
 with some variety of stress in the ether. This stress 
 produces a strain called displacement which in the ether 
 is permanent. In ordinary matter the displacement 
 strain varies according to whether the matter is elec- 
 trically conducting or non-conducting. If conducting, 
 the strain cannot be maintained ; if non-conducting, it is 
 progressive, or advances with time, like elastic fatigue in 
 materials under stress. The establishment of an elec- 
 tromotive force is, therefore, invariably attended, in the 
 case of ether or non-conductors, with the establish nient 
 of a temporary current, and, in the case of conductors or 
 a conducting circuit, of a continued current. 
 
 The entire series of phenomena accompanying the 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 203 Broadway, New York, N. Y. 
 
10 
 
 stress ol E. M. F., and the establishment of its displace- 
 ment strain, is called electrification. 
 
 13. Although the exact nature of a displacement 
 current is unknown, yet, quantitatively, it suggests 
 an analogy to the following phenomena. Suppose, for 
 example, that an electromotive source has its poles con- 
 nected respectively with two elastic conducting globular 
 or other surfaces placed in a homogeneous deformable 
 but incompressible jelly; and, that under the influence 
 of the E. M. F., push and pull stresses are respectively 
 exerted on the jelly at the surfaces connected with 
 positive and negative- poles, producing a positive pres- 
 sure or outward thrust at the positive pole, and a negative 
 pressure or inward thrust at the negative pole, measured 
 in dynes per square centimetre of surface. Then the 
 deformations, i. e. strains or displacements in the jelly 
 produced by the elastic expansion of the positive pole, 
 the elastic contraction of the negative pole, and the 
 yielding of the jelly between them, correspond to the 
 electrical displacements in the ether under the influence 
 of E. M. F. The amount of jelly displaced through a 
 bag surrounding either conducting surface would always 
 be the same, viz., the increment of volume of the 
 electro-positive pole, or the decrement of volume of the 
 electro-negative pole. The rate of displacement in the 
 jelly would evidently be &flow, just as the rate of elec- 
 trical displacement in the ether constitutes an electric 
 current. 
 
 The amount of displacement which will take place in 
 the jelly for a given pair of polar surfaces and a given 
 pressure in them, will vary with the distance between 
 
11 
 
 them; so too the electrical displacement that will take 
 place between two conducting surfaces at a given E. M. r. 
 varies with their distance and disposition. 
 
 It should be remembered, however, that the preceding 
 is an analogy only, and that the actual nature of dis- 
 placement may be quite different from what has just 
 been suggested. 
 
 14. An electromotive force is a vector quantity, 
 that is, a force which like a mechanical force has 
 
 necessarily both direction and magnitude, and, like a 
 mechanical force, can be resolved into components. 
 
 In the ether or any non-conductor, the E. M. F. pro- 
 ducing displacement strain is a localized vector ; that is, 
 possesses a definite magnitude at every point in space. In 
 a conducting circuit, however, the electromotive force 
 which is acting to send a current is equal to the sum or 
 line integral of all the E. M. F.'S residing in the circuit. 
 
 In the International c. G. s. system the practical unit 
 of E. M. F. is the volt. 
 
 15. E. M. F. like all other forces does no work unless 
 it is producing motion, i. e., an electric current, 
 
 and, just as the amount of work done by a force, is the 
 product of that force into the distance through which it 
 moves, or 
 
 W= Fd, 
 
 so the work done by an E. M. F. is equal to the product 
 of the E. M. F. and the amount of electric motion or 
 quantity. The practical unit of quantity in the inter- 
 national c. G. s. system is called the coulomb, and when 
 one volt acting on a circuit causes one coulomb of elec- 
 tric quantity to pass through the circuit, one joule of 
 
work, derived from the electric source, is expended by 
 the E. M. F. in the circuit. 
 
 Generally, therefore, if E, be the E. M. F. in a circuit 
 (expressed in volts), and q y the quantity of electricity 
 passing through the circuit (expressed in coulombs), then 
 the work done by the E. M. F. is 
 
 W = E q joules; 
 
 ( TF, is positive if ^and q have the same sign; and nega- 
 tive if E and q have different signs. Thus in Fig. 4. 
 the battery of E volts sends in a given time an electric 
 
 E. M.F. of E Volts 
 
 Elec.Anyineer 
 
 FIG. 4. FIG. 5. 
 
 EXPENDITURE OF E q JOULES. EXPENDITURE OF E q JOULES. 
 
 quantity of q coulombs through the conducting circuit. 
 The equation shows also that when W is negative, the 
 work done by the E. M. F. is negative, or work is done on 
 an E. M. F. when it opposes a current, this work appear- 
 ing in the electric source supplying the E. M. F. 
 
 16. This law is true both for conductors and non- 
 conductors, though in non-conductors no current 
 can be sustained. If, however, an E. M. F. E, be in com- 
 munication with two conductors insulated from each 
 other, such as two metal spheres, A and B, (Fig. 5.) 
 separated by an air space, an electro-positive or -f- charge 
 
13 
 
 of q coulombs on a third electric conductor c, say a small 
 insulated metal globe, between the two conductors A arid 
 B, will, in effect, be simultaneously attracted by B and re- 
 pelled by A. The total work which will be expended upon 
 c, in the passage from A to B, under these forces will be 
 W = E q joules, as before. 
 
 If, therefore, the quantity in the movable conductor 
 c, be one coulomb, then the amount of work in joules ex- 
 pended in the transfer from A to B, gives in volts the 
 E. M. F., E. But since work is expended continuously 
 throughout the entire journey, the work done in joules 
 from departure at A, to any intermediate point, measures 
 in volts the difference of potential between A, and the 
 intermediate point. 
 
 The difference of electric potential in volts between 
 two points, is the energy expended in joules which one 
 coulomb of electricity will perform in passing between 
 the points. 
 
 The sum of all the intermediate potential differences 
 (abbreviated P. D.'S.) in the path of c, between A and B,*is 
 obviously equal to the E. M. r. E\ and, generally, the 
 E. M. F. of any electric source at its poles is equal to the 
 total P. D. between its poles in the external circuit. Any 
 difference of potential is an E. M. F., but an E. M. F. is not 
 necessarily accompanied by a difference of potential. 
 An electric current tends to flow from a higher to a lower 
 potential, just as a thermal current (heat) tends to flow 
 from a higher to a lower temperature. 
 
 17. Devices for producing E. M. F.'S are called elec- 
 tric sources. They may be divided into classes 
 according to the nature of the energy they absorb when 
 in action, i. e., when they supply a current. 
 
Yoltaic cell ) Chemical Potential 
 
 Charged storage cell f Energy. 
 
 (3.} Selenium cell ) T> j A -n 
 
 ; . ( mi ( Kadiant Energy. 
 
 (4.) Thermo cell j 
 
 (5.) Frictional electric machine . -> 
 
 (#.) Influence electric machines. I .... 
 
 7 i, i . > Mechanical Energy. 
 
 Magneto machines | 
 
 Dynamo machines \ 
 
 Plants and animals \ Vital Energy. 
 
 The following table gives the E. M. r. of a 
 number of electric sources : 
 
 18. 
 
 CELL. 
 
 PLATES. 
 
 ELECTROLYTE. 
 
 E. M. F. 
 
 Volts. 
 
 Bichromate ) 
 or Grenet \ 
 Bichromate \ 
 double fluid f 
 Bunsen . . . 
 
 1 
 
 zinc carbon 
 
 zinc carbon 
 zinc carbon 
 
 zinc copper 
 zinc copper 
 zinc carbon 
 zinc platinum 
 zinc carbon 
 
 zinc silver with 
 chloride 
 
 electropoin 
 
 1.9 
 2.0 
 1.96 
 
 1.072 
 
 0.667 
 
 2.0 
 1.93 
 
 1.47 
 1.03 
 2.00 
 
 dilute sulphuric acid 
 
 j dilute sulphuric acid . . . 
 | dilute nitric acid 
 
 Daniell 
 
 j zinc sulphate, copper 
 
 Edison-Lalande. . 
 Fuller 
 
 dilute caustic soda 
 
 j dilute sulphuric acid . . . 
 { bichromate of potash. . . 
 j dilute sulphuric acid. . . 
 
 Grove 
 
 -Leclanche. . . 
 
 \ dilute nitric acid 
 
 sal ammoniac, manganese 
 dioxide 
 
 Silver chloride.. . 
 
 Secondary Cell or 
 Storage Battery 
 
 sal ammoniac 
 
 dilute sulphuric acid 
 
 
 The following E. M. F'S are not capable of precise limi- 
 tation. Average values and limits are given. 
 
 Plating dynamos 5 to 100 volts. 
 
 Continuous current incandescent dynamos. 50 to 150 volts. 
 
15 
 
 Arc light dynamos 250 to 10,000 volts. 
 
 Street railway dynamos 300 to TOO volts. 
 
 Alternators for transmission of 
 
 power 1,000 to 4,000 volts. 
 
 Frictional machines 500 kilovolts and over. 
 
 Influence machines. . . . 500 kilovolts and over. 
 
 Thermo-couple .a few millivolts, de- 
 pending on metals 
 used and tempera- 
 tures of their junc- 
 tion. 
 
 COPPER WIRfc 
 
 PARAFFINED CORK 
 
 PURE ZINC ROD ' 
 
 AIR SPACE 
 
 PLATINUM WIRE WITH 
 AMALGAMATED SURFACE 
 SECTION OF ONE FORM OF 
 CLARK STANDARD CELL 
 
 flec.Enyineer 
 
 FIG. 6. 
 
 19. The Clark cell is employed for accurate com- 
 parison and measurements of E. M. r., and, when 
 properly prepared, is considered to have an E. M. r. of 
 1.434 International volts at 15 C. It is made up with 
 pure mercury and pure zinc as the metallic elements, and 
 pastes of mercurous sulphate and zinc sulphate as the 
 electrolyte. 
 
 A common form of such cell is shown in FIG. 6, in 
 which a platinum wire P, is sealed into the glass cell at 
 its lower extremity. The part within the cell is first 
 amalgamated with pure mercury and is then surrounded 
 
16 
 
 by a paste consisting of a mixture of mercurous and zinc 
 sulphate. The temperature coefficient of this cell is usu- 
 ally taken as 0.077$ per C., so that 
 
 #==1.434 [1 0.00077 (t 15)] International volts. 
 When the highest accuracy is required in the use of this 
 cell, certain precautions are necessary in its preparation, 
 which are accurately described in specifications issued by 
 the British Board of Trade, a copy of which is published 
 in vol. x, of the Transactions of the American Institute 
 of Electrical Engineers, 1893, (page 19). 
 
 SYLLABUS. 
 
 . Electromotive force is the name given to the unknown 
 cause or force which produces or tends to produce an 
 electric current. 
 
 During the establishment of an E. M. F. displacement 
 currents are produced. 
 
 An E. M. F. is a vector quantity, i. e., possesses both 
 direction and magnitude. 
 
 An E. M. F. does no work unless it is producing 
 motion, i. e., an electric current. 
 
 E. M. F'S. are measured in International volts of which 
 a Clark cell is regarded as producing 1.434 at 15 C. 
 
 The practical unit of electric quantity is called the 
 International coulomb. 
 
 The transference of one coulomb through a difference 
 of potential of one volt is accompanied by an expendi- 
 ture of energy of one joule. 
 
 Difference of electric potential constitutes E. M. F. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.! 
 WEEKLY. 
 
 3 ITT-KTV ^O 1 k<U Price, - 10 Cents. 
 
 JUNK dO, 1 Subscription, $3.00. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GRADE. 
 
 RLECTRIC 
 
 20. The resistance of a conductor is that quality in 
 virtue of v/hich it limits the flow of electricity 
 
 through it under a given electromotive force. The exact 
 nature of resistance is unknown. 
 
 The resistance of a uniform, homogeneous conductor 
 varies directly as its length and inversely as its cross 
 sectional area. The resistance of a body of given shape, 
 depends upon the nature of the body. 
 
 21. The practical unit of electrical resistance is called 
 the International ohm, and, as nearly as can be 
 
 determined, is equal to the resistance offered by a uniform 
 column of mercury, 14.4521 grammes in weight and 106.3 
 centimetres in length, at the temperature of melting 
 ice. Such a column would have a cross-section of one 
 square millimetre. 
 
 22. Multiples and submultiples of the ohm are con- 
 veniently represented by certain prefixes a& 
 
 below. 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 203 Broadway, New York, N. Y. 
 
 [Entered as second-class matter at the New York, N. Y., Post Office, June 14, 1894.] 
 
18 
 
 MULTIPLES. DERIVATIVES. 
 
 deka.. 10 ten 10 
 
 hecto.. 100 one hundred 10 2 
 
 kilo... 1,000 one thousand. . .10* 
 
 mega.. 1,000,000 one million 10 6 , megohm. 
 
 bega . . 1,000,000,000 one billion 10 9 , begohm. 
 
 trega.. 1,000,000,000,000 one trillion 10 12 , tregohm. 
 
 quega 1,000,000,000,000.000 one quadrillion . .10 16 , quegohm. 
 
 SUB-MULTIPLES. DERIVATIVES. 
 
 deci 0.1 one tenth 10-* 
 
 centi .. . .0.01 one hundredth 10~ 2 
 
 milli 0.001 one thousandth 10~ 3 
 
 micro . . .0.000001 one millionth 10~ 6 , microhm. 
 
 bicro .... 0.000000001 one billionth 10~ 9 , bicrohm. 
 
 tricro.. . 0.000000000001 one trillionth 10- 1 3 , tricrohm. 
 
 The fundamental c. G. s. unit of resistance is a Mcrohm, 
 and its value is such that one c. G. s. unit of current 
 passing through it, expends an amount ^ of energy equal 
 to one erg each second. 
 
 23. By the resistivity or specific resistance of a body, 
 is understood the resistance of a cubic centimetre of 
 the body, measured between opposite faces, at the tem- 
 perature of zero centigrade. The following is a table of 
 the resistivities of various common substances expressed 
 in International ohms. Thus the resistivity of pure, soft 
 or annealed copper, the metal most frequently used in 
 electrical instruments, is 1.594 microhms at C., and 
 increases, as shown by the temperature coefficient in the 
 third column, according to Matthiessen, 0.388 per cent, 
 per degree centigrade for a small variation of tempera- 
 ture. An inspection of the table will show that while 
 the resistivity of almost all the pure metals is markedly 
 different, yet the temperature-coefficient for the small 
 
limits, already mentioned, is practically the same with 
 the exception of liquid mercury. The temperature- 
 coefficients of the alloys, however, is much less than that 
 of the ingredient metals. The resistivity of carbon 
 (graphite) is about 0.07 ohm, and its temperature- 
 coefficient is negative, that is to say, the resistance dimi- 
 nishes with the temperature. For example, in the 
 incandescent electric lamp, the resistance of the carbon 
 filament when cold, is about twice as great as at the in- 
 candescent working temperature. 
 
 Substance. 
 
 Tempera- 
 ture. 
 
 Resistivity. 
 
 Tem- 
 perature 
 Coeffi- 
 cient. 
 
 Authority. 
 
 Silver, annealed . . 
 Silver, hard drawn 
 Copper, annealed 
 (M a 1 1 h i e s en's 
 standard) 
 
 
 
 < 
 t 
 
 c. 
 
 ( 
 
 l.SOOmicr 
 1.53 
 
 1.594 
 1.629 
 2.052 
 2.089 
 
 2.903 
 5.598 
 9.030 
 9.687 
 12.420 
 13.17 
 19.57 
 35.40 
 130.8 
 94.84 
 
 2432 ' 
 
 ab't20.9 ' 
 " 32.7 < 
 
 " 68.0 ' 
 
 ohms 
 
 i 
 i 
 
 0.377 
 it 
 
 0.388 
 t 
 
 0.365 
 6.365 
 
 6.'365 
 0387 
 0.389 
 0.354 
 0.072 
 
 0.031 
 0.044 
 0.021 
 
 0.1.22 
 
 Ma.tth 
 Flemi 
 
 lessen. 
 Dg, 
 
 Copper, hard dr'wn 
 Gold, annealed... . 
 Gold, hard drawn.. 
 Aluminum, an- 
 nealed . . 
 
 Zinc, pressed 
 
 Platinum, annealed 
 Iron, annealed. . . . 
 Nickel, annealed . . 
 Tin, pressed 
 
 Lead, pressed 
 Antimony, pressed. 
 Bismuth, pressed .. 
 Mercury, liquid . . 
 Platinum-silver al- 
 loy, 2 parts Pt. 
 to one Ag. hard 
 or annealed 
 German silver ... 
 Platinoid 
 
 Hadfield's man- 
 ganese steel. . 
 
Substance. 
 
 Tempera- 
 ture. 
 
 Resistivity. 
 
 Tem- 
 perature 
 Coeffi- 
 cient. 
 
 Authority. 
 
 Selenium 
 Retort carbon 
 
 Graphite 
 
 0C. 
 
 " \ 
 
 ab't 59000ohms 
 " 0.07 " 
 from 0.0024 to 
 
 1.0 
 
 [ about 
 C 0.5 
 
 Mattheissen. 
 j- Everett. 
 
 Ice 
 
 } 
 124 
 
 0.042 ohms 
 2 24 begohms 
 
 ....-j 
 
 Ayrton & 
 
 Ice 
 
 0.2 
 
 0284 
 
 
 Perry. 
 
 Sulphate of zinc 
 saturated solu- 
 tion 
 
 10 
 
 33 6 ohms 
 
 
 Bwing & 
 Macsrrefiror 
 
 Sulphate of zinc . . 
 Common salt 
 
 10 
 
 28.22 " 1 >> 
 47" '"> 
 
 " \ 
 
 i 
 
 Kohlrausch 
 
 Sal ammoniac 
 Sulphate of soda. . 
 Sulphuric acid in 
 water 
 
 
 
 ' ' g - 
 2.5 S-S 
 11.3 " | 
 
 i 376 " ^5 
 
 " ( 
 
 & Nippoldt. 
 
 Nitric acid in water 
 Hydrochloric acid 
 in water 
 
 tt 
 
 1.287" oSJ 
 1 316 j ~ 
 
 
 
 < < 
 
 Pure water 
 
 , \ 
 
 about 3.75 meg- 
 
 I 
 
 Kohlrausch 
 
 Sample, of hydrant 
 water 
 
 I 
 15 C. \ 
 
 ohms 
 about 200,000 
 
 r; 
 [ 
 
 Kennelly. 
 
 Mica 
 Gutta-percha. 
 
 1 
 20 
 
 24 
 
 ohms 
 84 tregohms. . 
 
 449 " 
 
 f 
 j 
 
 Ayrton & 
 "Perry. 
 Latirner 
 
 Shellac. 
 
 28 
 
 9 Quegohms 
 
 '"( 
 
 Clark. 
 Ayrton & 
 
 Hard rubber .... 
 Paraffin 
 
 46 
 46 
 
 28 
 34 " 
 
 ""\ 
 
 Perry. 
 
 Glass flint . 
 
 
 
 16700 " 
 
 
 Foussereau 
 
 Porcelain 
 
 
 
 540 " 
 
 
 a 
 
 Commercial stearic 
 acid, 
 olive oil 
 
 15 
 
 440 tregohms 
 
 
 
 Kennelly. 
 
 " lard oil. 
 
 
 350 begohms . . 
 
 
 C 
 
 " creosote 
 " benzine. 
 " benzole. 
 
 
 5.4 megohms 
 14 tregohms 
 1.3 begohms. 
 
 
 i 
 
 t 
 
21 
 
 The resistivity of pure water has been observed by 
 Kohlrausch to be 3.75 megohms, and since an exceed- 
 
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 41 
 
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 III I I 
 
 FIG. 7. DIAGRAM OF RESISTIVITIES AT DIFFERENT TEMPERATURES, 
 (DEWAR AND FLEMING.) 
 
 ingly small trace of impurities greatly decreases its re- 
 sistance, it is probable that Kohlrausch's value is 
 
much below the resistivity of pure water, which in 
 the opinion of some would be almost infinite. The 
 temperature-coefficient of all liquids is negative. The 
 temperature-coefficient of all insulators is also negative. 
 
 In order to point out more clearly the relation of re- 
 sistance to temperature in different substances, the dia- 
 gram Fig. 7, gives a series of curves of observed 
 resistivities for different substances at various tempera- 
 tures. 
 
 Various formulae have been advanced at different 
 times for reducing the resistance or resistivity of a metal 
 at one temperature to its corresponding value at another, 
 but this temperature, variation* appears to differ appreci- 
 ably with different samples of even the purest metals, 
 or, at least, the experimental results are not yet in suffi- 
 ciently close accordance to make any formula reliable. 
 The most convenient supposition is, that the variations in 
 resistance are proportional to the variations in tempera- 
 ture which produce them, or that the curves in Fig. 7 
 are straight lines. Some of them do in fact appear 
 from the observations to be sensibly straight lines. On 
 this supposition 
 
 Pt = Po (1 + 
 
 where p t is the resistivity at any temperature t C., p 
 the resistivity at zero centigrade, and a is an experiment- 
 ally determined constant. 
 
 From the measurements of Dewar and Fleming as re- 
 presented in Fig. 7, the mean value of the constant , 
 between and 100 C. is, for 
 
 Platinum 0.00358 
 
 Gold . . .0.00376 
 
23 
 
 Silver ....................... 0.0040 
 
 Copper ....................... 0.00422 
 
 Aluminum ............. ..... ..0.00475 
 
 Nickel ...................... 0.00548 
 
 Iron .......................... 0.00655 
 
 Carbon ....................... 0.00391 
 
 Platinum Silver ................ 0.000224 
 
 Platinoid .................... 0.000253 
 
 German Silver ...... . ......... 0.000317 
 
 According to Matthiessen's observations which have 
 hitherto been generally accepted, the formula of correc- 
 tion for pure copper to any temperature between and 
 100 C. is approximately. 
 /> t = 14-0.00387(H + 5.968xlO- 6 t s 1.177X10- 8 t* 9.93 X 10- 11 * 4 . 
 
 The resistance of any homogeneous conductor may, 
 therefore, be calculated by the following formula 
 
 where I the length of the conductor in centimetres. 
 a its cross-section in square centimetres. 
 p t the resistass&y at the observed temperature 
 
 . 
 
 Thus the resisfc&^L of a mile of copper wire of 
 
 Matthiessen's standard, 1 sq. mm. in cross-section at 
 C. is 
 
 1 f\C\ Q^'-i 
 
 Q ^ X 1.594 microhms = 25,652,720 microhms 
 or 25.65 ohms approximately. 
 
SYLLABUS. 
 
 The resistance of a uniform homogeneous conductor 
 varies directly with its length and inversely with its area 
 of cross-section. 
 
 The International ohm is the practical unit of electric 
 resistance. 
 
 In order to conveniently designate the decimals, mul- 
 tiples and submultiples of a quantity, suitable prefixes 
 
 are employed. 
 ICT" 
 
 The bj&^ohm is the fundamental c. G. s. unit of re- 
 sistance. 
 
 The resistivity of a homogeneous isotropic body is the 
 resistance of a column of that body, having unit length 
 and cross-section. 
 
 The resistivity of all metals increases with tempera- 
 ture. 
 
 The resistivity of carbon, selenium, liquids and solu- 
 tions, as well as insulators diminishes with temperature. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.! 
 
 WEEKLY. 
 i 
 
 4. TITTV 7 1KQ4- Price > ' 10 Cellts> 
 
 JUIA 7, 1 Subscription, $3.00. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F.,R. A. S. 
 
 ADVANCED GlfcADE. 
 
 ELECTRIC 
 
 24. Conductivity is the reciprocal of resistivity, and 
 conductance the reciprocal of resistance. Thus the 
 minimum resistivity of an aqueous solution of nitric acid 
 being 1.287 ohms, the maximum conductivity is T.^T 
 0.777 mho, the mho (ohm spelled backwards) being the 
 unit of electrical conductance. A wire which has two 
 ohms resistance has 0.5 mho conductance. 
 
 The total resistance of a number of separate resist- 
 ances, connected in series, is equal to their sum, and the 
 total conductance of a number of separate conductances, 
 connected in parallel, is equal to their sum. 
 
 Thus, if a number of resistances of #, &, <?, ... n, 
 ohms, respectively, be connected in parallel, their respec- 
 tive conductances will be - 75 - . Their total con- 
 
 a o c n 
 
 ductance will be ( - -|- v -(---)-....+ - ) an d their 
 
 \ Cu (J Q' / 
 
 total resistance i " i * 
 a T) 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 203 Broadway, New York, N. Y. 
 
 [Entered as second-class matter at the New York, N. Y., Post Office, June 14, 1894.] 
 
Thus, if three resistances be connected in parallel of 
 20, 50, and 80 ohms respectively, their respective con- 
 ductances will be 0.05, 0.02, and 0.0125 mho. Their 
 joint conductance will be 0.0825 mho, and their joint 
 resistance 12.12 ohms. 
 
 25. The resistance of any metallic wire increases 
 with its temperature. Where a constant standard 
 
 resistance is required, this is an objectionable feature. 
 Since the effect of temperature is less marked on alloys 
 than on their ingredients, alloys are generally used for 
 standard resistances. 
 
 The alloys most frequently used for this purpose are 
 platinum-silver, german-silver, manganin, and platinoid, 
 or (german-silver with one or two per cent, of tungsten.) 
 
 The resistance of some alloys is, however, owing to a 
 tendency to crystallize, apt to be subject to slight vari- 
 ations with time. Platinum-silver or platinoid appear 
 to be the two alloys most nearly free from this objection, 
 and are, therefore, most frequently employed in the con- 
 struction of standard resistance coils. 
 
 26. All gases at ordinary temperatures and pressures 
 have such high resistivities that these have never 
 
 yet been measured. When, however, the pressure is 
 greatly reduced, the resistivity becomes very low, and in 
 certain recent experiments with air at a pressure of 0.01 
 min. mercury, or about 13 dynes per sq. cm., the resistivity 
 of the air was apparently about 1.4 ohms. 
 
 27. Resistances may be measured in various ways 
 which may be conveniently divided into classes 
 
 according to the magnitude of the resistances and the 
 degree of accuracy required. 
 
27 
 
 (1.) Very high resistances (upwards of one begohm) 
 by electrometer methods, in which the rate of loss of 
 charge by leakage is observed. 
 
 (#.) Resistances from one megohm to one begohm, by 
 galvanometer deflection, where a deflection through a 
 known resistance serves to vain ate the unknown resist- 
 ance. 
 
 (3.) From T i 7 ohm to one megohm, by a differential 
 galvanometer or a Wheatstone balance. 
 
 (4.) Below y^-Q ohm, by potentiometer measurements. 
 
 28. The method most frequently employed for the 
 usual range of resistances is the Wheatstone bridge 
 or balance, a form of which is represented in Fig. 8. 
 
 Elec-Engineer 
 
 FIG. 8. DIAGRAM OF WHEATSTONE BRIDGE. 
 In this method, as is well known, an unknown re- 
 sistance is measured in terms of a known resist- 
 ance by so proportioning the resistances A, B and C 
 that no current flows through a galvanometer, represented 
 
 by the resistance G-, connected to the circuit as shown. 
 
 
 When balance is obtained X = O -&. When the arms A, 
 
 and B, are equal, X = C and the unknown resistance is 
 equal to the resistance in the bridge. In practiced, and 
 B, are some multiple of 10 ohms between 10 and 10,000 
 
and the resistance (7, can be adjusted by single ohms be- 
 
 A 
 tween and 10,000, so that making the ratio - = 
 
 Klec.Engi 
 
 YIG. 9. VARIOUS FORMS OF RESISTANCES. 
 
 or i\\-2-, the total range of the instrument is from 
 __i_th ohm to 10 megohms. 
 
 The best resistance to employ in A and Z?, depends 
 
upon the resistance of the galvanometer and that of the 
 unknown resistance. Where these are small A and B, 
 should be comparatively small ; where they are large A 
 and B, should be large. 
 
 Fig. 9 represents various forms of resistances, a, is a 
 compact form of bridge with keys to close the battery 
 and galvanometer circuits. 5, is a slide form of meter 
 bridge in which the arms A and B, (in Fig. 8) are altered 
 simultaneously by the shifting of a contact along the 
 wire. Such a form is only used for the measurement of 
 low resistances, say under 20 ohms, c, is a form of dial 
 bridge with keys attached, d, and 6, are more elaborate 
 forms of dial bridges. The dial pattern, though some- 
 times more expensive than the ordinary box type of 
 Wheatstone bridge, has the advantage that there is less 
 chance of additional resistance being introduced by bad 
 contacts, only four or five plugs being used, so that the 
 danger of additional resistance by loose contacts is 
 largely avoided. At/", is shown a form of megohm, in 
 wire, carefully insulated and divided into ten coils of 
 100,000 ohms each. 
 
 At </, is represented a form of megohm in carbon 
 (pencil mark) on ground glass. This form of resistance 
 is not reliable for accurate measurements and is only 
 used for approximate work. 
 
 30. It is evident that the accuracy of measurement, 
 by whatever method that may be employed, de- 
 pends upon the accuracy of the standard resistances of 
 comparison. It has been found in practice most conveni- 
 ent to make this fundamental standard of the value of an 
 ohm. Three forms of standard ohms are shown in Fig. 
 10. At x is shown the form in common use. More 
 
30 
 
 modern forms are shown at Y and z. In all cases the 
 difficulty of employing the instrument is in determining 
 the true temperature of the coil of wire, the temper- 
 ature being inferred from that of a mass of water or oil 
 surrounding the coil. The improvements in Y and z, 
 Fig. 10, consist in exposing a large surface of the liquid 
 and providing means for stirring the same in order to 
 rapidly equalize the temperature within and without. 
 
 The standard megohms are employed for the purpose 
 of calibrating galvanometers. 
 
 FIG. 10. FORMS OF STANDARD RESISTANCES. 
 
 31. The materials of which the earth's crust is formed 
 have an exceedingly high resistivity when wholly 
 dry and may almost be classed as insulators, so that the 
 resistance of the earth's crust as a whole, if perfectly 
 dry, may be very great. In nearly all regions, however, 
 the surface strata are permanently moist, and, since such 
 moisture contains various saline matters in solution, the 
 resistivity of the ground is usually less than 100 ohms. 
 
31 
 
 Therefore, the ground may be used in place of a second 
 conductor to complete a circuit between two stations. 
 
 32. It may be supposed that like all conductors the 
 resistance of the ground as measured between 
 two ground plates would increase in proportion to the 
 distance between them. In the case, however, of a large 
 conducting mass such as that of the earth it can be 
 shown that such is not the case, for the following reason. 
 If two metallic hemispheres A and B (Fig. 11) be buried, 
 as shown, in the surface of a conducting medium, in- 
 finitely extended below the infinite horizontal plane c A 
 B D, the resistance as measured between A and B, will be 
 
 
 Elec.Engineer 
 
 FIG. 11. 
 
 where />, is the resistivity of the medium in ohms ; 
 - = 3.1416, /', is the radius of each hemisphere in centi- 
 metres ; and d, is the distance between the centres of the 
 hemispheres in centimetres. 
 
 From which it is evident that the distance between 
 the hemispheres does not appreciably aifect the value of 
 the .resistance 7?, which may be taken as 
 
 i + i 
 
 or, when the hemispheres have equal radius, 
 
32 
 
 TT r ' ,^: 
 
 Thus if />, the resistivity of the medium = 100 ohms, 
 and r, the radius of the hemispheres is 1 metre, the re- 
 sistance of the ground = 0.318 ohm. 
 
 The distance r/, fails to appreciably affect the resistance 
 72, owing to the fact that the current is by no means 
 confined to the portions of the medium lying directly 
 between A and B, but diffuses or spreads through the 
 entire mass of the infinitely extended medium. 
 
 SYLLABUS. 
 
 Very large resistances are usually measured by electro- 
 meters or galvanometer deflections. 
 
 Yery small resistances are usually measured by poten- 
 tiometers. 
 
 Intermediate resistances are usually measured by means 
 of the Wheatstone bridge by properly proportioning the 
 resistance in the bridge arms. The Wheatstone bridge, 
 as ordinarily constructed, may measure resistances from 
 T Jj-0th ohm to one megohm and is frequently constructed 
 for TT i _ -th ohm to 10 megohms. 
 
 In order accurately to determine the resistance of a 
 standard coil its true temperature requires to be known. 
 
 The resistivity of nearly all the materials forming the 
 earth's crust is high. The presence of water, however, 
 renders the resistivity of the mass much lower. The 
 resistance of a ground return in a circuit may, therefore, 
 be only a fraction of an ohm. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 ^ TTTTV 14- 1 8Q4. Price, - 10 Cents. 
 
 JUIA 14, 1 Subscription, $3.00. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GRADE. 
 
 ELECTRIC 
 
 33. If the resistivity of the insulating materials 
 alone had to be considered their specifications 
 
 would offer but little choice. In actual practice the re- 
 sistance of an insulator is determined not so much by 
 its dimensions and resistivity, as by the leakage afforded 
 through the film of dust and moisture which collects on 
 its surface. For this reason the best form of insulation 
 is that which affords the longest and narrowest path for 
 leakage. In cases where very high insulation is desired, 
 some form of oil insulator is employed, the principle 
 being to insert in the circuit of the leakage path a film 
 of oil whose resistivity is not only great, but which is 
 automatically kept clean by the tendency of dust to 
 settle and fall to the bottom. (See Fig. 12.) 
 
 34. The insulation resistance of a line or conductor 
 is measured in megohms, and this total insulation 
 
 multiplied by the length of the line in miles, gives the 
 average apparent insulation per mile in megohm-miles. 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 203 Broadway, New York, N. Y. 
 
 [Entered as second-class matter at the New York, N. Y., Post Office, June 14, 1894.] 
 
On the other hand, the metallic resistance of a conduc- 
 tor divided by its length gives its apparent conductor re- 
 sistance per mile. On long lines the effect of the escape 
 of the measuring current by leakage will be to make the 
 apparent insulation per mile, -7? appt too high, and the ap- 
 parent conductor resistance per mile, 7 i app( too low. These 
 values, corrected for leakage through uniform insulation, 
 are : 
 
 r = y J? app . /v P p. tanh- 1 
 
 
 ^app. 
 
 '^app. 
 ^?ann 
 
 app, 
 
 FIG. 12. OIL INSULATOR. 
 
 For example : If the apparent insulation R^v. ^ a 
 uniform line 200 miles long, was 6024 ohms, and when 
 grounded at the distant end its apparent conductor resis- 
 tance was 2656 ohms, then the corrected conductor 
 
 resistance = |/6024 X 2656 tanh- 1 V f|S? = 4000 X 
 
 6024 
 
 0.8 = 3200 ; that is, 16 ohms per mile and its corrected 
 
 . /Ofv^l-t 
 
 V ~ = 
 
 _ 
 
 insulation R = </6024 X 2656 
 
 4000 
 
35 
 
 X 1.25 = 5000 ohms; that is, 1 megohm mile. The 
 apparent values would be 13.28 ohms per mile and 
 1.2048 megohm miles. But 6024 X 2656 = 5000 X 
 3200 = 16,000,000, and in all cases where leakage 
 through uniform insulation resistance has the effect of 
 diminishing the conductor resistance by any ratio, the 
 insulation resistance apparently increases in the same 
 ratio, so that the product of insulation resistance and 
 conductor resistance remains constant. 
 
 35. The best resistance to give to the coils of any 
 electromagnetic relay or other receptive device 
 operated at the receiving end in a ground return cir- 
 cuit, is the resistance which the circuit offers from the 
 receiving end. This resistance, owing to the influence 
 of leakage, may be considerably less than the conductor 
 resistance of the line. This rule applies, strictly speak- 
 ing, to a very slow rate of signalling in telegraphy, and 
 for rapid signalling the resistance of the relay should 
 be much lower. 
 
 35A. We have seen that the resistance of a conductor 
 depends upon its resistivity and its geometrical 
 form. When the form is simple, as in the case of wires, 
 the computation of the resistance offers no difficulty. 
 When, however, the form is more complex a difficulty 
 arises, for example, in determining the insulation resist- 
 ance of a uniform cable consisting of a conducting wire 
 and concentric external sheath, the insulator having 
 known resistivity and known dimensions. In this case 
 the resistance per centimetre would be expressed by the 
 formula, 
 
36 
 
 where 0, equals the resistivity (ohms.) 
 1), equals the external diameter. 
 <f, equals the internal diameter. 
 s, equals the ISTaperian base. 
 
 That is, if p = 300 begohms, D = 1 inch, d = 0.5 
 
 inch, then ; ^ = 2, log ~ = 0.30103 ; 
 cl> cL 
 
 R = 0.3665 X 300 X 10 9 X 0.30103 ; = 33.1 beg- 
 ohms per centimetre ; this divided by 160,933, the num- 
 ber of centimetres in a mile, gives 0.2057 megohms to 
 the mile, i. e., 0.2057 megohm-mile. 
 
 36. A common error in less recent text-books is 
 found in the belief that electric resistance par- 
 takes of the nature of a velocity. This, however, while 
 true for the existing system of electrical dimensions 
 in the electromagnetic system, where resistance appears 
 as a length divided by a time, is only a misconception de- 
 rived from incomplete knowledge. The real nature of 
 resistance is yet unknown. 
 
 37. When a galvanometer in a circuit gives too high 
 a deflection, it is usual to reduce this deflection 
 
 by the introduction of a bypath or shunt. For ex- 
 ample, when the galvanometer of resistance 6r, has its 
 terminals connected by the shunt S 9 its deflection will 
 
 O fl I o 
 
 be reduced by the factor ^, whose reciprocal, 3l 
 
 6r + XS 
 
 is called the multiplying power of a shunt. To obtain, 
 therefore, a shunt with a multiplying power of 1000 for a 
 
 KAAA | & 
 
 galvanometer of 5000 ohms resistance, we have ' 
 
 o 
 
 = 1000, so that 8 $gg$- or -^th part of the galva- 
 
37 
 
 nometer's resistance, and generally the resistance of a 
 shunt must be (n 1) times less than the resistance of 
 the galvanometer in order to have the multiplying, 
 power of n. 
 
 38. In the use of any high resistance apparatus it 
 is absolutely necessary that the insulation of the 
 apparatus be as high as possible, for the effect of leak- 
 age may be to considerably reduce the resistance of the 
 apparatus as computed. For example, a box containing 
 one megohm in resistance might easily have a leakage 
 resistance over the surface of the box between the ter- 
 minals of one begohm. The effect of this very small 
 leakage would be to shunt the megohm by a resistance one 
 thousand times as great, and the effect would be to re- 
 duce the resistance of the box by about 1000 ohms, and 
 leave the apparent total of 999,000 ohms approximately. 
 
 In practice the problem frequently presents itself of 
 determining the size of wire required to fill a spool or 
 bobbin of certain dimensions. To do this we first cal- 
 culate the volume of space required to be filled by the 
 wire, and then employ the following formula : 
 
 d = t + V # 4- 0.0009432 V ; 
 
 r 
 
 where d = diameter of the wire in inches 
 
 t = thickness of insulation (inches). If D be 
 
 the covered diameter, 2 t = J) d. 
 v = volume of winding space in cubic inches 
 r = the resistance required in the winding (ohms) 
 
 The resistivity of the wire is here assumed to be 1.775 
 X 10" 6 (copper of 0.97 Matthiessen's conductivity at 
 
38 
 
 In practice t has the following values : 
 
 Silk, single covering, 0.0005 to 0.001 inch. 
 Silk, double covering, 0.0015 to 0.002 inch. 
 Cotton, single covering, 0.0035 to 0.004 inch. 
 Cotton, double covering, 0.005 to 0.007 inch. 
 The precise thickness of the coat depends upon the 
 size of the wire. Large wires usually take heavier 
 thicknesses of insulator. 
 
 Thus a spool of two inches intern 1 ange, i. e., length 
 between flanges, h&s an internal or core diameter of 0.5 
 inch, and an external diameter when fully wound of 1.0 
 inch. The resistance of the winding is to be 20 ohms, 
 with a double silk covered copper wire, in which the 
 insulation increases the diameter of the wire by three 
 mils. Find the required diameter. 
 Here t = 0.0015;^ = 2 X 0.5891 = 1.1 782 cubic inches; 
 r 20, v/r = 0.05891 \fvjr = 0.2427. 
 d = 0.0015 + 1/0.0000023 + 0.0002289 
 
 - 0.0015 + 0.0152 = 0.0137 inch. 
 The nearest size to this is No. 27. B. & S., 0.0142 
 inch, which, when covered with the required thickness 
 of silk has a diameter of 0.0172 inch. There would be 
 15 layers of this wire, each layer having 11(3 turns, 
 supposing the winding perfectly regular and complete. 
 The total number of turns would, therefore, be 1740; 
 and the mean turn length being 2.356 inch the total 
 length of wire = 341.6 feet. =18 ohms. The resistance 
 is two ohms less than that required, owing to the differ- 
 ence between the diameter of the wire that has to be 
 selected and the calculated diameter. 
 
 When the thickness of insulation is very small, the 
 formula becomes approximately 
 
39 
 
 d = t + 0.03071 
 
 r 
 Thus, taking the above case, 
 
 V - = 0.4926, 
 
 T 
 
 and d = 0.0015 + 0.0151 
 
 = 0.0136 inch. 
 
 39. When plates of pure amalgamated zinc are im- 
 mersed in an aqueous solution* of pure zinc sul- 
 phate it has been observed that no appreciable resistance 
 exists in the surface of contact between the two. If, 
 therefore, the resistivity of zinc and the resistivity of the 
 solution were known, the resistance of the combination 
 could be determined.' Generally, however, such contact 
 surfaces between metals and liquids appear to possess a 
 small definite resistance, called surface-contact resistance, 
 in addition to the electromotive force which is usually 
 established there. 
 
 SYLLABUS. 
 
 The insulation resistance of a line or conductor is 
 usually measured in megohms and its apparent insulation 
 per mile in megohm-miles. 
 
 The apparent conductor resistance of a line divided by 
 its length in miles gives the apparent conductor re- 
 sistance per mile. 
 
 An electromagnetic relay or other receptive device at 
 the receiving end of a ground return circuit should with 
 a slow rate of signalling, preferably have a resistance 
 equal to the resistance which the circuit offers from the 
 receiving end. 
 
 The resistance of a conductor depends upon its re- 
 
 V 'ra* ^ 
 
 fUiriVERSITT; 
 
sistivity, on its geometrical form, but in all except very 
 simple forms the computation becomes complex. 
 
 It is a mistake to believe that the nature of electric 
 resistance is of the nature of velocity, its real nature 
 being unknown. 
 
 A by-path or shunt is often employed with a galvan- 
 ometer or other device which may carry too much 
 current. 
 
 By the multiplying power of a shunt is meant the 
 ratio in which the shunt reduces the current through the 
 device shunted and is represented by unity plus the ratio 
 of the resistance of the device to the resistance of the 
 shunt. 
 
 A very small leakage in a high resistance apparatus 
 may materially reduce the resistance proper to that appa- 
 ratus. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 No fi IITFY 91 1X<U Price ' 10Cents - 
 
 UIA ZL, J Subscription, $3.00. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GRADE. 
 
 KLKCTRIC CURRKNT. 
 
 40. It is a popular belief that an electric current con- 
 sists actually of the passage of electricity through 
 a conductor. Like most popular beliefs this is erroneous. 
 According to modern views, when a telegraph circuit, 
 say, between New York to Philadelphia, has an E. M. F. 
 impressed upon its terminals at New York, it is no longer 
 believed that electricity leaves the electromotive source 
 or dynamo and flows through the conductor to Phila- 
 delphia like water through a pipe. When an 'electromo- 
 tive source, such as a battery, is placed on open circuit, 
 it produces in the surrounding ether a certain small 
 electric stress. When, however, the conducting line or 
 circuit, which may be 100 miles long, is connected to 
 its terminals, this electric stress breaks down in the ether 
 around the battery, and a flow of energy in the form 
 of an electro-magnetic wave moves outward from the 
 battery around and along the surface of the wire, with 
 the velocity of light. According to this view, the real 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 203 Broadway, New York, N. Y. 
 
 [Entered as second-class matter at the New York, N. Y., Post Office, June 14, 1894.] 
 
42 
 
 province of the conductor is to direct the flow of energy 
 from the battery, the conductor acting as a sink or line of 
 absorption in the dielectric medium, and determines the di- 
 rection of movement of the energy. A conductor, there- 
 fore, directs the passage of energy through the medium, 
 at the same time expending some of that energy in pro- 
 gress, converting it into heat within the substance of the 
 wire. The electric current cannot, consequently, be con- 
 veniently regarded as passing through the wire, but 
 rather through the ether surrounding the wire, the 
 energy, as it moves forward, converging and being rained 
 down upon the wire. 
 
 However true this theory may be, and it is in 
 general acceptance by the advanced thinkers of to-day, 
 it is much more convenient for practical purposes to 
 retain the old notions concerning the passage of a cur- 
 rent through the wire like water through a pipe, since 
 the effects of electric currents can be more readily dealt 
 with by the simpler theory than by one which is probably 
 more nearly correct. 
 
 41. When an electromotive force is impressed on 
 a condenser, energy enters the dielectric and the 
 condenser receives an electric charge, a certain quantity 
 of electricity entering the condenser. The unit of elec- 
 tric quantity is called the coulomb. While the electric 
 charge is entering the condenser, its time-rate-of-change 
 is called the electric flow or current. A time-rate-of- 
 change of one coulomb per second is called an ampere. 
 If q, be the quantity of electricity or charge, in coulombs, 
 which is entering the conductor or passed through a con- 
 ducting circuit, and /, be the strength of current in 
 
43 
 
 amperes, flowing through the conductor, then at any 
 instant, 
 
 ^~3T 
 
 that is, a current is the time-rate-of-change of the quan- 
 tity, or the instantaneous rate of flow. 1 
 
 When a quantity of electricity moves through a cir- 
 cuit under the action of an electromotive force, work is 
 
 1. For the sake of readers who have not yet mastered the elements 
 of differential calculus, the following explanation of the symbols here 
 employed may be acceptable. If Jti be the space passed through by a 
 moving body, reckoned from a given instant of time, then if the 
 spaces moved over in equal intervals of time be equal, the body will 
 be moving with uniform velocity, and the length of any portion of its 
 path, divided by the time required to describe it, will always give the 
 same value of the velocity. Thus, if the body be moving with the 
 velocity of 20 feet a second, the quotient of any distance it has 
 moved over, divided by the time occupied in travelling though it, will 
 always be equal to 20; but if the velocity of the body be varying, the quo- 
 tient of the space traversed by the time occupied in traversing will gen- 
 erally be different. Thus, a body falling to the ground from rest, is 
 continually accelerating its velocity, and the quotient of space by time 
 will vary, not only with the position of space selected, but also with 
 the length of the space traversed. The velocity at any point of its 
 descent is, therefore, only to be defined by the quotient of space tra- 
 versed by time occupied in traversing, for an extremely short, and in 
 theory, for an infinitely short, distance. For this conception a special 
 
 symbol is introduced; thus, if = , be the velocity of a body, and 
 
 different values of S, divided by their appropriate intervals of t, give 
 different values of ; then, proceeding to the ideal infinitely small spaces 
 and the infinitely short intervals of time in traversing it, which may be 
 represented, respectively, by the symbols d #, and d t, the true velocity 
 
 at any moment is expressed as before, by the quotient = . 
 
 d t 
 
 A similar method is adopted for dealing with all variable quantities 
 whose rates of variation are not constant. As for example, in the 
 
 case before used in the context, where amperes = ? . Here the 
 
 d t 
 
 quantity of electricity varying perhaps irregularly with time, shows 
 that the current may' not have the same value at different times, but 
 
 the symbol ^L gives us a means of expressing the actual instantane- 
 
 it t 
 
 ous value at any moment. 
 
44 
 
 done, just as when a mechanical force moves through a 
 distance. If the quantity of electricity moved is known 
 in coulombs, and the force with which it is moved in 
 volts, their product will represent the volt-coulombs or 
 the joules of work expended in the process, so that 
 
 W = E q joules. 
 
 If now we know the rate per second at which the quan- 
 tity is flowing or ^7 > the current strength in amperes, 
 
 and multiply this by the E. M. F., we obtain the volt- 
 amperes or the activity of the circuit in watts, 
 
 d W 
 
 -jj P = El watts. 
 
 In mechanics the activity of a force is measured by 
 the product of the force and the distance through which 
 it acts or 
 
 P = F -= cos a ergs per second ;* 
 d t 
 
 where /*, is the activity ; F, the force in dynes; -^ 
 
 the time rate of displacement in cms. per second ; and a 
 the angle between the directions of displacement and 
 the direction of the force. So in electricity, 
 
 P = E ~2 cos a (watts) ; 
 d t 
 
 d o 
 where P, is the activity, K the E. M. F. in volts, ^ the 
 
 current strength, and a the angle between the direction 
 
 1. The symbol cos a, represents the cosine of the angle a, and is always 
 some number between minus one and plus one, which can be found 
 for any given angle from trigonometrical tables. For example, if <i 
 60, cos 60 = 0.5; so that in this case the number O.fi might be sub- 
 stituted for the symbol cos a 
 
45 
 
 of the E. M. F. and the current. In almost all cases the 
 current and E. M. F. are in the same line, so that cos a 
 
 becomes unity, and P = E ( Li = E 1. 
 
 42. Although the coulomb, or ampere-second, is the 
 unit of electric quantity, yet the ordinary com- 
 mercial unit of electric quantity is the ampere-hour. 
 This is because the second is a too small a unit of time for 
 practical use. The ampere-hour, is 3,600 coulombs ; i.e., 
 the number of seconds in an hour. 
 
 43. When a uniform conductor in the form of a 
 wire has a cross-section of, say, 0.6 sq. cm. and 
 
 carries a steady current of 15 amperes, the current den- 
 
 ,i /> 
 sity would be -^ = 0.04 ampere per square centimetre, 
 
 J.O 
 
 and would be uniform for the entire cross-section of the 
 conductor. Current density is, therefore, the intensity 
 of current per normal unit area, and is expressed in am- 
 peres per square centimetre. 
 
 44. Attempts have at different times been made to 
 formulate rules for the carrying capacity of con- 
 ductors and of copper wires by specifying a definite cur- 
 rent density, for example, 1,000 amperes per square inch 
 of cross-section. Such a rule, however, cannot prescribe 
 uniform temperature elevations in conductors of differ- 
 ent sizes, for the reason that the surface of the con- 
 ductor only increases as the square root of the cross- 
 sectional area, and the surface area is the principal 
 factor determining the rate of escape of heat from the 
 wire. 
 
46 
 
 45. When the strength of a current is rapidly alter- 
 ing, as in pulsatory or alternating currents, it be- 
 comes necessary to define how that varying current 
 strength shall be estimated. 
 
 For example, the mean magnetic strengtli of that cur- 
 rent or the mean electrolytic effect of that current might 
 be taken as determining its value. In these cases, the 
 strengtli would be the arithmetical mean or average of 
 the current strength in amperes during the time under 
 consideration. In practice, however, rapidly varying 
 
 FIG. 13. THOMSON MIRROR GAL- FIG. 14. THOMSON MARINE GAL- 
 
 VANOSCOPE FOR SIGNALLING VANOMETER FOR USE ON R.OLL- 
 
 ON SUBMARINE CABLES. ING VESSEL AT SEA. 
 
 currents are measured by their mean heating effects, and 
 since the heating effect of a current depends upon the 
 square of its strength, currents are determined in their 
 effective values by the average of their squares taken 
 during the period under consideration. If half an am- 
 pere of continuous current just suffices to heat the fila- 
 ment of an incandescent lamp up to a certain degree of 
 incandescence, then any rapidly pulsatory or alternating 
 current which will bring the lamp to the same degree of 
 incandescence is just half an ampere in strength. 
 
47 
 
 46. Various methods may be employed for measur- 
 ing the strength of an electric current, but prac- 
 tically the magnetic method alone is employed. 
 
 When an electric current passes through a conductor, 
 it is accompanied by the distribution of magnetic flux or 
 magnetism in its vicinity. This flux is attended by 
 stresses in the space so occupied, which stresses acting 
 either on iron or active conductors, produce movements 
 
 Fiu. 15. HIGH-GRADE THOMSON MIRROR GALVANOMETER FOR 
 MEASURING HIGH INSULATION RESISTANCES. 
 
 in the same, which movements are opposed by springs 
 or gravitational forces. The amount of motion pro- 
 duced is usually read off by a pointer or index upon a 
 graduated scale. 
 
 Fig. 13 shows a common form of Thomson mirror 
 galvanoscope employed for the reception of telegraph 
 signals on long submarine cables. A circular coil of 
 wire in the upper part of the instrument carries at its 
 
48 
 
 centre a small magnetic needle attached to the back of a 
 small glass mirror, and suspended on a fibre. 
 
 Fig. 14 shows a form of this instrument intended for 
 use on board ship. The coil and mirror are enclosed in 
 a soft iron case one inch thick, in order to reduce as far 
 as possible the disturbing effect of the earth's magnetic 
 field on the suspended magnet when the ship turns about. 
 
 Fig. 15 shows a form of double coil Thomson galvan- 
 ometer prepared for careful insulation tests. The coils 
 are supported on long corrugated hard rubber pillars. 
 
 SYLLABUS. 
 
 It is no longer believed that electricity flows through 
 a conductor but rather through the dielectric surround- 
 ing the conductor. 
 
 The presence of a conductor directs the energy, and at 
 the same time absorbs some of it in progress. 
 
 The unit of electric quantity is called the coulomb. 
 
 The time rate of change in quantity that has passed 
 through a circuit is the current in that circuit, and is ex- 
 pressed in units called amperes. 
 
 The unit of electric quantity, the ampere-second or 
 coulomb is not used in commercial practice, being re- 
 placed by the ampere-hour. 
 
 The density of electric current is expressed in am- 
 peres per square centimetre. It is uniform only in the 
 case of steady currents, and that only, where the conduc- 
 tors are very long and are uniform in nature and cross- 
 section. 
 
 Galvanoscopes are used to indicate the presence of a 
 current, and galvanometers to measure its strength. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia, 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 
 WEEKLY. 
 
 vr 7 T 9 o 1S(U Price, - 10 Cents. 
 
 UIA J, 1 **. Subscription, $3.00. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED 
 
 OHM'S 
 
 47. Ohm's law as discovered and annunciated by 
 
 Dr. Ohm of Berlin in 1825, is generally expressed 
 
 as follows : The current strength in any continuous 
 
 current circuit is directly proportional to the total E. M. p., 
 
 and inversely proportional to the total resistance, or 
 
 (' = ~; or, as written in foreign countries, / = _ (1.) 
 R H 
 
 Ohm's law, as expressed above, assumes that the full 
 current strength in the circuit has been reached. Strictly 
 speaking, a continuous current requires an indefinitely 
 long time to attain full strength, although practically, 
 within the limits of measurement, the maximum strength 
 is usually reached in a small fraction of a second. 
 
 At the International Electrical Congress at Chicago 
 in 1893, it was recommended that a uniform system of 
 notation should be internationally adopted, and since the 
 symbol /was selected for current strength in this nota- 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 203 Broadway, New York, N. V r * . 
 
 [Entered as second-class matter at the New York, N, Y., Post Office, June 14, 
 
 1894.] 
 
50 
 
 tion, and (7, for capacity, we propose to follow the inter- 
 national notation. From equation (1) we obtain, 
 
 E = IR (2.) 
 
 and R^^ (3.) 
 
 so that in any continuous current circuit, any two of the 
 essential quantities, (electromotive force, resistance and 
 current) being known, the third can be determined. 
 
 48. These formulae apply not only to a complete 
 circuit, but also to any portion of the same. Thus the 
 electromotive force in a circuit distributes itself in such 
 a manner that the current strength in the circuit is equal 
 throughout. The electromotive force required to drive 
 a current through any portion of a circuit against the 
 resistance in that portion, is usually called the "drop" 
 in that circuit. Thus with a dynamo supplying a con- 
 tinuous current at a pressure, across the brushes, of 125 
 volts, to incandescent lamps in parallel, it may be required 
 to limit the drop in the supply mains to eight per cent,, 
 meaning that eight per cent, of the 125 volts, or ten 
 volts,, would be the limit of pressure required to drive 
 the supply current through the mains, leaving 115.0 
 volts at the lamps. 
 
 If the total number of lamps was 500, each of 50 
 watts, and since the product of the current consumed 
 and E. M. F. delivered is the activity in the lamp, the cur- 
 rent supplied to each lamp would be -ff^ = 0.4348 
 amperes, so that the total current is 500 X 0.4348 = 217.4 
 amperes, representing a total activity of 115 X 217.4 
 = 25,000 watts, or 25 K. w. The drop of ten volts 
 allowed in the two conducting wires, or five volts in 
 
51 
 
 each wire, requires that the resistance of each wire 
 
 should in conformity with the formula, r , be 
 
 ?, 
 
 = 0.023 ohm. The resistance of each lamp must 
 217.4 
 
 in conformity with the same law be, 
 
 r = = 115 = 264.4 ohms. 
 i 0.4348 
 
 The joint resistance of all the lamps is, = -^ = 0.5288 
 
 ouU 
 
 ohm. 
 
 If the resistance of the dynamo be 0.015 ohm, the 
 drop in the dynamo must also be 0.01 5 X 217.4 = 3.26 
 volte, so that the E. M. F. in the circuit must be 125 -f- 
 3.26 = 128.26. 
 
 The total resistance in the circuit would be, 
 
 Dynamo armature ............... 0.015 ohm. 
 
 . Leads .............. 2 X 0.023 = 0.046 " 
 
 Lamps ........................ 0.5288 " 
 
 0.5898 " 
 So that the total current in the circuit would be 
 
 128.26 
 
 The activity in the circuit, 7^=217.4X128.26=27.884 K. w. 
 
 Of this the activity in the dynamo is, Ie Y =21 7.4x3. 26= 0.709 K. w. 
 The activity in the leads is, .Zfc 2 +0 3 )=217.4XlO= 2.175 ." 
 The activity in the lamps is, /0 4 =217.4x 115=25.000 " 
 
 27.884 " 
 
 The electrical efficiency of distribution is the ratio of 
 the energy in the lamps to the energy in the circuit or 
 
52 
 
 49. Applying the same law to branch, derived or 
 shunt circuits, the current in any particular branch 
 is equal to the electromotive force at the terminals of that 
 branch, divided by its resistance. Thus in the preceding 
 figure, the current in any one lamp, is 115 volts divided 
 by 264.4 ohms = 0.4348 ampere. This is true no 
 matter how complex the network of conductors may be. 
 
 FIG. 16. APPLICATION OF OHM'S LAW TO A CIRCUIT. 
 
 50. 
 
 In complete networks of circuits, there are cer- 
 tain corollaries of Ohm's law which enable the 
 current strength to be deduced in any branch. These 
 may be expressed as follows : 
 
 (1.) No current can be absorbed at any branch point. 
 Thus in Fig. 17, i l =i s -\-i B because if this identity did not 
 hold, the current arriving at the point A, would be 
 greater or less than the current leaving it, so that gen- 
 eration or absorption of current would occur at the 
 point A. 
 
(2.) The total E. M. F. in any closed loop must be equal 
 to the sum of the potential differences in the loop due 
 to IE. 
 
 Thus in Fig. 1 7, E e % r^ + i s r s i t r 4 -|- 4 /' 5 , 
 because if this identity did not hold, the total E. M. F. 
 acting in the loop would be greater or less than the total 
 counter E. M. F. of 1R established by the current, 
 whereas, in any continuous current loop or circuit, these 
 two quantities must be equal. 
 
 (3.) The P. D. at the extremities of any line must he 
 equal to the sum of the P. D'S due to IR, in that line to- 
 gether with the sum, of E. M. F.'S contained in it. 
 
 E 
 
 FIG. 17. NETWORK OF CONDUCTORS. 
 
 Thus calling 17, the potential difference between A 
 
 and B 
 
 e. 
 
 This follows by the same reasoning as in the preceding 
 case, of which it is a direct consequence, for, U =E- i r^ 
 
 (4.) The current in any ~branch is the sum of the cur- 
 rents that all the E. M. F.'S in the network would produce 
 if each of the E. M. F.'S were successively permitted to act 
 dngly. 
 
 Thus calling i m the current which would be establish- 
 ed in r s if the E. M. F., 6, existed alone, and a n , the cur- 
 rent which would be established in /' 3 , if ^existed alone, 
 
then, when both E. M. F.'S exist, as shown in the figure, 
 the resulting current i s = i m -\- i n . 
 
 (5.) Taking any two branches such as r 8 and r 5 , the 
 current which would be set up in r 5 by inserting a given 
 E. M. F. in 7*3, is equal to the current strength which 
 would be set up in r s by the insertion of the same E. M. F. 
 in r 5 . 
 
 Thus considering the figure as representing the co'n- 
 nections of a Wheatstone bridge, the current set up in 
 the galvanometer branch r 4 by the testing battery in 
 
 0.47 VOLTS 
 r = 3.135 OHM 
 
 !^ 3.O23 AMP^ 
 f % =3.135 OHM 
 
 r -H 
 
 h-114.4 V<5LTS-^ 
 
 37.857 OHMS 
 
 2 
 
 HUH 
 
 44.167 OHMS 
 
 X^ < O.356 AMP. 
 
 -^ 8.36 VOLTS 
 ^ r 5 = 3.135 OHM 
 
 P 7 
 t 1 1 7. 8 VOLTS-> 
 
 I 
 
 STJTJ 
 
 . 
 
 < 2.667 AMP. 
 
 
 FIG. 18. THREE-WIRE SYSTEM. 
 
 is equal to the current which would be set up in TI 
 by removing the testing E. M. F. to r 4 . 
 
 These rules can all be deduced directly from Ohm's 
 law. Numbers (1) and (2) are frequently called Kirchoff 's 
 laws. In all cases care must be taken to observe the di- 
 rections of the various E. M. F.'S and currents, since the 
 geometrical and not the mere arithmetrical sums of these 
 quantities are under discussion. Also the E. M. F.'S must 
 be considered independently of the resistance which 
 practically accompany them. In (5) for example, when 
 we consider the transference of the E. M. F. in a battery, 
 
55 
 
 we have to regard the resistance of the battery as im- 
 movable, and the E. M. F. only to be transferred. 
 
 51. In order to determine the current strength in 
 any or all the n branches of a conducting net- 
 work in which all the E. M. F.'S and resistances are known, 
 it is customary to write down n independent simultaneous 
 equations with the aid of (1) and (2), and then solve 
 these equations by the ordinary algebraic processes. 
 Thus Fig. 18 represents the connections of a "three- 
 wire system" in which two dynamos in series operate 
 two groups of incandescent lamps with a " neutral " 
 wire from the connection of the dynamos to the con- 
 nection of the lamp groups. We may determine the 
 current strength in the various conductors as follows : 
 
 '*/! = ^ (/' 3 + /* 6 ) + 1 4 r 4 
 
 % = 4 (r & + r?) i 4 r 4 
 
 % = i* + k 
 Solving these equations for i%, i 4 and i- M we obtain 
 
 _ ff> 4 + % * 
 
 " r< (E, + B,) + ^i * 
 
 ' _ 't-h R* U>2 RI /rx 
 
 " n (B, + Bj + B l E, 
 
 U r 4 -{- u 2 R^ , x 
 
 " r 4 (R, + B,) + B, //,, 
 
 wliere P^ (/' 3 + r 6 ); R, = (/v, + /,); and tf=u l -\- y/ 2 
 It follows, therefore, from (J), that whatever the two 
 resistances r and /v, may be, that is to say, whatever the 
 two incandescent lamp loads may be, balance in the sys- 
 tem will be obtained, and no current will flow through v 4 
 when M! : <i, :: B 1 : R%. 
 
 For example, suppose (Fig. 18) that the positive load 
 
56 
 
 consists of seven lamps of 265 ohms each, and the nega- 
 tive load of six lamps of 265 ohms each, while the pres- 
 sure at dynamo terminals is 125 volts = U{ = u^ and the 
 resistance of each conductor = 3.135 ohm. 
 
 Then r % = 37.857 ohms, and r? = 44.167. 
 E, = 40.992 " " R z = 47.302. 
 Then by (\ t, = - -^ X 3.135 + 125 X 47.302 
 
 3.135 X 88.294 + 40.992 X 47.302 
 
 
 *6 = 
 
 ii = 
 
 2.667 
 0.356 
 
 The drop in 
 Pressure at 
 
 r s = 
 
 A =: 
 B := 
 
 9.47 volts. 
 8.360 " 
 114.38 " 
 117.79 " 
 
 250.00 
 
 SYLLABUS. 
 
 The current strength in any continuous current cir- 
 cuit after full strength has been attained, is directly pro- 
 portional to the total E. M. F., and inversely proportional 
 to the total resistance. This is called Ohm's Law. 
 
 Ohm's law applies not only to an entire circuit, but 
 also to any part of a circuit. 
 
 The fall of pressure or "drop' 1 in a conductor carry- 
 ing a current is the pressure required, to drive the current 
 through the conductor, and is equal to I R, the product 
 of the current and the resistance. 
 
 Laboratory of Houston & Kennelly. 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 No. 8. AUGUST 4, 1894. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GRADE. 
 
 ELBCTRIC CIRCUITS 
 
 52. The term circuit, as generally understood, em- 
 braces a complete conducting path established 
 
 between the electric source and the electro-receptive de- 
 vices that in practice are connected therewith. Ordinarily, 
 the circuit consists of a true conducting path, principally 
 or wholly of metal ; but circuit paths may, however, lie 
 through a non-conducting dielectric, as in the case of the 
 dielectric circuit. In the electric circuit, the current 
 strength may be unvarying ; in the dielectric circuit, it 
 can never be uniform. All conducting circuits belong 
 to the former type ; all electrostatic circuits, to the latter 
 type. 
 
 53. Conducting circuits may be conveniently grouped 
 into four general classes ; namely, 
 
 (1.) Series circuits. 
 (2.) Multiple circuits. 
 (3.) Multiple-series circuits. 
 (4.) Series-multiple circuits. 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 203 Broadway, New York, N. Y. 
 
 [Entered as second-class matter at the New York, N. Y., Post Office, June 14, 1894.! 
 
58 
 
 54. In the series connection of electro-receptive 
 
 devices, the separate devices are placed so as to 
 
 be successively traversed by the current. The current 
 
 strength is maintained constant no matter how many 
 
 FIG. 19. SERIES CIRCUIT. 
 
 separate devices are included in the circuit ; consequently, 
 in all such cases, the electromotive force of the source 
 must be varied in accordance with the number of devices 
 in circuit. This variation is generally obtained auto- 
 matically from constant-current dynamos. 
 
 Fig. 19 shows a dynamo of E. M. F., E, connected with 
 a number of electro-receptive devices connected by the 
 conducting circuit r l9 etc. Here the total resistance of 
 the circuit is (^ + ^4. . . . +JS s )+(r 1 + r 2 + . . . + r 8 ) 
 and the current in the circuit is equal to the E. M. F., E, 
 divided by this resistance. Calling this current 7, the 
 activity yielded by the source is ^/watts, and the activity 
 in any separate device is P It, developed entirely as 
 heat, while the activity in any section of conducting wire 
 is P r ; so that the activity in the circuit is entirely ex- 
 
 FIG. 20. SERIES CIRCUIT CONTAINING COUNTER E. M. F. 
 
 pended in producing heat either in the receptive devices, 
 or in the conducting wires connecting the same. Such 
 activity is commonly called P 7?, activity, and the loss 
 of energy accompanying such currents is the P R, loss. 
 
59 
 
 Fig. 20 shows a dynamo of E. M. F., E, connected in 
 series with a number of electro-receptive devices each of 
 which supplies not only the resistance 7?, but also a counter 
 electromotive force e. The resistance in this circuit is 
 obtained as in the preceding case, but the current is now, 
 
 the activity yielded by the dynamo to the external cir- 
 cuit is E /, watts as before, but the energy liberated in 
 each device is now (/ 2 R -j- e /) watts. The first term 
 is entirely thermal, but the energy corresponding to the 
 second term may be mechanical, chemical, or thermal, 
 
 FIG. 21. MULTIPLE CIRCUIT. 
 
 depending upon the nature of the receptive device. In 
 the case of the arc lamp, e I, is thermal ; in the case 
 of the magnetic device, e /, is generally mechanical ; and 
 in the case of electrolysis, e /, may be partly mechanical, 
 but is principally chemical. 
 
 55. In the multiple connection of electro-receptive 
 devices, all the positive terminals of the devices 
 are connected to a single positive lead, and all the nega- 
 tive terminals similarly connected to a single negative 
 lead. Thus in Fig. 21 a number of receptive devices 
 represented by the resistances E I? Ba, etc. are connected 
 as shown with the positive and negative leads respec- 
 tively of the dynamo of electromotive force E. In this 
 
 UITI7BESIT7 
 
60 
 
 case the resistance of the circuit is the complex expres- 
 sion obtained in the following manner : 
 
 The resistance at E, 7? K = R$. 
 
 The resistance at D, R^ = _ _ 
 
 Resistance at C = R = 
 
 56. In the multiple-series connection of electro-re- 
 
 ceptive devices, the electro-receptive devices are 
 
 connected in series groups, and these groups subsequently 
 
 < Elec.Engineer 
 
 FIG. 22. MULTIPLE SERIES CIRCUIT. 
 
 connected in parallel. Thus in Fig. 22, a number of re- 
 ceptive devices r l9 r^ etc., are connected, as shown, in 
 three separate groups in series, and these groups sub- 
 sequently connected in multiple. If H l9 R^ R^ and 
 RI, are the resistances of each group, then the total joint 
 resistance of the circuit 
 
 _ 1 , _, _. 
 
 57. In the series-multiple connection of receptive de- 
 vices, the separate devices are connected in groups 
 in multiple, and these separate groups subsequently con- 
 nected in series. 
 
61 
 
 Such an arrangement is indicated in Fig. 23, where 
 four groups of four lamps each are operated in series. By 
 this means the current in the supply mains, for a given 
 number of lamps equally divided into groups, is reduced 
 four times, and the operating pressure at main terminals 
 is increased four times. Such an arrangement, with the 
 addition of the equalizing wires c D, E F, and G H, is 
 practically employed, and is called & five-wire system. 
 
 58. All E. M. F.'S developed in a circuit by a con- 
 tinuous current are counter E. M. F.'S. A current /, 
 flowing through a resistance It, sets up a virtual counter 
 E. M. F. of / It, volts. When flowing through an elec- 
 
 A 
 
 B 
 
 4 
 
 $ O 4 
 
 +3f 
 
 0000 
 
 VG 
 
 0000 
 
 t'i' 
 
 oooo 
 
 j 
 
 Elec. Engineer K 
 
 FIG. 23. SERIES-MULTIPLE CIRCUIT. 
 
 trolyte it usually establishes a counter E. M. F. of polari- 
 zation. When passing through a coil, loop, or 
 electromagnet, it sets up, during the initial period of 
 rise to full strength, a counter E. M. F. of induction, as 
 will be subsequently explained. When it passes through 
 a motor and causes its armature to rotate, it develops in 
 the rotating armature a counter E. M. F. In all these 
 cases the current does work upon the counter E. M. F. 
 and expends that work as heat in the resistance, as 
 chemical energy in the electrolyte, as magnetic energy 
 sometimes taking the form of mechanical work in the 
 coil or magnet, and as mechanical work in the rotating 
 motor. 
 
If the E. M. F. developed in a circuit by a current were 
 not a counter E. M. F. but aided the current, it would 
 do work on the current. This work would have to be 
 drawn from the source of the aiding E. M. F., so that it 
 would be only necessary to expend some work in the 
 circuit, to involve the expenditure of additional work 
 from some other portion or portions, indicating a condi- 
 tion of unstable electrical equilibrium. 
 
 In all cases, therefore, where work is done in a circuit 
 by the action of a current, that work is due to the de- 
 velopment and action of a counter E. M. F. and the 
 greater this counter E. M. F. for a given current strength, 
 the greater the amount of energy that is absorbed by its 
 source, and the greater the amount of work which may 
 be expended. A counter E. M. F. is, therefore, not pre- 
 judicial to the action of an electric source. On the con- 
 trary, it is the means by which work can be delivered to 
 the circuit. 
 
 59. The preceding facts may be tabularly arranged 
 as follows : 
 
 VARIETIES OF COUNTER E. M. F. DEVELOPED BY 
 ALTERNATING OR CONTINUOUS CURRENTS. 
 
 Varieties of E. M. F. 
 
 Types. 
 
 Varieties of Energy. 
 
 1. Virtual Counter E. M. F 
 2 Counter E M F of Polarization 
 
 (IS)..,, 
 (e) 
 
 (IR}I=1* R= Heat 
 in Resistance. 
 (e 1 ) chemical energy 
 
 3. Counter E. M. F. of Induction.. . 
 4. Motor E. M., F 
 
 (e) 
 (e) 
 
 in electrolyte. 
 (e 1) = magnetic energy 
 and mechanical work 
 in coil in magnet. 
 (e /) mechanical work 
 
 
 
 in rotation of motor. 
 
63 
 
 60. Ohm's law is essentially the law applying to any 
 circuit or to any conductor forming portion of a 
 
 circuit. The fundamental law which underlies the ex- 
 
 -p< 
 pression I = -= - is, however, as follows, 
 
 Ji 
 
 = 9 oT0gi 
 
 where i is the current density at any point of a circuit, 
 e a the E. M. F. at that point, being considered as a vector 
 or directed quantity, and being also equal to the drop of 
 pressure per centimetre of length, ^, the resistivity of the 
 medium at that point, and </, its reciprocal, the conduct- 
 ivity. This law, therefore, expresses the fact that 
 Avherever the electromotive force is acting, the current 
 density is in direction of that E. M. F., and equal to the 
 value of that E. M. F. multiplied by the local value of ^, 
 the conductivity. This is Ohm's law expressed for 
 localized action and not for generalized action. 
 
 The formula J- =^ 
 
 is generally employed with the practical units of the am- 
 pere, ohm and volt. It is evident, however, that it is also 
 applicable to the fundamental c. G. s. units. So that when 
 J?is expressed in units of 10 bicro volts, or 10~ 8 volts, and 
 7? in bicrohms ; i. e., 10~ 9 ohms, the current strength be- 
 comes evaluated in c. G. s. units of 10 amperes each. 
 
 SYLLABUS. 
 
 In an electric circuit the current strength may be uni- 
 form ; in a dielectric circuit it can never be uniform. 
 
 Conducting circuits may be series, multiple, multiple- 
 series, or series-multiple. 
 
A series circuit is frequently called a constant current 
 circuit. In such a circuit the current is usually main- 
 tained constant even though the resistance be variable. 
 
 A multiple circuit is frequently called a constant po- 
 tential circuit. The current in the leads is variable, but 
 the E. M. F. is constant. 
 
 The E. M. F.'S developed in a circuit by a current are 
 all counter E. M. F.'S. These counter E. M. F.'S may be 
 divided into four classes ; viz., the virtual counter E. M. F. 
 of resistance, the counter E. M. F. of polarization, the 
 counter E. M. F. of induction, and the motor electromotive 
 force of a motor. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 ~NY> Q ArrnmsTll 1 KQ4- Price, - 10 Cents. 
 
 11, 1 ^4. Subscription, $3.00. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E.-J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GF?ADE. 
 
 VOLTAIC CELL. 
 
 61. When a plate of chemically pure zinc and a 
 plate of chemically pure copper are plunged into 
 
 a dilute solution of sulphuric acid, no visible action 
 takes place as long as the plates are electrically discon- 
 nected outside the acid liquid. When, however, the 
 two plates are connected outside the liquid by a con- 
 ducting wire, the completion of the electric circuit is 
 immediately attended by the establishment of an elec- 
 tric current through the circuit, and a more or less visi- 
 ble action on the zinc, as evidenced by the evolution of 
 hydrogen and the gradual solution of the zinc plate. 
 Such an arrangement forms what is called a voltaic cell. 
 
 62. The electromotive force which produces the 
 electric current, exists at the contact surfaces of 
 
 the two plates with the liquid. As we have already 
 seen, whenever an E. M. F. acts in the direction of an 
 electric current, energy is absorbed from the source of 
 the E. M. F.; that is, work is done on the current and 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 203 Broadway, New York, N. Y. 
 
 [Entered as second-class matter at the New York, N. Y M Post Office, June 14, 1894.] 
 
66 
 
 appears in the circuit. So here, when an E. M. r. sets 
 up a current in the voltaic circuit, energy is absorbed at 
 the source of the E. M. r.; namely, at the junction sur- 
 faces between the plates and the liquid in which they 
 are immersed. Such a combination or couple of two 
 plates or elements, with the conducting solution or elec- 
 trolyte is called a voltaic cell. It follows, therefore, 
 that the particular combination of elements and electro- 
 lyte in a voltaic cell, which will insure the most powerful 
 E. M. r., will be that combination which will ensure the 
 maximum resultant amount of work being absorbed at the 
 immersed surfaces when the circuit is closed. In an ac- 
 tive voltaic cell, one of the elements or plates is dissolved 
 by the electrolyte while the other plate remains unat- 
 tacked. The plate which is dissolved is called \\\v posi- 
 tive plate of the couple and the other the negative plate. 
 The current flows through the liquid from the posi- 
 tive to the negative plates, as shown by the arrows, 
 when the external circuit c D E is completed, and the 
 terminal c, at which the current leaves the cell is, ac- 
 cording to convention, called the positive pole or terminal, 
 and the terminal z, where it returns to the cell, the 
 negative pole or terminal. It will be seen, therefore, 
 that the negative terminal is connected with the positive 
 plate, and the positive terminal is connected with the 
 negative plate. This classification, although generally 
 used, is apt to mislead. In reality, the plate A, (allowing 
 for any existing drop of pressure) must have the same 
 potential throughout its substance ; and, similarly, the 
 plate B, must be positive throughout. Since the electro- 
 motive force is resident at the surface of contact be- 
 tween the plates and the liquid, it follows that the entire 
 
67 
 
 plate B, is positive to the liquid and the entire plate 'A, 
 negative to the liquid. The terms positive plate and 
 negative plate, however, are in universal use, and if 
 properly understood introduce no error. We shall, 
 therefore, hereafter employ them. 
 
 63. It has frequently been stated in text-books of less 
 recent date that the seat of the E. M. r., for ex- 
 ample, the zinc-copper couple shown in Fig. 24 is at the 
 
 V z c / 
 
 
 
 | 
 
 1 
 
 
 
 ^ 
 
 A B 
 
 3 ^_ 
 
 CC '', 
 Ul ' 
 
 tt. : 
 
 
 
 Q. : 
 
 ; ^ 
 
 
 8 ; 
 
 \ 
 
 5 
 
 ,;/% 
 
 PIG, 24. SIMPLE FORM OF VOLTAIC CELL. 
 
 metallic contact of the zinc plate and the copper wire 
 outside the cell. This is, however, erroneous. The only 
 E. M. F. which can exist at this metallic junction is what is 
 called a thermo-electric E. M. F., and as such is altogether 
 two small to account for the E. M. F. of the cell. As 
 has already been pointed out, wherever an E. M. F. aids 
 or opposes a current, work is done by or on the E. M. F. 
 If, therefore, the E. M. F. of the voltaic cell resided at 
 the zinc-copper contact outside the cell, it would follow 
 
 UHI7BRSIT7 
 
68 
 
 that the energy of the cell would be supplied at this 
 contact, i. e. outside the cell, and would therefore be in- 
 dependent of such energy relations s existed within the 
 cell. In point of fact, however, the energy is absorbed, 
 not at this contact, but at the contact surfaces of the 
 plates with the electrolyte, and it is to these surfaces, 
 therefore, that we have to look for the E. M. F. of the cell. 
 
 64. In every voltaic cell there are two distinct 
 sources of E. M. F., viz : 
 
 (1.) An E. M. F. at the contact surface of the positive 
 plate with the liquid. 
 
 (2.) An E. M. F. at the contact surface of the negative 
 plate with the liquid. 
 
 When a cell, such as shown in Fig. 24, has a positive 
 plate of zinc, a negative plate of copper, and an elec- 
 trolyte of dilute sulphuric acid, on the closing of the 
 circuit hydrogen sulphate, Jf 2 SO^ in the electrolyte is 
 decomposed. The negative radical, (SO^) enters into com- 
 bination with the zinc, to form zinc sulphate, ZnSO^ and 
 the hydrogen radical H^ is liberated at the negative 
 plate in the form of bubbles of gas. Before closing the 
 voltaic circuit, we have a condition of affairs in the cell 
 represented by the chemical expression 
 
 Zm, + // 2 SO i + On, 
 and after closing, Zn/SO^ -f- H 2 + Cu. 
 
 65. The most economical voltaic cell that has been 
 yet developed, is incapable of producing, on a large 
 
 scale, electric energy as cheaply as a dynamo electric 
 machine. A careful consideration will show how hope- 
 less it is to expect any existing voltaic cell economically 
 to compete with an efficient dynamo. As we have 
 
already pointed out, the source of energy in the cell is 
 the chemical potential energy in the positive plate and 
 electrolyte. For example, taking for the positive ele- 
 ment the metal which experience has shown to be the 
 most economical and suitable, namely zinc, one pound of 
 zinc, of the requisite degree of purity, costs, when made 
 up in large quantities into plates, say $0.07. This pound 
 of zinc dissolved in a voltaic cell without loss by local 
 action, produces a delivery of about 1,347,500 coulombs, 
 and if the E. M. F, of the cell be two volts, 2,695,000 volt- 
 coulombs, i. e.y 2,695,000 joules of electrical energy, 
 equal to 0.7486 kilowatt- hours, so that, leaving out of 
 consideration the cost of the electrolytes employed in the 
 battery, as well as labor, interest and depreciation, the 
 cost of a kilowatt-hour in zinc consumed, is 9.352 cents 
 per kilowatt-hour in the battery circuit. On the other 
 hand, it is known that 1.8 Ibs. of coal in the best large 
 steam plants will furnish one average indicated horse- 
 power-hour ; or 2.4 Ibs. of coal, one average indicated 
 kilowatt-hour, which with an efficiency of conversion in 
 dynamo machines of 0.9, represents an expenditure of 
 2f Ibs. coal per kilowatt-hour of electrical energy in the 
 dynamo circuit. With coal costing $3.00 per ton of 
 2,240 Ibs., the cost of a kilowatt-hour is thus approxi- 
 mately 0.357 cent for coal consumed, leaving out of 
 consideration water, oil, waste, labor, interest and depre- 
 ciation. In a large steam dynamo central station, the 
 total cost of producing and delivering a kilowatt-hour 
 over a long line to consumers is sometimes seven cents. 
 
 66. If the working E. M. r. of a cell be denoted by 
 e (volts) and its internal resistance by r (ohms) 
 
 then may be called the electrical capability of the 
 
cell, and is equal to the activity of tlie cell, when short 
 circuited, expressed in watts. If now an activity of P 
 watts is required from the battery in its external circuit, the 
 minimum number of cells which will supply this activity 
 
 is4.P-^( J. This number of cells will, therefore, 
 
 represent the most economical installation or first cost. 
 
 Thus if a given type of cell has an E. M. F. of 2 volts, 
 and a resistance of 0.1 ohm, its electrical capability is 40 
 watts. If a battery of these cells has to yield 160 watts 
 in its external circuit, the minimum number of cells re- 
 quired is 4 X = 16. Each cell will yield to the 
 
 circuit 20 watts, or one-half of its capability, and will 
 yield to the external circuit 10 watts or one-quarter of 
 its capability. In other words, minimum installation 
 cost requires an efficiency of 0.5 from the battery, and 
 half the capability of each cell. 
 
 67. When the requisite number of cells has been 
 determined by the preceding rule, the grouping 
 
 of the cells does not alter their activity. In the case 
 considered, if 16 cells be operated in series the terminal 
 E. M. F. would be 16 volts and the current 10 amperes. 
 If the battery was arranged "in 2 rows of 8 cells, the 
 terminal E. M. F. would be 8 volts, and 20 amperes, 
 similarly for 4 rows of 4 cells, 8 rows of 2, or 16 rows 
 of 1, the output would be 160 watts. The grouping 
 adopted would in practice depend upon the nature of 
 the receptive device ; i. e. the motor or lamp operated. 
 
 68. It sometimes happens that the activity required 
 from a cell for minimum installation cost, namely 
 
 one-half of its capability, is greater than the cell can 
 
71 
 
 sustain. In such cases the rule must be modified. If 
 '*, be the maximum current strength in amperes which 
 the cell can sustain, then e i, is its maximum yield to the 
 circuit, and e i i* r, its maximum delivery to the ex- 
 ternal circuit. Hence if JP, be the external activity re- 
 quired, the minimum number of cells which will yield 
 
 it is . ., . 
 
 e ^ v* r 
 
 For example, in the cells already considered, the 
 theoretical current obtainable from them on short-cir- 
 cuit would be 2 T 20 amperes and the most economical 
 working current in regard to first cost of battery would 
 be ten amperes. But if the maximum current practi- 
 cally obtainable from these cells without undue polari- 
 zation was four amperes, then the minimum number 
 required to yield 160 watts in the external circuit would 
 
 be - - - = 25, and this might be arranged in one, 
 8 1.6 
 
 or five rows, according to requirements. The efficiency 
 of the battery would no longer be 0.5. In this instance 
 it would be 0.8. 
 
 69. It should be observed that in order to obtain 
 the best economy in operating and maintaining a 
 battery for a given activity, the cost of materials and 
 superintendence have to be considered as well as interest, 
 depreciation, and first cost, so that the number of cells 
 for best working economy, may be very different from 
 the number of cells for lowest first cost of installation. 
 
 TO. The value of any type of cell, in regard to the 
 
 minimum number that must be installed for the 
 
 supply of a given power is proportional to its capability, 
 
72 
 
 and if p, be the price in dollars of any given type of cell, its 
 economic value for cost of installation is proportional to 
 
 <> 
 
 Thus, two cells would have equal economic value 
 
 p r 
 
 for the delivery of a small quantity of power, reckoned 
 on the basis of first cost in installation, if one had two 
 volts 0.1 ohm, and cost $1.00 ; while the other had 0.6 
 volt, 0.012 ohm and cost $0.75. 
 
 71. "Whenever in order to secure the maximum first 
 cost of battery by obtaining an efficiency of 0.5, 
 the cells of a battery have to be joined up in multiple 
 series, it is preferable to employ larger cells in a single 
 series if possible. Such a proceeding is not only more 
 economical, since large cells cost relatively less than 
 smaller ones, but will also be a safegard against defec- 
 tive action by the failure of cells in any series, thereby 
 allowing the neighboring series to discharge through it 
 thus seriously interfering with the effectiveness of the 
 battery. 
 
 SYLLABUS. 
 
 The seat of E. M. F. in a voltaic cell is at the contact 
 surfaces of the plates or elements of the voltaic couple 
 with the electrolyte or electrolytes. 
 
 It is erroneous to ascribe the seat of E. M. F. in a vol- 
 taic cell to the metallic junction outside the cell. 
 
 In any cell, the ratio of the square of the E. M. F. to 
 the resistance, may be called the capability of the cell. 
 
 The economic value of a cell, so far as regards first 
 cost, is its capability divided by its price. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 No 10 Arrrnvr 1$ 1 SQ4- Price > ' 10 Ccuts - 
 
 lb, 1 M. Subscription, $3.00. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GRADE. 
 
 THE VOLTAIC CELL. 
 
 72. The conduction of an electric current by an 
 electrolyte is of a different nature from the con- 
 duction afforded by metals. In the latter case, apart 
 from an elevation of temperature, the passage of the 
 current is attended by no change in the metal. In the 
 case of an electrolyte, however, the passage of an elec- 
 tric current is invariably attended by a decomposition or 
 dissociation of some of the constituent molecules. This is 
 accounted for on the supposition, that in liquids, only the 
 ions, i.e., the dissociated molecules, are capable of carry- 
 ing an electric current, and, if no dissociated molecules 
 existed in the solution, that solution would act as an in- 
 sulator. The action of an E. M. F. on an electrolyte is, 
 therefore, to direct the movement of the ions. 
 
 Since atoms possess definite electric capacity, differing 
 for different kinds of atoms, but always the same for the 
 same kind of atom, it follows that the passage of a definite 
 quantity of electricity, say one coulomb, must necessitate 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 203 Broadway, New York, N. Y. 
 
 [Entered as second-class matter at the New York, N. Y., Post Office, June 14, 1894.] 
 
the transfer of a definite number of atoms or radicals, 
 different in the case of hydrogen than in that of oxygen; 
 consequently a definite quantity or mass of any given radi- 
 
 TABLE OF ELECTRO-CHEMICAL EQUIVALENTS. 
 
 Element. 
 
 Atomic Weight. 
 
 &* 
 o 
 
 c 
 
 1 
 
 Electro -chemi- 
 cal Equival- 
 ents. Milli- 
 grammes per 
 Coulomb. 
 
 Coulombs per 
 Gramme. 
 
 B* 
 l| 
 kl 
 
 H 
 
 ^ 
 
 Hydrogen 
 
 1 
 
 1 
 
 01038 
 
 96340 
 
 12140 
 
 Potassium 
 
 39 03 
 
 1 
 
 4051 
 
 2469 
 
 311 1 
 
 Sodium 
 
 23.0U 
 
 1 
 
 2387 
 
 4189 
 
 527 8 
 
 Silver 
 
 1U7.7 
 
 1 
 
 1.118 
 
 894 5 
 
 112 7' 
 
 Copper, in cuprous combina- 
 tions 
 
 63 18 
 
 1 
 
 6558 
 
 1525 
 
 192 1 
 
 Mercury, in mercurous com- 
 binations 
 
 199 8 
 
 1 
 
 2 074 
 
 482 2 
 
 60 75 
 
 Chlorine ... 
 
 35 37 
 
 1 
 
 3671 
 
 2724 
 
 343 2 
 
 Iodine .... 
 
 126 54 
 
 1 
 
 1 3134 
 
 761 4 
 
 95 93 
 
 Bromine 
 
 79 76 
 
 1 
 
 U 8279 
 
 1208 
 
 1522 
 
 Copper, in cupric combina- 
 tions 
 Mercury, in mercuric com- 
 binations 
 Tin, in stannous combina- 
 tions 
 
 63.18 
 199.8 
 117.4 
 
 2 
 2 
 
 9, 
 
 0.3279 
 1.037 
 0.6093 
 
 3050. 
 964.3 
 1641 
 
 384.3 
 121.5 
 2068 
 
 Iron, in ferrous combinations 
 Nickel 
 
 55.88 
 58.6 
 
 2 
 2 
 
 0.2900 
 0.3042 
 
 3448. 
 
 3287. 
 
 434.4 
 414.1 
 
 Zinc . 
 
 64.88 
 
 9, 
 
 3367 
 
 2970 
 
 374.2 
 
 Lead 
 
 2U6.4 
 
 2 
 
 1 071 
 
 933.7 
 
 117.6 
 
 Oxygen . . 
 
 15.96 
 
 2 
 
 0.08283 
 
 12070. 
 
 1521. 
 
 Gold 
 
 196 2 
 
 g 
 
 0.6789 
 
 1473 
 
 185 6 
 
 Iron, in ferric combinations. 
 Aluminum 
 
 55.88 
 27.04 
 
 3 
 3 
 
 0.1934 
 0.0935 
 
 5171. 
 10700. 
 
 651.5 
 1348. 
 
 Nitrogen 
 Tin, in stannic combinations 
 
 14.U1 
 117.4 
 
 3 
 
 4 
 
 0.04847 
 0.3046 
 
 20630. 
 3283. 
 
 2599. 
 413.6 
 
 cal is invariably dissociated and transferred by the 
 passage of one coulomb of electricity. This mass ex- 
 pressed in grammes is called the electro-chemical equiv- 
 
75 
 
 alent of the radical. For example, one coulomb of 
 electricity passing through an electrolyte will transfer 
 0.00001038 gramme of hydrogen. 
 
 A table of electro-chemical equivalents is given on 
 page 74, 
 
 73. It will be seen from the table that the electro- 
 chemical equivalent of silver is 1.118 milli- 
 grammes ; therefore, each coulomb of electricity will 
 liberate 1.118 milligrammes of silver, and each ampere- 
 hour will liberate 3600 X Vwo = 4.0248 grammes of 
 silver. 
 
 It will also be observed that the electro-chemical 
 equivalent of any monad element, such as hydrogen, 
 chlorine, nitrogen, iodine, etc., is directly proportional to 
 its atomic weight. Thus the electro-chemical equivalent 
 of chlorine is 35.37 times the electro-chemical equivalent 
 of hydrogen. This is tantamount to the statement that 
 all monad atoms or radicals carry the same electric charge; 
 that all dyad atoms or radicals carry twice the charge of 
 a monad atom ; that all triad atoms or radicals carry 
 three times the charge of a monad atom ; that all tetrad 
 atoms or radicals carry four times the charge of a monad 
 atom. Consequently, when an electric current passes in 
 series through solutions of various chemical substances, 
 there will be liberated one-fourth as many tetrad, one- 
 third as many triad, and one-half as many dyad, as monad 
 atoms or radicals. 
 
 Thus, one coulomb of electricity will liberate 
 0.00001038 X ^y- 8 grammes of copper from cupric 
 solutions, for the reason that the atomic weight of cop- 
 per is 63.18, and copper, in such salts, is a dyad radical. 
 
76 
 
 Generally, in the case of any element or radical, the 
 mass in grammes liberated by one coulomb is, 
 
 0.00001038 X ~' Weij;ht 
 
 valency 
 
 74. Whenever a definite chemical combination oc- 
 curs, a certain amount of energy is either ab- 
 sorbed or liberated. In the case of the mere chemical 
 formation of zinc sulphate from metallic zinc and sul- 
 phuric acid, energy is liberated as heat. If, however, 
 the same combination is effected in a voltaic cell, when 
 the circuit is closed, this energy is no longer liberated as 
 heat, but as electric energy, and the same number of 
 joules appear in the circuit as before. It is evident, 
 therefore, that the E. M. F. is capable of being calcu- 
 lated when the thermo-chemical equivalents of its forma- 
 tion products are known. 
 
 By the thermo-chemical equivalent of a substance is 
 meant the amount of energy liberated by the chemical 
 combination of its molecular weight with any other sub- 
 stance. This energy is usually expressed in gramme- 
 calories, i. <?., the amount of heat necessary to raise the 
 temperature of one gramme of water 1 C., but may be 
 expressed in joules. 
 
 Suppose that exactly one coulomb of electricity flows 
 through a circuit from a Daniell cell. There will be 
 0.00001038 X Mj- 8 - 8 = 0.0003367 grammes of zinc dis- 
 solved and converted into zinc sulphate. There will also 
 be 0.00001038 X 4 y^ = 0.0003279 grammes of copper 
 deposited on the negative plate. 
 
 Heat is evolved by the normal formation of zinc-sul- 
 phate from zinc, and, one gramme of zinc, converted 
 into ZnSOt and dissolved in water, is known by experi- 
 
77 
 
 ment to yield 16,090 joules of energy in the form of 
 heat, so that 0.0003367 gramme of zinc dissolved by 
 ordinary chemical processes would yield 5.417 joules. 
 
 But, on the other hand, work requires to be expended 
 in order to reduce copper from a solution of copper 
 sulphate, and it has also been found by measurement 
 that the energy necessary to resolve one gramme of cop- 
 per in this manner is 13,190 joules, or to resolve 
 0.0003279 gramme, 4.324 joules. Thus for every 
 coulomb of electricity generated by the cell, chemical 
 changes are effected within it which would represent 
 5.417 joules produced at the positive plate, and 4.324 
 joules expended at the negative plate, leaving a balance 
 of 1.093 joules developed in the cell. 
 
 If the chemical changes occurred under chemical 
 action alone, the 1.093 joules would be expended in 
 heating the contents of the cell, just as water is heated 
 by the admixture of sulphuric acid. As, however, the 
 changes occur under electrical action, the 1.093 joules do 
 not appear as heat in the cell, but in the entire circuit as 
 electrical energy, of the type E q, (see Paragraph 15), and 
 since E q = 1.093 joules, and q is here chosen as unity, 
 we have E 1.093 volts. 
 
 75. According to the principles of the conservation 
 of energy we have thus determined that the 
 E. M. F. of the Daniell cell must be 1.093 volts, in order 
 that the energy accompanying the chemical changes in 
 the cell should be wholly developed in the circuit, and 
 assuming that the experimentally determined energy 
 valuations of these chemical changes, i.e., their thermo- 
 chemical equivalents, have been accurately measured. 
 
 In fact, 1.09 volts is very nearly the E. M. F. of a 
 
78 
 
 Daniell cell freshly set up, with pure metal plates, and 
 pure saturated solutions. In practice, owing to a variety 
 of causes, the E. M. F. is usually lower than this, and, on 
 closed circuit work, may even be below one volt. 
 
 We have remarked that the E. M. r. was calculated on 
 the assumption that the chemical energy developed in 
 the cell was not liberated there as heat. Practically, 
 however, some heat is generated in the cell during its 
 electric activity. This is only a secondary consequence 
 of the electric resistance of the cell ; and its share of 
 the total resistance in the circuit, determines the propor- 
 tion of heat that will be developed within the cell. If 
 the cell be so constructed as to offer a negligibly small 
 resistance, then the amount of heat electrically devel- 
 oped by the current would be negligibly small, and all 
 the chemical energy developed by chemical changes in 
 the cell would be liberated outside the cell, i.e., in the 
 external circuit, by the electric agencies. 
 
 It should be remarked, however, that owing to the 
 incompleteness of our knowledge of thermo-chemical 
 equivalents, and of the exact nature of the electro-chemi- 
 cal actions in the cell, the E. M. F. of a cell can in only a 
 few instances be practically predetermined. 
 
 A voltaic cell is, therefore, a device for liberating 
 outside the cell the energy developed by its chemical 
 activities, and if the amount of those chemical activities 
 is completely known, the E. M. F. of the cell is deter- 
 minate by purely thermo-chemical measurements. 
 
 Irrespective of the cost of materials, the best type of 
 cell would be one in which the thermo-chemical energy 
 developed in the changes effected at the positive plate 
 would be a maximum, and in which the expenditure of 
 
79 
 
 thermochemical energy developed in' the changes effected 
 at the negative plate would be a minimum. Such a cell 
 would possess the maximum E. M. F. 
 
 76. From the hundreds of combinations that have 
 been tried, the zinc-carbon chromic acid type of 
 cell appears to possess the greatest E. M. F. practically 
 available ; viz., about two volts. 
 
 The disadvantage of this cell, however, lies in the 
 fact, that since the chromic acid around the negative 
 plate freely attacks zinc, it is necessary to employ a 
 porous jar to contain it, and even this resource only re- 
 tards diffusion and causes waste of zinc on open circuit, 
 besides adding considerably to the resistance of the cell. 
 
 SYLLABUS. 
 
 In metallic conduction no visible change in the con- 
 ducting circuit is produced beyond a change in its tem- 
 perature. 
 
 In electrolytic conduction the passage of the current 
 is invariably attended by the dissociation of some of the 
 constituent molecules of the liquid conductor, i.e., of 
 its electrolyte. 
 
 The electrical capacity of the ultimate atoms of matter 
 differs for different kinds of atom, but is invariably the 
 same for the same kind of atoms. 
 
 In electrolytic conduction the passage of one coulomb 
 of electricity necessitates the transfer of a number of 
 atoms or radicals dependent on their electro-chemical 
 equivalents. 
 
 The electric carrying capacity, or charge, of all monad 
 atoms is the same. The charge of all dyad atoms is 
 
80 
 
 twice, of all triad atoms three times, and of all tetrad 
 atoms four times that of a monad atom ; consequently, 
 the electro-chemical equivalent of an atom of any element 
 will be proportional to its atomic weight divided by its 
 valency. 
 
 The E. M. F. produced by any voltaic cell may be cal- 
 culated when the thermo-chemical equivalents of its 
 formation products are known, and is equal to the total 
 resulting joules developed in the cell by its chemical 
 action, per coulomb of electricity passing through it. 
 
 In every voltaic cell thermo-chemical energy is liber- 
 ated at the positive plate and absorbed at the negative 
 plate. The maximum E. M. F. will, therefore, be pro- 
 duced when the former action is greater than the latter. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 NY> 11 AiTnniT 9^ 1SQ4- Price, - 10 Cents. 
 
 1 J0, 1 M. Subscription, $3.00. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GRADE. 
 
 THE VOLTAIC CKLL 
 
 77. The hydrogen evolved at the surface of the 
 negative plate adheres to the plate, and produces 
 
 by its contact an electromotive force, counter or opposed 
 to that of the cell. This is called the counter E. M. F. 
 of polarization. Various methods are employed to pre- 
 vent polarization. These consist, practically, of methods 
 by which the hydrogen is either prevented from being 
 evolved at the negative plate ; or, if evolved, prevented 
 from forming there by entering into combination with 
 some suitable substance surrounding the negative plate. 
 This substance is called a depolarizer. 
 
 78. Voltaic cells may be divided into the following 
 classes according to the presence or absence of 
 
 a depolarizer and its character, viz. : 
 
 (1.) Single-fluid cells or those which possess an excit- 
 ing fluid but no depolarizer. 
 
 (2.) Single-fluid cells with solid depolarizers surround- 
 ing, or in contact with, the negative plate. 
 
 Published by 
 
 THE' ELECTRICAL ENGINEER, 
 203 Broadway, New York N. Y. 
 
 [Entered as second-class matter at the New York, N. Y., Post Office, June 14 1894.] 
 
82 
 
 (3.) Double-fluid cells, or those with an exciting fluid 
 and a fluid depolarizer. 
 
 79. In single-fluid cells no steps are taken to avoid 
 polarization. It is evident, therefore, that the 
 
 cells cannot be successfully employed for furnishing a 
 continued electric current. Indeed, even for temporary 
 currents, they are inferior to most forms of efficient cells 
 with depolarizers. 
 
 One of the earliest forms of single-fluid cell was the 
 Smee cell, a zinc-silver couple, immersed in an electro- 
 lyte of dilute sulphuric acid in water. This cell was at 
 one time largely used in telegraphy and in electroplating. 
 It has now almost entirely disappeared, being replaced 
 by more efficient types of cell, or by dynamo electric 
 machines. 
 
 80. A form of single-fluid (fell, which is still em- 
 ployed for producing powerful currents for brief 
 
 intervals of time, is the zinc-carbon couple immersed in 
 a solution of sal-ammoniac in water. 
 
 Like all cells of the single-fluid type without depolar- 
 izers, this cell requires long intervals of rest in order to 
 regain its full E. M. F. 
 
 81. The Grenet, the bichromate, or the Poggendorf 
 cell, as it is indifferently called, consists of a zinc- 
 carbon couple immersed in an electrolyte of bichromate of 
 potash and sulphuric acid. The reactions occuring in this 
 cell, when at work, are probably represented as follows : 
 
 Before action, 
 
 3 Zm, + 7 H 2 SO, + ^ 2 Or., 0, + C. 
 After action, 
 3 ZnSOi + 7 ff 2 O + KI SO \ + Or* (SO^ + C. 
 
In the Grenet cell, the zinc plate should be removed 
 from the electrolyte when not in use, since otherwise 
 deleterious local action, or irregular consumption of the 
 zinc will occur. For this purpose some arrangement is 
 generally made to lift either the zinc only, or both the 
 zinc and carbon from the liquid, as shown in Fig. 25, 
 where a form of cell suitable for use in driving the motor 
 of a phonograph is illustrated. Although the Grenet 
 cell may be regarded as a single -fluid cell without any 
 separate depolarizer, yet, in point of fact, the exciting 
 
 FIG. 25. FORM OF GRENET FIG. 26. FORM OP GRAVITY 
 
 CELL. DANIELL CELL. 
 
 solution acts both as an exciting liquid ai^d as a depolar- 
 izer, since no free hydrogen makes its appearance at the 
 negative plates. Such a cell as is represented in Fig. 25 
 will supply three amperes steadily. 
 
 82. In double-fluid cells, in order to prevent the 
 
 depolarizing liquid from mixing with the exciting 
 
 liquid, the depolarizing liquid is generally placed in a 
 
 porous jar. The presence of the porous jar greatly in- 
 
creases the internal resistance of the voltaic cell on account 
 of the high resistivity of the unglazed earthenware of which 
 it is formed. 
 
 The Daniell cell possesses the great advantage of giving 
 a continuous, steady current, provided the current density 
 in the cell is not excessive. 
 
 The reaction which occurs in this cell is probably ex- 
 pressed by the following equation : 
 
 Before action, 
 
 2n + H 2 80, + Cu SO, + Gu. 
 
 After action, 
 
 ZifiSO, + HI SO, + Cu + Cu. 
 
 83. In practice, the inconvenience arising from the 
 use of a porous jar, led Callaud to modify the 
 Daniell cell for closed-circuit work. In the Callaud cell 
 the porous partition is entirely dispensed with, and the 
 zinc sulphate and copper sulphate solutions are separated 
 entirely by reason of their differences of density. Fig. 26 
 shows the Callaud or gravity cell. The copper element 
 consists of a sheet of copper, bent as shown, placed at the 
 bottom of the cell and provided with an insulated wire 
 passing out at the top. The zinc plate has generally the 
 form of a star or crowfoot, and is suspended near the top of 
 the jar. After the battery has been in use for some time, 
 the zinc sulphate formed by its action, will be seen as a 
 clear transparent liquid layer separated from the dense 
 blue copper sulphate solution, in the lower part of the 
 jar, by a sharply marked boundary. After the cell has 
 been in use some time, some of the zinc sulphate solution 
 requires to be drawn off, a handful of copper sulphate 
 crystals thrown in, and fresh water added. A film of 
 
85 
 
 oil is frequently poured on the liquid so as to avoid the 
 effects of creeping, and to prevent evaporation. 
 
 The ordinary form of Callaud cell should not be called 
 upon to deliver more than J ampere steadily. Special 
 forms of gravity cell are sometimes employed, called 
 Tray cells, which will supply five amperes steadily. 
 
 84. Fig. 27 shows the Leclanche cell, which has a 
 
 zinc-carbon couple. The zinc is in the form of a 
 
 rod. The carbon is placed inside a porous cell and closely 
 
 packed with powdered carbon and black oxide of mangan- 
 
 FIG. 27. FORM OF LECLANCHE CELL. FIG. 28. PARTZ GRAVITY CELL. 
 
 ese, the latter acting as a solid depolarizer. The exciting 
 liquid is a solution of sal-ammoniac in water. This cell is 
 made in a variety of forms. In one form, called the 
 agglomerate form, the porous cell is dispensed with, and 
 the crushed carbon and manganese dioxide are moulded 
 around the carbon plate under great pressure. 
 
 The action of the Leclanche cell is probably represented 
 as follows : 
 
 Before action, 
 
 Zn + 2 NEt Cl + 2 MnO 2 + C. 
 
 After action, 
 
 2 NH* + M.NI o, + zr a o + o. 
 
"When the cell is overworked, the reactions that take 
 place are very obscure. 
 
 85. Fig. 28 shows a Partz acid gravity cell. It is 
 com posed of a zinc-carbon couple ; the carbon plate 
 rests on the bottom of the jar, while the zinc is sus- 
 pended near the top. 
 
 On charging, the jar is partly filled with an aqueous 
 solution of common salt or of sulphate of magnesia. A 
 specially prepared salt, consisting of a mixture of chromic 
 and sulphuric acids is now added through the funnel 
 
 FIG. 29. FULLER CELL 
 
 FIG. 30. EDISON-LALANDE CELL. 
 
 tube shown at the side. This salt, on reaching the bot- 
 tom of the cell, dissolves and spreads over the surface of 
 the carbon plate and acts as a depolarizer. Its greater 
 density keeps it at the bottom of the vessel. 
 
 86. Fig. 29 shows a Fuller mercury bichromate cell, 
 which consists of a zinc-carbon couple with the 
 carbon immersed in an electrolyte, consisting of a solu- 
 tion of bichromate of potash, sulphuric acid and water, and 
 the zinc, which is usually in the form of a truncated 
 cone, placed inside a porous cell filled with dilute sul- 
 phuric acid in water. A small quantity of mercury is 
 
8Y 
 
 poured into the porous cell to thciuughly amalgamate 
 the zinc. This cell gives a high electromotive force and 
 a fairly steady current, but possesses the disadvantage 
 attending all cells with porous partitions of a compara- 
 tively high internal resistance, and waste of chemicals on 
 open circuit. 
 
 87. Fig. 30 shows an Edison-Lalande cell, which 
 consists of a zinc-copper couple in a solution of 
 
 caustic soda in water. A solid depolarizer is used in 
 this cell consisting of a block of black oxide of copper 
 supported in a frame or grid of copper. The action 
 consists in the formation of a zincate of soda, and the 
 reduction of the copper oxide to metallic copper on the 
 external surface of the block. Owing to the fact that 
 the zinc and copper plates have large surfaces placed in 
 close proximity to each other, the internal resistance of 
 this cell 13 remarkably low, and forms the nearest ap- 
 proach, on the part of a primary battery, to the internal 
 resistance of a storage cell. For this reason it is capable 
 of supplying strong currents, although its E. M. r. is 
 comparatively low (-- volt). Its local action is usually 
 negligible. 
 
 88. The chloride of silver cell consists of a zinc-silver 
 couple immersed in a solution of sal-ammoniac in 
 
 water. The depolarizer is a mass of chloride of silver 
 fused as a rod around a silver wire. The electromotive 
 force of this cell is very uniform, but owing to the ex- 
 pense of silver plates these can not be given a large sur- 
 face, and hence the cells possess a comparatively high 
 internal resistance and are unsuited to the delivery of 
 strong currents. For testing purposes, however, the 
 
88 
 
 portability and constancy of the cell renders its use 
 admirable, and it is frequently made up into portable 
 batteries, one of which is shown in Fig. 31. 
 
 89. Fig. 32 shows two of Clark's standard cells en- 
 closed in a brass box with a hard rubber cover and 
 a thermometer suitably placed to indicate the tempera- 
 ture of the interior. 
 
 FIG. 31. BATTERY OF SILVER CHLOR- FIG. 32. PAIROF<JLAKK STAND- 
 IDE CELLS IN SERIES. ARD CELL^ ENCLOSED IN A 
 
 CASE WITH A THERMOMETER. 
 
 SYLLABUS. 
 
 Yoltaic cells are of three general classes, viz. : single- 
 fluid cells with an exciting liquid and no depolarizer; 
 single-fluid cells with an exciting liquid and a solid depo- 
 larizer, and double-fluid cells with both an exciting 
 liquid and a liquid depolarizer. 
 
 Voltaic cells without depolarizers are generally un- 
 serviceable. 
 
 Voltaic cells with solid depolarizers have come into 
 very extended use. 
 
 Laboratory of Houston & Kennelly, 
 'Philadelphia, 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 No. 12. SEPTEMBER 1, 1894. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED 
 
 \4asnetomotive Korce 
 
 90. The space surrounding a magnet, known tech- 
 nically as a magnetic field, is a region trav- 
 ersed or permeated by magnetic flux. Although the 
 physical nature of magnetic flux is unknown, yet it 
 possesses both magnitude and direction, and its presence 
 is accompanied by a condition of stress in the ether. It 
 is assumed that the direction of magnetic flux is such 
 that it issues from the positive or north-seeking pole of 
 a magnet, commonly called the north pole, and, after 
 passing through the region outside the magnet, re-enters 
 it at its negative or south-seeking pole, completing the 
 circuit through the substance of the magnet. The direc- 
 tion of the flux, at any point of a path, is that which 
 would be assumed, at that point, by the magnetic axis of 
 a freely suspended small magnetic needle. The strength 
 of this magnetic flux rapidly diminishes with the distance 
 from the magnet. 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 203 Broadway, New York N. Y. 
 
 [Entered as second-class matter at the New York, N. Y., Post Office, June 14, 1894.! 
 
90 
 
 91. Outside the magnet the magnetic flux is strong- 
 est in the neighborhood of the poles, where its 
 
 density is said to be a maximum. The unit of magnetic 
 flux is called the weber. Flux-density, or flux intensity, 
 is defined as being the quantity of flux passing through 
 a normal or perpendicular square centimetre of area, so 
 that unit flux-density is a flux of one weber through a 
 normal square centimetre, and is called a gauss. Flux- 
 density is usually represented by the symbol (B. In the 
 open country, in the neighborhood of New York, the 
 flux-density of the earth's magnetic field is about 0.0 gauss, 
 directed downwards at an inclination of about 72. 
 Although the flux-density, in the space outside a magnet, 
 is greatest in the neighborhood of its poles, yet, in the 
 case of a homogeneous magnet, the flux-density in the 
 magnetic circuit is usually greatest at some point within 
 the magnet. 
 
 92. If the distribution of magnetic flux outside along 
 cylindrical bar magnet be mapped out by the aid 
 
 of a small magnetic needle, it will be found that the flux- 
 paths are similar in direction and magnitude to the 
 stream-lines which would exist in an incompressible fluid 
 surrounding the magnet, if this were a hollow tube con- 
 taining a force pump so operated that the fluid was con- 
 tinually being forced out at one end and in at the other. 
 
 93. A magnetic flux differs from any material flux 
 with which we are acquainted, in that while it is 
 
 associated with energy, since in all cases it requires an 
 expenditure of energy to establish it, yet, it requires 
 no expenditure of energy to maintain its existence after 
 it has been once established. The amount of energy 
 
91 
 
 stored up in magnetic flux is represented by H-J ergs per 
 
 cubic centimetre of air or other non-magnetic material, 
 so that the amount of energy existing in a cubic centi- 
 metre of air, in the neighborhood of New York, owing 
 to the existence of the earth's magnetic flux, is about 
 
 A marked difference exists in this respect between the 
 electric and magnetic circuit, since, in the electric circuit, 
 a constant expenditure of energy to the amount of $ p 
 ergs per cubic centimetre where *', is the current density, 
 and p, the resistivity of the material in the circuit has to 
 be maintained as long as the current is flowing ; whereas, 
 in the magnetic circuit, no energy is required to maintain 
 the flux when once established, as, for example, in the 
 permanent magnet. 
 
 94. Just as the presence of electric flux or current 
 necessitates the existence of an E. M. F. to produce 
 
 it, so the presence of a magnetic flux necessitates the 
 presence of a magnetomotive force (abbreviated M. M. F.) 
 to produce it. 
 
 Magnetic flux, unlike electric flux, cannot be insulated. 
 Therefore, magnetic flux cannot be confined to a parti- 
 cular conductor. 
 
 95. There are two varieties of M. M. F. The per- 
 manent and the transient. A permanent mag- 
 
 netomotive force is found in the case of a permanent 
 magnet. Here an expenditure of energy has been initi- 
 ally necessary to magnetize the bar, but since the bar 
 maintains the flux indefinitely after the withdrawal of 
 the magnetizing force, there must exist in the magnetized 
 
bar a true M. M. F. which sustains the flux. It is assumed, 
 that in the case of the magnetizable metals, the ultimate 
 atoms or the molecules naturally possess true M. M. F.'S, 
 which, however, distribute their magnetic circuits in all 
 directions and thus neutralize each other's influences. On 
 the application of the magnetizing force, however, these 
 separate molecular M. M. F.'S are brought more nearly 
 into a common line or direction, thus mutually assisting 
 each other, and exerting a definite external influence. 
 When all the molecules in a bar are thus brought into 
 line, its M. M. F. is at a maximum and the magnet is said 
 to be magnetically saturated. 
 
 96. Most practical magnetic circuits extend almost 
 throughout their entire length through iron. In 
 
 order to force magnetic flux through a circuit, it is 
 necessary to wind the circuit with turns of insulated wire 
 and to send a current through these turns of wire. The 
 M. M. F. depends upon the number of turns so linked with 
 the circuit, and upon the strength of the current. Their 
 product, usually expressed in ampere-turns, measures the 
 magnetomotive force produced. 
 
 97. The unit of M. M. F. is the gilbert, and is such a 
 M. M. F. as would be produced by or 0.7958 
 
 (roughly 0.8) ampere-turn. 
 
 The gilbert and the ampere-turn, as units of M. M. F., 
 are related in a similar manner to the kilowatt and 
 the horse-power as units of activity in engineering; 
 i. e.y by a numerical ratio. It is commonly conveni- 
 ent to express activities in horse-power, in order to 
 conform to usage, and the classification of existing 
 machinery ; but for computations and simplicity of reason- 
 
93 
 
 ing and description, it is usually advantageous to employ 
 the more fundamental and scientific unit, the kilowatt. 
 Similarly, in dealing with M. M. F.'S it is commonly con- 
 venient to express their values in ampere-turns, but for 
 purposes of computation and simplicity of reasoning, it 
 is usually advantageous to employ the more fundamental 
 and scientific unit, the gilbert. 
 
 98. In order to follow the effects of iron on the mag- 
 netic flux produced by a current, as already pointed 
 out, let us take the simple case of an air-core solenoid, or 
 hollow anchor ring, of the form shown in Fig. 33. If such 
 a ring were wound with 100 turns of insulated wire carrying 
 a current of five amperes, the M. M. r. exerted would be 
 500 ampere-turns = 628.5 gilberts. We may suppose 
 that in a ring of the dimensions shown, the flux through 
 the core produced by this M.M.F. would be 62.85 webers. 
 If the ring were composed of copper or wood, or any 
 material except the magnetic metals, this total flux would 
 be practically the same. If, however, Fig. 33 represents 
 an iron solenoid of the same size and wound with the 
 same wire, then the magnetic flux set up in this iron core, 
 on the passage of the same magnetizing current, would 
 be, perhaps, 500 times greater. Here the additional flux 
 is due to a M. M. F., previously existing in the iron 
 in a freely distributed state, but now aligned and brought 
 into action by the current. On the cessation of the cur- 
 rent in the solenoid, this structural M. M. F. in the iron 
 may remain largely intact, as shown in Fig. 34, produc- 
 ing a flux of say 20,000 webers, which is called residual 
 magnetism. Although the above are the conditions as 
 they appear to actually exist in a ferric magnetic cir- 
 cuit, i.e., a magnetic circuit of iron, still it is practi- 
 
cally much more convenient to assume that the iron is 
 destitute of M. M. F., but that it conducts magnetic flux 
 much more readily than air. That is to say, it is practi- 
 cally more convenient to suppose that the iron does not 
 act as a source but as a good conductor of flux. 
 
 The form of magnetic circuit shown in the above 
 figure is the only form known in which the magnetic 
 flux-paths are definitely limited, being confined, at least 
 
 5 Amperes 
 
 M' 
 
 Elte^Engmetr 
 
 FIG. 33. M.M.F. OF 500 AMPERE- FIG. 34. SAME COIL AND IRON 
 TURNS, OR 628.5 GILBERTS CORE WITH PRIME M. M. F. RE- 
 APPLIED TO A CLOSED CIRCULAR MOVED, LEAVING A RESIDUAL 
 COIL WOUND ON AN IRON CORE, M. M. F. IN THE IRON OF ABOUT 
 ESTABLISHING A M. M. F. OF 200,000 GILBERTS. RESIDUAL 
 250,000 AMPERE-TURNS OR 312,- FLUX, 20,000 WEBERS. 
 250 GILBERTS. FLUX, 31,250 
 WEBERS. 
 
 for a theoretically wound solenoid of this type, entirely 
 to the interior of the coil. The flux-paths are, there- 
 fore, all circles, and the density is uniform around any 
 circle. 
 
 99. When a bar of iron is brought into a magnetic 
 
 flux and the flux passes lengthwise through it, the 
 
 bar thereby becomes magnetized. The end where the 
 
95 
 
 nlagnetic flux enters, becomes of south-seeking polarity, 
 and the end where it leaves, of north-seeking polarity, 
 ft is, for convenience, generally assumed that such a bar 
 concentrates the flux of the field in which it is placed 
 owing to the greater magnetic permeability or conduct- 
 ivity of the iron for flux. Although this is a conveni- 
 ent way of treating the matter for practical purposes, 
 yet it is inconsistent with the facts. A new or local 
 
 FIG. 35. SECTION OP A COMMON TYPE OF DYNAMO WITH MAGNETIC 
 CIRCUIT INDICATED. 
 
 magnetic circuit is, in reality, called into existence by the 
 prime flux, having its local M. M. F. in the iron bar, and 
 its flux similarly directed in the mass of the bar and op- 
 positely directed in the air outside it, to the prime flux. 
 
 100. Fig. 35 represents diagrammatically the distribu- 
 tion of magnetic flux in the magnetic circuit of a 
 particular type of bipolar dynamo. Here the magnetiz- 
 ing coils M! M! and M 2 M 2 , when excited by "the passage of 
 
96 
 
 a continuous current, become the source of a M. M. F. 
 which drives magnetic flux through the circuit. Most of 
 this flux passes through the cores, yoke, and pole pieces 
 of the magnets, through the air gaps A A and the arma- 
 ture core B. Some of the flux, however, completes its 
 circuit by leakage paths such as a b c and d ef, through 
 the surrounding air. The M. M. F. of the coils M : M 2 , 
 evidently depends upon the number of turns of wire, 
 and upon the strength of the circulating current, i.e., 
 upon the number of ampere-turns or gilberts. 
 
 SYLLABUS. 
 
 A magnetic field is a region traversed by magnetic 
 flux, and is attended by a stress in the surrounding ether. 
 
 The unit of magnetic flux is called the weber. 
 
 The unit of magnetic flux-density is called the gauss, 
 or one weber per normal square centimetre. 
 
 The unit of M. M. F. is the gilbert, and is the M. M. F. 
 produced by 0.7958 ampere-turn, approximately. 
 
 Magnetic flux-density is usually denoted by (B, and has 
 direction as well as magnitude. 
 
 The energy attending a magnetic flux amounts, in non- 
 
 (B 2 
 magnetic media, to - - ergs per cubic centimetre. 
 
 A closed circular coil or solenoid, with or without an 
 iron core, has no external magnetic influence ; -i.e., all its 
 magnetic circuit is confined to the interior of its coil. 
 
 Magnetic flux is due to the existence of M. M. F. 
 
 There are two varieties of M. M. F., the permanent and 
 the transient. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 No. 13. SEPTEMBEE 8, 1894. |Xriptiol!! 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GRADE. 
 
 Magnetic Reluctance. 
 
 101. The rebuctcvnce of a magnetic circuit corres- 
 ponds to resistance in the electric circuit, and is 
 that quantity which limits the flux of magnetism under a 
 given M. M. F. The flux in any magnetic circuit can only 
 be increased by either increasing the M. M. F., or by dimin- 
 ishing the reluctance. 
 
 The unit of reluctance is named the oersted, after Hans 
 Christian Oersted, who, in 1820, discovered the magnetic 
 action of an electric current. The oersted is the reluct- 
 ance offered by a centimetre cube, of air-pump vacuum, 
 between opposed surfaces. 
 
 The specific reluctance of a body is called its reluctiv- 
 ity, and is the reluctance offered by a centimetre cube of 
 the body between opposed parallel faces, just as the spe- 
 cific electric resistance of a body is called its resistivity. 
 The reluctivity of nearly all substances, other than the 
 magnetic metals, is sensibly that of vacuum, is equal to 
 unity, and is independent of the flux density. 
 
 J* < nHnrv-wm ** 
 
 Published by 
 CTRICAL E 
 203 Broadway, New York 
 
 \.G* 
 
 [.Entered as second-class matter at the New York, N. Y., Post Office, June 14, 1894.] 
 
 \rQ9is3i* 
 
 ,.., 
 
98 
 
 102. If an anchor ring of copper, wood, glass or other 
 non-magnetic material be uniformly wrapped with 
 a magnetizing coil, the reluctance of the circuit will de- 
 pend upon the length of the circuit, and on its area of 
 cross-section. In this particular case all the magnetic flux 
 will be confined to the interior of the winding, a compass 
 needle held outside the winding indicating no deflection. 
 Thus, if the mean diameter of the ring in Fig. 36, be 20 
 
 d, 
 
 
 Vlec.Enaineer 
 
 FIG. 36, 
 
 A non-ferric magnetic circuit in which 
 the magnetizing force or flux density is 
 uniform along any circle of radius, such 
 as a, and equal to the M. M. F. divided by 
 the circumference, 2 TCCI. 
 
 
 |r_ j_ -MI 
 
 sji rj 
 
 X v , .-^^ 
 
 v 
 
 I 
 / 
 
 *" .Elec.Enaineer 
 
 PIG. 37. 
 
 A non-ferric magnet circuit in which 
 the magnetizing force or flux density (in 
 the absence of iron) is not the same at 
 different parts of the circuit, and where 
 the quotient of M. M. F. by the flux path 
 length on'y gives the average intensity. 
 
 cms., and its cross-section five square centimetres, the mean 
 length of the magnetic circuit will be 62.83 centimetres, 
 
 and the reluctance of the circuit approximately ^ 
 = 12.566 oersteds. 
 
 62.83 
 
 103. If now the same coil be wound on a core of iron 
 of the same dimensions, the magnetic flux within 
 the iron will be far greater than within the previous copper, 
 wood and glass core. 
 
99 
 
 104. In the voltaic circuit, as we have seen, there 
 exists in nearly all cases that practically occur, 
 
 a distribution of electric potential, and the total difference 
 of potential expressed in volts is the E. M. F. in the 
 circuit. 
 
 Similarly, in the magnetic circuit, in nearly all cases 
 that practically occur, there exists a distribution of mag- 
 netic potential and the total difference of potential ex- 
 pressed in gilberts is the M. M. r. in the circuit. 
 
 The distribution of potential is diagrammatically 
 indicated in any magnetic circuit by broken lines, 
 which are the sections, in the plane of the paper, of 
 surfaces connecting all points in the magnetic circuit 
 having the same potential, that is, equipotential sur- 
 faces. These imaginary equipotential surfaces may be 
 made as numerous as desired. If correctly drawn, they 
 would everywhere intersect the magnetic flux-paths or 
 stream-lines at right angles. In other words, the flux 
 at a point is always normal to the equipotential surface 
 through the point. 
 
 105. The magnetizing force, or, as it is sometimes 
 termed, the magnetic force in the circuit, is the 
 
 space rate of change or gradient of the potential. That is 
 to say, the magnetizing force at a point is numerically equal 
 to the number of gilberts variation of potential per cen- 
 timetre of flux-path. Its direction is along the lines of 
 flux, normal to the equipotential surfaces. Where the rate 
 of change of potential along the flux-path is one gilbert 
 per centimetre, as guaged by an indefinitely small ex- 
 cursion, the magnetic force is unity, or one gauss. If 
 the rate of change in potential per centimetre of flux- 
 path were 500 gilberts, the magnetizing force there ex- 
 
100 
 
 isting would be 500 gausses. It is customary to express 
 magnetizing force by 3C, and by the foregoing definition, 
 
 3C = i ; where 0, is the magnetic potential and n, 
 an 
 
 the normal to the equipotential surface at the point. It 
 will be seen that if, gilbert by gilbert, all the equipoten- 
 tial surfaces in a magnetic circuit are drawn ; where they 
 lie close together, the number of gilberts per centimetre 
 will be great, and 3C is great ; and where they lie far apart, 
 the gradient of potential is small, and 5C, is small. "When 
 the equipotential surfaces lines are straight and parallel, 
 they are also equidistant, so that 3C, is uniform, and has 
 everywhere the same strength and direction. Where 
 they are concave or convex in the direction of the flux, 
 there 5C is either convergent and increasing, or divergent 
 and decreasing. 
 
 "When the circuit is non-ferric, the magnetic force 3C, is 
 identical with the flux density, which we have hitherto 
 denoted by (B. When, however, the circuit contains 
 iron, the distribution of 3C, or the prime flux, sets up a 
 structural M. M. F. in the iron, whose flux, merged with 
 5C, gives a resultant distribution, represented by (&. 
 
 It is evident tha since 3C, is the gradient of the poten- 
 tial, the product of the gradient and a small length of 
 flux-path gives the fall of magnetic potential in that 
 length. Summing up in this way, along any flux-path, 
 the product of gradients and small distances, in succes- 
 sion, the sums will be the total difference of magnetic 
 potential in the circuit, or the M. M. F. In other words, 
 the M. M. F. is the line integral of the magnetic force. 
 
 Thus, referring to Fig. 30, if a, be the radius in centi- 
 metres of any flux-path, then the length of that path 
 
101 
 
 is 2 TT #, and since the intensity OC, in gausses, has the 
 same value all round this circle, the line integral once 
 round the circuit on this flux path is 
 
 or or 
 
 2 TT a 5C = F gilberts ; or, 3C = _ _ gausses ; 
 
 1 JT d JL/ 
 
 where .Z, is the length of the flux-path considered. 
 
 106. In general, however, this rule can not be applied. 
 For if, in the non-ferric circuit shown in Fig. 37, 
 formed by a helix of, say, twenty turns carrying one 
 ampere, if we divide the M. M. F. of 20 ampere turns, i. e., 
 25.14 gilberts, along any path of flux, such as a b c d ef, 
 by the length of the path, we only obtain the average 
 magnetic force. The magnetic force will be greater 
 than this mean value within the helix, and less than this 
 mean value outside the helix where the paths diverge. 
 
 The magnetic force receives its name from the fact 
 that if a unit magnetic pole could be isolated (a physical 
 impossibility) and introduced into the magnetic circuit 
 at any point, such as c, the mechanical force which would 
 be exerted upon this unit magnetic pole would be equal 
 in dynes to the value of 3C, in gausses, at that point. 
 
 It has been found that a comparatively simple relation 
 holds between the magnetizing force exerted through 
 iron or steel, and the apparent magnetic reluctance it 
 offers. We have already pointed out that it is not the 
 reluctance, but a structural M. M. r. which varies under 
 the action of an impressed prime magnetizing force. 
 Practically, however, it is convenient to regard the effect 
 as one of change of reluctance. Fig. 38 represents the 
 variation of the apparent reluctance of various samples 
 of iron and steel under a continuously increased magnetic 
 force. It will be seen that the reluctance commences in 
 
102 
 
 70 80 90 
 
 Elec. Engine* 
 
 10 20 30 40 6>" 
 
 MAGNETIZING FORCE crC (GAUSSES)- PRIME FLUX, 
 FIG. 38. 
 
 Curves of reluctivity in iron and steel in relation to magnetizing force. 
 
103 
 
 all cases at a certain value, and diminishes as the mag- 
 netic force is increased, to a critical value, where the 
 reluctance turns and commences rising steadily in a 
 straight line. 
 
 Thus the lowest full line curve, No. VII, represents 
 the reluctivity of soft annealed Norway iron. For 
 magnetizing forces above 3 gausses, the reluctivity fol- 
 lows an ascending straight line, and at 90 gausses reaches 
 5.45 millioersteds. If reluctivity be denoted by the 
 Greek symbol v, we have, therefore, beyond the value of 
 3C = 3 
 
 v = (0.3 + 0.057 X) -T- 1000, 
 
 and similarly for other samples of iron or steel. 
 
 Reluctivity is, strictly speaking, expressed in the c. G. s. 
 system, as a numeric. In Fig. 38, it is, for convenience, 
 expressed in millioersteds, and the curves may be there- 
 fore directly interpreted as representing the reluctance 
 of a centimetre cube. 
 
 107. Since the ether pervades even the densest mat- 
 ter, the reluctivity of any medium may be re- 
 garded 'as the reluctivity of that ether and of the medium 
 taken in parallel. For low values of the magnetizing 
 force, the reluctivity of the ether is so much greater than 
 that of iron (say, 1,000 times greater), that it may be 
 neglected. This linear relation v a + & 3C, which ap- 
 pears to hold from experimental evidence, refers only to 
 the metallic reluctivity of the iron or steel, independ- 
 ently of the ether which prevades the metal. When, 
 however, very high magnetizing forces are reached, the 
 reluctivity of the iron increases greatly and becomes 
 much greater than that of the ether, whose reluctivity 
 therefore controls. The reluctivity of iron and the 
 
104 
 
 ether together can, therefore, never be greater than unity. 
 For practical purposes, however, iron is always worked 
 at such magnetizing forces, that its metallic reluctivity 
 is always much lower than unity, and consequently the 
 metallic reluctivity may be taken within the limits of 
 the diagram to be sensibly equal to the real reluctivity 
 of the ether and iron together. 
 
 SYLLABUS. 
 
 Reluctance is that quantity in a magnetic circuit which 
 limits the flux under a given M. M. F. 
 
 The reluctivity of any medium is its specific reluct- 
 ance, and, in the c. G. s.- system, is the reluctance offered 
 by a cubic centimetre of the body between opposed 
 faces. 
 
 The unit of reluctance is called the oersted, and is the 
 reluctance of a cubic centimetre of air-pump vacuum. 
 
 The reluctivity of all media with the exception of the 
 non-magnetic metals is practically the same, i. e., unity. 
 
 The reciprocal of magnetic reluctivity is called mag- 
 netic permeability, and both quantities are mere numerics 
 in the existing c. G. s. system of units, but are probably 
 not simple numerics in the, as yet, undiscovered true 
 relations of this system. 
 
 It is erroneous to suppose that magnetic permeability 
 or reluctivity varies in iron under magnetic force, except, 
 perhaps, within small limits. The apparent variation is 
 due to the existence of a structural M. M. F. induced in 
 tlie iron under the influence of a prime magnetic force. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.") 
 
 WEEKLY. 
 
 
 
 .No. U. SEPTEMBER 15, 1894. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GTCADE 
 
 iVtAQNETIC 
 
 108. The fundamental equation 01 the magnetic cir- 
 cuit is 
 
 = - ; or, the webers = ilbert8 . (1) 
 
 (R oersteds 
 
 From this we 6btain 
 
 & = <J> (R, (2) 
 
 and 
 
 = ; (3) 
 
 There are, therefore, two ways of varying the mag- 
 netic flux i:i any circuit ; namely, by increasing the 
 M. M. F., and by decreasing the reluctamce. 
 
 As we have already seen, a linear relation exists be- 
 tween the reluctivity of a magnetic metal and the mag- 
 netizing force, but in many practical magnetic problems 
 it is the flux density, rather than the magnetizing force, 
 which is known, and from which the reluctivity has to 
 be determined. It becomes necessary, therefore, to know 
 
 Published by 
 THE ELECTRICAL ENGINEER, 
 
 203 Broadway, New Vork N. Y. 
 
 [Entered as second-class matter at the New York, N. Y., Post Office, June 14, 1894.] 
 
106 
 
 the value of the reluctance of the circuit from point to 
 point at the existing flux density, in order that the total 
 reluctance of the circuit may be determined. 
 From the relation 
 
 v = a + b 3C (4) 
 
 and 
 
 corresponding to i = for the electric circuit, we obtain 
 
 109. Fig. 39 represents a series of curves showing 
 the reluctivity of various samples of iron and 
 
 steel at different flux densities up to 19 kilogausses, 
 taken from actual observations with materials employed 
 in dynamo construction. These curves conform to 
 equation (6), through the ascending branch, the corres- 
 spoiiding flux densities of which are those practically 
 employed in designing dynamo machinery. The des- 
 cending branches are not expressed by equation (6). 
 They belong to the reluctivity at early stages of the mag- 
 netizing force or flux density. 
 
 In order to show the application of the preceding 
 formulae, we will consider some cases similar to those 
 which may arise in practice. We will first take the simple 
 case of the ferric^ circuit, in anchor ring form, shown in 
 Fig. 40, uniformly wound so as to have no leakage. 
 
 110. The corresponding case of electric flux is shown 
 in Fig. 41, where a number of voltaic cells are 
 
 connected in a circle in series. Here, neglecting the in- 
 fluence of temperature, the resistance of the circuit be- 
 comes independent of the current density. The case is 
 
lor 
 
 ABSCISSAE; FLUX DENSITY, GAUSSES(CJ&) 
 
 I I I I I I I 1 I I I I I I I 1 | | 
 
 I-H' c$W^*ooi>ccoiO-i j eo H* us to t~ oo 
 
 TOTA' MAGNETIC INTENSITY OR FLUX DENSITY (SS) GAUSSES EUc.Engineer 
 
 FIG. 39. 
 
 Curves of reluctivity ia iron and steel in relation to fluy density, from measurements 
 by Kennelly. 
 
108 
 
 not an exact analogue unless the reluctivity of the 
 electric conductor be modified to suit the magnetic 
 intensity. Suppose this ring composed of Norway 
 iron, to be of the dimensions shown, and wound with 
 300 turns of insulated wire which carries a current of 
 4 amperes. The M. M. F. for this winding will be 1,200 
 ampere-turns = 1508.1 gilberts. The magnetizing force 
 
 Elec-Enaineer 
 
 FIG. 40. FIG. 41. 
 
 Sections of a Norway iron ring. Ferric Diagrammatic representation of electric 
 
 magnetic circuit. Mean circumference circuit. The analogue of magnetic cir- 
 94.25 cms. Cross-section 19.635 sq. cms. cuit in Fig. 40. 
 
 will be this M. M. r. divided by the length of the mag- 
 netic circuit, which will vary between the limits of the 
 outer and inner circumferences. Taking the mean circum- 
 ference, the mean prime intensity will be - 1 -^|^ 4 - = 16.01 
 gausses, and this would be the flux density if the ring 
 were made of wood instead of iron. By reference to 
 Fig. 38, it will be seen that, at this magnetizing force, 
 the reluctivity of Norway iron is 0.00121 ; and, since 
 the cross-section of the core is 19.635 sq. cms. the re- 
 luctance of the circuit is -$5 X 1.21 = 5.807 milli- 
 
109 
 
 oersteds = 0.005807 oersted, and the flux produced in 
 the circuit will, therefore, be T .V|&%*T = 272,200 webers 
 or 272.2 kilowebers, with a mean flux density of Sfgrfff. 
 = 13,860 gausses, or webers per square centimetre of 
 cross-section, i.e., 13.86 kilogausses. 
 
 111. Taking now the case of an electro-magnet of 
 
 the dimensions shown in Fig. 42, the magnetic 
 
 circuit having two air-gaps in series, we will first assume 
 
 01.3 crnj. 
 
 Elec. Engineer 
 
 FIG. 42. 
 
 Electromagnet of wrought iron, aero-ferric circuit. Air gaps % in. = 1.27 cm. Mean 
 length of magnetic circuit 140.24 cms. Cross-section of magnetic circuit 25 sq. cms. 
 
 that the leakage is negligibly small. The magnetic cir- 
 cuit is, therefore, considered as entirely confined to the 
 path of the arrows, 1, 2, 3, 4, leaving the other paths for 
 later consideration. Let us suppose that it is required to 
 find the M. M. r. which will be necessary to produce a 
 flux of 250 kilowebers, through the keeper. Assuming 
 that this magnet is entirely constructed of wrought iron, 
 and that the air-gap is fixed, as, for example, by means 
 of wooden wedges, so that the keeper is unable to ap- 
 proach the poles, then the reluctance in each gap is 
 i-|j 0.0508 oersted. The density of the flux in the 
 iron of the circuit is 10 kilogausses, and by referring to 
 
110 
 
 Curve YL, Fig. 39, it will be seen that at this density the 
 reluctivity of ordinary wrought iron is 0.00095. Since 
 the mean length of the circuit in the iron is 137.7 
 cms., and its cross-section is 25 sq. cms., the reluctance 
 of the iron will, therefore, tie -if -JJ X 0.95 == 5.23 milli- 
 oersteds 0.00523 oersted, and the total reluctance of 
 the circuit 0.1068 oersted. The M. M. F. required to send 
 
 0.001476 Ohm 
 309 Volts Elec.Engineer 
 
 FIG. 43. ELECTRIC CIRCUIT ANALOGUE. WITHOUT LEAKAGE. 
 250,000 webers through this circuit, will be 250,000 X 
 0.1068 = 26,700 gilberts = 21,256 ampere-turns. If 
 the spools have the same winding there must be 10,628 
 ampere-turns on each spool. 
 
 The corresponding electric case is shown in Fig. 43. 
 
 112. Let us now assume that the electro-magnet pos- 
 sesses an appreciable leakage, and let us assume 
 that this leakage takes place, as shown diagrammatically 
 in Fig. 42, along the paths 5, 6, 7, 8, 9, 10, 11, 12 and 
 13, 14, 15, 16. Let it be ascertained that this leakage 
 amounts to 33| per cent, of the total flux, so that for 
 
Ill 
 
 every 100 webers of flux in the interior of the field cores 
 only 66 1 pass through the keeper. It is required to find 
 the M. M. F., which will enable 250 Mlowebers, as before, 
 to pass through the keeper under these circumstances. 
 
 The effect of leakage is not only to reduce the effective 
 cross-section, which may carry the main circuit flux, but 
 also, owing to the increase in density, to increase the re- 
 luctivity of that reduced cross-section. 
 
 Similarly, if it be known that the leakage flux through 
 the yoke, in the path 6, 7, is 50 kilo webers, the total 
 
 KEEPER 
 
 FIG. 44. ELECTRIC CIRCUIT ANALOGUE. WITH LEAKAGE. 
 
 flux through the yoke will bo 300 kilowebers, and the 
 flux density there -%- = 12 kilogausses. At this den- 
 sity, the reluctivity of wrought iron by Curve VI., Fig. 
 30, is seen to be .001316. 
 
 113. Referring to Fig. 44, which represents the elec- 
 trical analogue of this case, observe that each core 
 may be regarded as the seat of an E. M. r. impressed on 
 three independent circuits, numbered to correspond with 
 Fig. 42. J A , 7? B , and 7? c , are fixed reluctances through 
 air, depending upon the dimensions and arrangement of 
 
112 
 
 the various parts of the magnet. They have perfectly 
 definite values, but these values may be very tedious 
 and difficult to compute. The reluctances O i9 <7 2 , 63, 
 4? <?? ft? ^3 an d ^e depend upon the share of iron 
 allotted to each branch circuit, and also to the flux den- 
 sity. We proceed to determine the various reluctances 
 6 y 2 , '^3, G, ^?5, ^j? an( l #a> in tne main circuit, and call- 
 ing their sum (R, we have the simple relation 
 
 
 
 G 
 
 o 
 
 UP 
 
 i 
 
 
 
 gj 
 
 
 
 F 
 
 1 
 
 18* 
 
 - 
 
 M 
 
 * 
 
 
 
 s 
 
 W c 
 
 v.-, C?Cr 
 
 3 . 
 
 
 
 *j en 
 
 Reluctance Oersteds. 
 
 
 
 
 
 E 2 
 
 .r w 
 
 
 
 d 
 
 o 
 
 A 
 
 
 
 o fc * 
 
 LjS 
 
 $i 
 
 ^ 
 
 
 
 I 
 
 cr 
 
 ^uiz 
 
 Is 
 
 sa 
 
 J2 w 
 
 
 (2 
 
 J 
 
 H 
 
 C/3 
 
 H 
 
 Q 
 
 OS 
 
 
 Core 
 
 3 
 
 25 
 
 16.667 
 
 375 
 
 15 
 
 3-77 
 
 ,-^X ^=0.005539 
 
 Yoke.... 
 
 38.85 
 
 2 5 
 
 20.833 
 
 300 
 
 12 
 
 1.316 
 
 38.85 X 1 -3i6 
 
 20.833 looo" - 00245 ^ 
 
 Core .... 
 
 3 
 
 25 
 
 16.667 
 
 375 
 
 15 
 
 3-77 
 
 I ^ 7 X^=o.oo S 539 
 
 Air-gap.. 
 
 1.2 7 
 
 2 5 
 
 25 
 
 250 
 
 10 
 
 1000 
 
 1.27 
 X i =0.050800 
 
 Keeper .. 
 
 38.85 
 
 25 
 
 25 
 
 250 
 
 IO 
 
 0-95 
 
 38 85 0.95 
 
 Air-gap. 
 
 1.27 
 
 25 
 
 2 5 
 
 250 
 
 10 
 
 1000 
 
 1.27 ^ T 0.050800 
 
 25 o.i 1 6608 
 
 To force 250 t:ilowebers through the main circuit 
 through this reluctance, a M. M. r. will be needed of 
 250,000 X 0.116608 = 29,152 gilberts, or 23,200 am- 
 pere-turns 11,600 to each spool. 
 
 SYLLABUS. 
 The fundamental equation of the magnetic circuit is 
 
 F gilberts 
 
 = S rtheWeberS ^ oersteds' 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 No. 15. SEPTEMBER 22, 1894. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GRADE. 
 
 ELBCTROMAQNBTS. 
 
 114. The polarity of an electromagnet may be deter- 
 mined by noticing the character of the magnetiz- 
 ing coils, whether right-handed or left-handed, and the 
 direction in which the current traverses them. A right- 
 handed helix carries the flux in the same direction as 
 that in which the current advances along the helix, while 
 a left-handed helix carries the flux in the opposite direc- 
 tion of the advance of the current.. As already pointed 
 out, the flux in an electromagnet is of two distinct 
 characters ; namely, the prime or magnetizing flux, and 
 the induced or structural magnetic flux, which is called 
 into play by the action of the prime flux. 
 
 115. Electro-magnets may be divided into two classes; 
 namely, the tractive and the portative ; the former 
 
 are designed to exert a pull on their armature at some 
 distance from the poles, and the latter are designed to 
 support a pull upon the armature when the armature is 
 placed in contact with the poles. 
 
 Published by 
 THE ELECTRICAL ENGINEER, 
 
 203 Broadway, New York N. Y. 
 
 [Entered as second-class matter at the New York, N. Y., Post Office, June 14, 1894.] 
 
114 
 
 In all practical cases an electromagnet exerts a 
 pull upon the iron or steel of the armature whether 
 the armature be separated from the poles by an air- 
 gap, or whether it be in actual contact with the poles, 
 and the same process of calculation has to be employed 
 in each case in order to compute the attractive force. 
 This process is substantially as follows : The reluctances 
 of the different parts of the circuit have to be de- 
 termined and summed, the M. M. F. acting in the cir- 
 cuit has then to be ascertained, and from these the flux 
 in the circuit is deduced. From the flux and its distri- 
 bution, the flux density in the air-gap between the keeper 
 and poles has to be found, and from this flux density, 
 the intensity of the attractive force is determined from 
 point to point. The total attractive force on the arma- 
 ture will be the surface integral of this attractive force 
 over the area of the attracting surfaces. 
 
 116. The fundamental law of attractive force is as 
 follows: At any element of surface on iron or 
 steel at which flux enters or emerges perpendicularly, 
 the attractive force in dynes, exerted upon the element, 
 will be the product of the elementary surface area into 
 the square of the flux density (expressed in gausses), 
 divided by 8 TT ; that is, 
 
 dF=dS dynes, 
 
 STT J 
 
 where (B, is the normal flux density ; d F, the element 
 of attractive force, and d $, the element of surface in 
 square centimetres ; and this force will be exerted along 
 the flux paths, or perpendicular to the surface. If, how- 
 ever, the entering or emerging flux makes an angle 6, 
 with the normal to the surface, then the above rule re- 
 
115 
 
 quires slight modification. The equivalent normal 
 surface, on which the attractive effort is exerted, is d S 
 cos 0, so that the attractive force becomes, 
 
 1 C1 a /T 9 
 
 dynes, 
 
 Sx 
 
 exerted in the direction of the flux-paths of which the 
 component perpendicular to the surface is, 
 
 FIG. 45. 
 
 Flux normal to opposed plane parallel 
 polar surfaces. 
 
 Elec. Engineer 
 
 FIG. 46. 
 
 Flux oblique to polar surfaces. 
 
 117. Let A B c D, and A' B' c' D', Fig. 45, be portions 
 of two parallel plane polar faces of iron between 
 which the magnetic flux passes perpendicularly across 
 the intervening space A A', or c c'. If the flux intensity 
 is uniform over these surfaces and equal to five kilo- 
 gausses, then the mechanical force exerted between any 
 pair of opposed unit areas, such as the shaded portions 
 e f ff h, and e' f g' h r , each one square centimetre, will 
 
116 
 
 be 500Q X 50QQ or approximately 994,800 dynes, or 
 
 8 7T 
 
 1,015 grammes weight (2.238 pounds), at Washington. 
 Since the total area A B c D, or A' B' c' D' is 25. square 
 cms., the total mechanical force exerted between these 
 surfaces will be 25.375 kilogrammes (55.95 pounds). The 
 magnitude of the attractive force does not depend upon 
 the distance A A', separating the polar faces, nor does it 
 depend upon the direction of the flux between them. 
 All that is essential is that the flux should be perpendi- 
 cular to the faces. Increasing the air-gap will, in prac- 
 tice, usually diminish the total flux, and, therefore, the 
 flux intensity over the surfaces, also causing the flux 
 paths to deviate from the perpendicular by lateral dif- 
 fusion ; but if these secondary effects could be compen- 
 sated and removed, the attraction between the surfaces 
 would not vary witli the length, of air-gap. 
 
 118. Fig. 46 represents a case where the flux passes 
 between the parallel polar faces at an angle /?, 
 with their normal. If a I c d, and e f g A, are areas 
 limited by the flux-paths a e p, 1} I q, c g r and d h n, 
 then the attractive force between these areas will be 
 such as would be experienced by two surfaces each of 
 the area Icl g m, standing perpendicularly across the 
 flux. If a b G d, and e f g A, have each an area of one 
 square cm., the surface k I g m, will have an area of 
 cos /? square cms. With 10 kilowebers passing through 
 each of the shaded areas, the flux density will be 
 
 = ^ . The attractive force between two opposed 
 
 cos/3 
 
 /r>2 
 
 parallel surfaces of area Tc I g m, will be cos /? ex- 
 
 8 71 
 
117 
 
 erted along the flux paths. The component of this ten- 
 sion exerted across the actual surfaces abed, and ef g k, 
 
 (B 2 
 
 will be cos 2 /9, and the component tending to make 
 8 JT 
 
 II 
 
 ie.000 
 
 15.000 
 14,000 
 13,000 
 18,000 
 11,000 
 10,000 
 9,0000 
 8,0000 
 7,0000 
 0,0000 
 6,0000 
 4,0000 
 3,0000 
 2.0000 
 1,0000 
 
 !! 
 
 I 
 
 16,000,000 
 15,000,000 
 14,000,000 
 18,000,000 
 12,000,000 
 11,000,000 
 10.000,000 
 
 9.000,000 
 8,000,000 
 7.000,000 
 6,000,000 
 6,000,000 
 4,000,000 
 8,000,000 
 2.POO.OOO 
 
 l.ooo.ooo 
 
 
 
 Ii 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 200 
 190 
 
 uo 
 III 
 
 170 
 
 160 
 150 
 140 
 130 
 
 IM 
 
 no 
 
 100 
 90 
 
 70 
 CO 
 
 40 
 30 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 , 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 II] 
 
 / 
 
 
 ii 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 ,f 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 f 
 
 
 t 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 '/ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 /' 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 J 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 f 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 ,/ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .' 
 
 
 J? 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 * 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 V 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 r-^ 
 
 >> 
 
 -^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Mis 
 
 KILOGAUSSES 
 
 B2 9 & 2 9 tf 1 3 1 1 2 2 2 I 2 2 2 d 
 
 K * *. a 
 p- ^ a 
 
 KILOWEBERSPERSQ. 
 
 Elec.Engineer 
 Cvt\e& representing the intensity of magnetic stress, for all values of 30 
 
 from O to 20 Kilogausses. O to 129 Kilowebers per sq. in. 
 I in. dynes per square centimetre.il in grammes weight per square centimetre 
 III jn pounds weight per square inch. 
 
 FIG. 47. 
 these surfaces shear across one another would be 
 
 (B 21 
 
 - sin ft cos ft. 
 
 O 71 
 
 In practice, the useful flux exerting tractive force be- 
 
118 
 
 tween the polar surfaces of electromagnets may be con- 
 sidered as crossing those surfaces at right angles, so that 
 the simpler formula may generally be applied. 
 
 119. As a consequence of the preceding formulae it 
 is evident that the active polar surfaces of a port- 
 ative electromagnet should have as great an area as pos- 
 sible, provided that the flux density over them be made 
 as great as possible. In other words, the polar surfaces 
 should have maximum areas consistent with their mag- 
 
 Elec.Engineer 
 
 FIG. 48. 
 Section of Portative Electromagnet through Axis, and Polar Surfaces. 
 
 netic saturation. The curves in Fig. 47 show that at a 
 density of 18 kilogausses, which is readily obtainable in 
 ferric magnetic circuits employing soft Norway iron, the 
 attraction becomes 1 3.14 kilogrammes per square cm., or 
 186.6 pounds per square inch of opposed polar surfaces. 
 
 120. A convenient practical form of electromagnet 
 
 for sustaining heavy weights is shown in Fig. 48. 
 
 The magnetic circuit is indicated by the lines of arrows. 
 
119 
 
 The external surface of the magnet when the keeper 
 is in place, being entirely of iron, the magnet is usually 
 described as belonging to the ironclad type. The con- 
 tact polar surfaces should be carefully planed and kept 
 clean if the best attractive results are to be obtained. 
 The space allowed for the exciting coil is made as small 
 as is consistent with saturation of the polar surfaces. 
 The limiting M. M. F. that can be employed for a given 
 winding space depends upon the heating of the coil by 
 the current, and not upon the size of the wire. Practi- 
 cally, however, a large wire with few turns can be better 
 protected against damage from a high temperature, than 
 a small wire with many turns. It is essential that the 
 flux density should be a maximum in the circuit at the 
 polar surfaces, and for this reason the surface area of 
 the inner core and outer ring should be kept equal while 
 a slight constriction in the iron should 'be made at the 
 poles. 
 
 If such a magnet have a cross-sectional area of 20 
 square cms. at the inner or core polar surfaces, and also 
 10 square cms. at the outer or annular polar surfaces, the 
 portative power of the magnet may readily be 40 X 15 
 = 600 kilogrammes weight. 
 
 121. When an electromagnet has to exert a tractive 
 force upon its armature at a distance, through one 
 or more air-gaps of given length, the best area of polar 
 surface to employ with a fixed M. M. F., and the size of 
 magnet are those which make the reluctance of the air, 
 equal to the reluctance of the iron in the circuit. If, 
 for example, an electromagnet has two poles each four 
 centimetres in diameter, and the air-gap or distance be- 
 tween poles and armature be 0.25 cm., then the area of 
 
120 
 
 each pole face will be 12.57 square cms., and the reluct- 
 ance of the air 0.0398 oersted. If the reluctance in the 
 iron be, say, 0.050 oersted, under these conditions with 
 the M. M. F. employed, it will be advantageous to increase 
 the air reluctance by constricting the polar surfaces until 
 the air and iron reluctances equate. This assumes, how- 
 ever, as negligible, leakage and diffusion of flux at the 
 polar surfaces. In consequence of leakage and diffusion, 
 it is preferable to make the air reluctance somewhat less 
 than the iron reluctance. 
 
 SYLLABUS. 
 
 The direction of magnetic flux within a coil is in the 
 direction along which the current traverses the coil if 
 the coil be right-handed, and opposite to the direction 
 of the current if the helix be left-handed. 
 
 The fundamental law of tractive force upon a mag- 
 netized surface, at which flux enters or issues perpendir 
 
 cularly, is d F = d 8 dynes. 
 
 8 7T 
 
 Portative electromagnets are designed to have as large 
 an area of saturated polar surfaces as possible. 
 
 Powerful tractive magnets are designed to have their 
 reluctance about equally divided between air and iron. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 No. 16. SEPTEMBER 29, 1894. 
 
 Electrical Engineering Leaflets, 
 
 BY 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A, S. 
 
 ADVANCED GRADE. 
 
 INDUCED EX IVL K. 
 
 122. Whenever relative motion exists between mag- 
 netic flux and an electric conductor, so that one 
 
 moves across the other, an E. M. F. will be set up in the 
 conductor. This relative motion between flux and con- 
 ductor may occur in two ways ; namely, 
 
 (1.) When the conductor moves across the flux. 
 
 (&) When the flux moves across the conductor. 
 Both cases may occur together, but in (1) we suppose 
 that the flux may be considered as at rest, and in (2), 
 that the conductor may be considered at rest. 
 
 123. We will now consider case (1), in which the 
 conductor moves across a magnetic flux. Al- 
 though the mechanism by which E. M. F. is induced is 
 unknown, yet the E. M. F. produced is directly propor- 
 tional to the total amount of flux per second cut by the 
 conductor, and this clearly depends on two quantities ; 
 namely, upon the velocity of the conductor across the 
 flux, and, upon the intensity of the flux. 
 
 Published by 
 THE ELECTRICAL ENGINEER, 
 
 203 Broadway, New Vork N. Y. 
 
 [Entered as second-class matter at the New York, N. Y M Post Office, June 14, 1894.] 
 
122 
 
 124. Consider, first, a uniform magnetic flux, whose 
 intensity at a given point is equal to (B, and is di- 
 rected as shown by the arrows, Fig. 49. A rectilinear 
 conductor A B, normal to the flux, is moved in a direction 
 normal to the flux with a velocity v, which would carry 
 it in one second to A' B'. Then the total amount of flux 
 cut per second would be the amount passing through the 
 rectangle ABB' A', -and this is clearly equal to 
 
 e = v I (B c. G. s. units of E. M. F. 
 
 Suppose, however, that a conductor lying in a position 
 oblique to the flux, as shown in Fig. 50, is moved in a 
 
 B ^ 
 
 
 
 * ^ 
 
 
 
 -* 
 
 *>' ^ 
 
 
 N< 
 >* 
 
 /l^*- B' 
 
 
 -* 
 
 ^^^^^x 
 
 b' 
 
 "* ^ 
 
 A ^*^C^ ** ^i 
 
 ''T~-^ 
 
 . 
 
 ^ i ^ ^ ^ i H 
 
 a r'--^j^^^^ B ' 
 
 3 ". 
 
 U ^ T^ 1 
 
 
 ~k 
 
 ^ ^ -*b| *i 
 
 > S^ 
 
 
 'A ^ **+ % 
 
 ^ ,--. ^/ i/, , x 
 
 
 V. ~Sk. -X^ 1^1 
 
 :\^^ B 
 
 R>^A / 
 
 ^ <^'*/^. ^^' 
 
 
 ^ 
 
 ^ 
 
 FIG. 49 FIG. 50. FIG. 51. 
 
 Conductor normal toflux. Conductor oblique, to flux, Conductor oblique to flux, 
 moving in direction normal moving of conductor in di- moving in direction othque 
 to flux. rection normal to flux. to flux. 
 
 direction normal to the uniform flux with a uniform 
 velocity v ; then the total amount of flux cut per second 
 will be that enclosed by the rectangle A J 1}' A', where 
 A J, is the virtual length of the conductor equal to 
 A B cos /9, that is, the projected length normal to the flux, 
 and the E. M. r. is equal to 
 
 e = v I cos /9 (B c. G. s. units. 
 If both the position of the conductor, and its motion 
 are oblique to the direction of the flux, as in Fig. 51, 
 
123 
 
 then the total flux cut per second will be that enclosed 
 by the rectangle A b ~b' A', where A B, is the virtual 
 length of the conductor, as before, and A a', is the virtual 
 velocity normal to the flux, or A A' cos . So that 
 
 e = v cos a I cos ft & c. o. s. units. 
 
 Since one volt equals 10 8 c. G. s. units of E. M. F., the 
 E. M. F. as above obtained, must be divided by 10* in 
 order to obtain its value in volts. 
 
 FIG. 52. 
 
 125. The direction of the induced E. M. F. varies both 
 with the direction of the flux and with the direc- 
 tion of the motion. The simplest rule for memorizing 
 this direction is, probably, Fleming* B hand rule. 
 
 If the right hand be held, as shown in Fig. 52, with 
 the extended /ore-finger pointing in the direction of the 
 /"lux, and the thumb in the direction of the motion, then 
 
124 
 
 the E. M. F. induced will be directed along the direction 
 in which the middle finger points. 
 
 126. In practice when a conductor is moved through 
 a magnetic flux, it generally happens that neither 
 
 the intensity of the flux nor the velocity in the direction 
 of motion is uniform. Nevertheless, the above law is 
 true for any small element of the conductor at any mo- 
 ment, when its direction and the intensity of the flux in 
 which it moves are taken into account. 
 
 127. Turning now to case (2) where the flux moves 
 across a conductor. The fundamental rule re- 
 mains the same as in the preceding case ; if v, be the 
 velocity of the field at any point, where the intensity is 
 <&, and I be the virtual length of conductor at right 
 angles to the flux and the motion, then the E. M. F. in 
 c. G. s. units is v (B Z, as before. 
 
 128. In order that the induced E. M. F. in a conductor 
 may produce a current, the circuit of that con- 
 ductor must be closed, that is, a conducting loop must 
 be formed, although only a portion of this loop may be 
 active in cutting through flux and generating E. M. F. 
 It is obviously the same whether we speak of the rate at 
 which the portions of the loop are cutting through flux, 
 or of the rate at which a loop is enclosing flux, since the 
 sum of all the lines cut through per second around a 
 loop must be equal to the amount of flux enclosed by 
 the loop in that time. Similarly, when flux is withdrawn 
 from a loop, the E. M. F. will be introduced around the 
 loop in the opposite direction. All these results may be 
 included in the following equation : 
 
 =<** 
 
 dt' 
 
125 
 
 where 0, is the flux enclosed by the loop (webers) in the 
 positive direction, and - the instantaneous rate of 
 
 Ci t 
 
 change of that flux. 
 
 129. A consideration of Figs. 49, 50 and 51 will 
 
 render it -evident that E. M. F. is never produced 
 
 by the relative motion of magnetic flux and a conductor, 
 
 unless a change exists in the amount of flux enclosed by 
 
 FIG. 53. 
 
 Conducting ring normal to flux, mov- 
 ing in plane normal to uniform flux. 
 
 FIG. 54. 
 
 Conducting ring normal to flux, mov- 
 ing in a plane normal to a non-uniform 
 flux. 
 
 the conducting circuit. It is evident, therefore, that if 
 the conducting ring, shown in Fig. 53, though normal to 
 the uniform magnetic flux, and moving at right angles 
 to such flux, so as to cut the flux, has, nevertheless, no 
 resultant E. M. F. generated in it, since at any moment of 
 time the flux it encloses is constant ; or, if regarded from 
 the standpoint of Fig. 49, the E. M. F. generated by the 
 cutting in the upper half of the loop, is exactly equal 
 and opposite to the cutting in the lower half. 
 
126 
 
 The conducting ring, shown in Fig. 54, placed normal 
 to the non-uniform flux, if moved in its own plane in 
 any direction except in the directions F G, or G F, will 
 have a resultant E. M. F. generated in it, since the amount 
 of flux enclosed by the loop will otherwise increase or 
 diminish. 
 
 130. If a conducting loop, placed in a uniform mag- 
 netic flux, be rotated about any axis, as, for ex- 
 ample, about the axis H K, in Fig. 55, a resultant E. M. F. 
 
 FIG. 55. 
 
 Rotation of a Loop in a Magnetic Flux. 
 
 will be induced in it, since the amount of flux enclosed 
 by the loop will vary. Thus, in rotating the loop from 
 A to A', the flux enclosed will be reduced from the total 
 area ABC, to the virtual area def. Since the value 
 of the E. M. F., at any instant, is the time rate of change 
 of the flux enclosed by the circuit, it is evident that the 
 maximum E. M. F. is produced when the plane of the loop 
 is parallel to the direction of the flux. 
 
12Y 
 
 131. When a current through a conductor is chang- 
 ing its strength, there will, as we have already 
 seen, be a change in the amount and intensity of the 
 flux surrounding the conductor. Since the entire con- 
 ducting circuit, in which the current flows, may be 
 regarded as a loop, or combination of loops, these varia- 
 tions in the flux linked with the conducting loop will 
 induce in the conductor an E. M. F. of exactly the same 
 strength as though the current remained unchanged, but 
 the same flux variations passed through the conducting 
 loop. This E. M. F. induced in a circuit by variations in 
 its current strength is known as a self-induced E. M. F., 
 or an E. M. F. of self-induction. 
 
 Projection of Magnetic Flux through Conducting Loops. 
 
 132. If a current be sent through the electromagnetic 
 helix, shown in Fig. 56, in such a direction as to 
 produce the poles s, N, then the flux established is shown 
 in part by the curved arrows, in the neighborhood of the 
 north pole. As this flux emerges, it will pass through 
 the loops A, D, B, and c; but whereas the same amount of 
 flux passes through each of the two loops A, or B, is 
 greater than that which flows through p, the E. M. F. gene- 
 rated in A, or B, during the change will be greater than 
 that in c, while the double loop D, will have double the 
 E. M. F. in it. The direction of the E. M. F. in these loops, 
 
 UNIVERSITY 
 
128 
 
 on making the magnet circuit, is opposite to that on 
 breaking : for in one case the flux passes through the loop 
 to the right, and in the other case; to the left. Even 
 when the existence of the flux that passes through the 
 loop cannot be determined by the aid of a compass 
 needle, as, for example, in Fig. 57, where the closed cir- 
 cular coil is linked with three separate conducting loops 
 j k Z, h e f g, and m, yet on varying the current in 
 the coil the same E. M. F. will be induced in all three 
 
 FIG. 57. 
 
 Closed Circular Coil linked with three Loops of Conductor. 
 
 loops. This case is apparently an independent demon- 
 stration of the fact that the velocity of the propagation 
 of magnetic disturbances is finite. 
 
 SYLLABUS. 
 
 If $, be the total flux in webers linked with a con- 
 ducting circuit in the positive direction, then ^-^ X 10" 8 
 
 cL t 
 
 is the E. M. F. induced in that circuit in International 
 volts. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER,] 
 
 WEEKLY. 
 
 1 7 fWrmvT? ft 1 SQ4. Price, - 10 Cents. 
 
 rOBER 6, 1 J4. Subscription, $3.00. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GRADE. 
 
 DYNAMO. 
 
 133. A continuous current dynamo, depending as it 
 does for the production of its E. M. F. on the 
 movement of conductors through a magnetic flux, de- 
 termines the magnitude of that E. M. F. in accordance 
 with the relation, 
 
 E = $ n w c. G. s. units, 
 
 n w 10~ 8 volts. 
 
 where <#, is the total useful magnetic flux through one 
 pole passing into the armature (webers) ; n, the number 
 of revolutions made by the armature per second; and w, 
 the number of conductors on the surface of the arma- 
 ture counted in one complete revolution. That is to 
 say, the E. M. F. is directly proportional to the product 
 of the total useful magnetic flux through each pole, the 
 rate of speed of the armature, and to the number of 
 turns of wire. Thus, Fig. 58, represents a four-pole 
 generator for 550 volts. The useful flux through each 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 203 Broadway, New York N. Y. 
 
 Entered as second-class matter at the New York, N. Y., Post Office, June 14, 1894.] 
 
130 
 
 pole may be, say, 55 megawebers ; there are, say, 200 
 conductors embedded in the surface of the armature, 
 and the speed of rotation is assumed to be 300 revolu- 
 tions per minute, or tive revolutions per second. The 
 E. M. F. generated by the machine is, therefore, 
 
 L = 5 X 200 X 55 X 10 6 X 10~ 8 = 550 volts. 
 
 FIG. 58. 
 
 550 Volt Four-Pole Generator. 
 
 134. The output of a generator, or its capacity, is 
 usually expressed in kilowatts, and is the electri- 
 cal activity which the machine can maintain at its ter- 
 minals. This, within wide limits, is independent of the 
 electromotive force ; that is to say, the 100 K. w. machine 
 can be constructed for 1,000 volts and 100 amperes, or 
 for 100 volts and 1000 amperes, or 50 volts and 2,000 am- 
 peres output. There is, however, a practical limit to the 
 E. M. F. which can be obtained from a machine without 
 
131 
 
 altering its rating ; for, very small E. M. r.'s may require 
 such massive construction in their commutators and ad- 
 jacent conducting parts, to carry off the enormous cor- 
 responding currents generated, that the whole structure 
 of the machine may require to be modified, while, when 
 high electromotive forces are reached the great thickness 
 of insulating material required, may so reduce the avail- 
 able winding space as to seriously reduce the output. 
 
 135. When a dynamo-electric generator is operated 
 on open circuit, it is, of course, doing no work, 
 
 since the resistance of its external circuit is infinite. As 
 the resistance of the external circuit is decreased, the 
 amount of work in its circuit increases, until, when the 
 external circuit has no resistance, or the machine is 
 short-circuited, the amount of work in the electric cir- 
 cuit of the machine would be a maximum, and, if it 
 could be reached, would be expressed by the formula, 
 
 E* 
 
 P watts ; where E, is the E. M. F. generated in the 
 r 
 
 armature, and r, is the internal resistance of the machine. 
 This activity may be called the electric capability of the 
 machine, and is similar in nature to the electric capability 
 of a voltaic cell. Of course, no machine of any con- 
 siderable size could be made to run on short-circuit. 
 
 136. Since, useful output can be computed as a cer- 
 tain fraction of the electrical capability, depend- 
 ing on the output of the machine, the electrical capability 
 is by no means of merely theoretical interest. The frac- 
 tion of the electrical capability which represents the 
 output of a machine, may be called the coefficient of 
 reduction from capability to output ', and varies with the 
 
132 
 
 size of the generator, and the details of its structure. 
 For example, in a particular series of bipolar generators, 
 of different sizes, this fraction is 0.15 for generators of 
 one K. w. capacity, and reduces to 0.034 for generators 
 of 100 K. w. capacity. This reduction in the coefficient 
 is partly due to the fact that as the size of the machine 
 increases, the active surface of the armature, offered for 
 the dissipation of heat, increases less rapidly than the 
 mass in which the heat is developed, thus necessitating a 
 relatively diminished output. 
 
 The electrical capability of a generator is independent 
 of the character of the winding, provided the amount 
 of winding space remains constant. This is true, how- 
 ever, only so long as the proportion of winding space, 
 devoted to insulation, remains constant through all sizes 
 of wire ; thus, if the number of turns in the armature 
 be doubled, the E. M. F. will be doubled, but the resist- 
 ance will be quadrupled, since there will be twice as 
 great a length of wire of half the cross section ; hence 
 the ratio of E* to /*, remains the same. 
 
 137. Since the E. M. F. of a continuous current gene- 
 rator is proportional to n w, and its resistance 
 
 is proportional to 2 , where Z, is the length of one turn 
 ct p 
 
 of conductor, , its cross-section, and p, the number of 
 poles, the electrical capability of a machine is propor- 
 tional to <P* n 2 w 2 ^ = tf>* n 2 p z , that is, propor- 
 w I I 
 
 tional to C ( ^j-?\ . w here (7, is the weight of copper 
 on the armature. Consequently, for a given weight of 
 
133 
 
 copper conductor on the armature, and a given cross-sec- 
 tion of armature core, the output of the machine in- 
 creases as the square of the speed of rotation, and as the 
 square of the number of poles in the field frame. Vari- 
 ous considerations, however, incidentally limit the range 
 over which this rule can apply. Thus an increased 
 capability and output may be attended by increased heat- 
 ing or sparking at the brushes, so that the coefficient of 
 output may be lowered. A doubled speed of rotation 
 would double the E. M. F. of the machine, and would 
 quadruple the electric capability, enable twice the cur- 
 rent strength to be delivered at full load at the same 
 electrical efficiency, thus quadrupling the output ; but, 
 if, at the doubled speed, and with the doubled current, 
 the armature unduly heated, the safe load, and coeffi- 
 cient of reduction, would require to be lowered. 
 
 138. In the design of a dynamo, the problem which 
 presents itself is to produce the desired electro- 
 motive force at a given speed of rotation of the arma- 
 ture, determined by mechanical considerations, and to 
 maintain a given current strength at that E. M. F. The 
 problem, therefore, resolves itself into the proper pro- 
 portioning of the amount of flux, the number of turns 
 and size of conductor, and the number of poles in the 
 machine. The value of the output which it is desired 
 to produce, will, in reality, determine whether the ma- 
 chine is to be bipolar, or multipolar, since large sizes of 
 bipolar machines are usually objectionable, partly owing 
 to the large dimensions required. Having determined 
 upon the number of poles, the total flux and the number 
 of turns on the armature only remain to be determined. 
 
 The proper resistance of the armature for the type of 
 
machine required, is known by reference to tables of co- 
 efficients for the electrical capability and output, and, 
 from this resistance one relation between the total flux, 
 the length and the cross-section of wire is given. By 
 trial the size of armature is found upon which the 
 amount of wire of the necessary cross-section and mun- 
 .ber of turns is arrived at. 
 
 139. The magnetic flux requisite under a given con- 
 dition of speed and armature turns, now remains 
 
 to be provided for. The first step is to provide a path 
 of sufficient cross-sectional area through the iron field 
 frame and armature. In order to assign the proper flux 
 density in the magnet cores, it is necessary to assume a 
 certain quantity of leakage. The proportion of leakage 
 is generally taken from observations made on machines 
 of similar type, and is the principal source of uncertainty 
 in the design of any given generator. The ratio of total 
 flux to the useful flux passing through the armature 
 varies from 1.2 to 2.1 in different types of machine. 
 When this ratio is known, the total flux passing through 
 the field cores is known, and the area of cross-section 
 necessary for a given flux density is arrived at. 
 
 140. It will be seen that the reluctivity of the iron 
 employed in the framework of the machine is a 
 
 very important consideration, since on this depends the 
 area of cross-section that must be employed for a given 
 total flux. The core of the armature is always con- 
 structed of a given quality of laminated soft iron, with the 
 flux passing parallel to the laminations. The field mag- 
 nets are sometimes entirely constructed of cast iron, some- 
 times of cast steel, and sometimes of wrought iron in 
 
135 
 
 the core, united with cast iron iii the yoke. The choice 
 of materials depends upon the character of the work the 
 generator is to perform. In the case of cast iron, a flux 
 density of 7.5 kilogausses is approximately the practical 
 limit, while in wrought iron, or cast open hearth steel, a 
 density as high as 17 kilogausses can be employed. The 
 balance of advantage lies between cost of materials and 
 limitations of size and weight. 
 
 141. Slight impurities in wrought iron or soft cast 
 steel have a marked influence upon their reluc- 
 tivity. The most common impurities in iron are carbon, 
 silicon, sulphur, phosphorus and manganese. Of these, 
 carbon produces the greatest influence on reluctivity, 
 and taking the reluctivity of pure wrought iron at an 
 intensity of 7.5 kilogausses as 0.0005, the influence of 
 small quantities of these impurities on the reluctivity 
 appear to be expressed as follows: Carbon, 0.25; silicon, 
 0.11; manganese, 0.06; phosphorus, 0.04, and sulphur, 
 inappreciable. 
 
 Thus, one per cent, of carbon added to pure wrought 
 iron might be expected to increase its reluctivity at 7.5 
 
 kilogausses from 0.0005 to 0.0005 + ' 2 X l = 0.003; 
 
 100 
 
 i.e., to three rnillioersteds in a cubic centimetre of ma- 
 terial. These values can only be regarded as approxi- 
 mations. They appear to vary in different qualities of 
 steel. 
 
136 
 
 SYLLABUS. 
 
 The electromotive force produced by a dynamo, ex- 
 pressed in c. G. s. units, is the product of the flux, the 
 revolutions per second and the number of conductors 
 counted once around the armature, divided by the num- 
 ber of poles. The electrical capability of a dynamo, in 
 watts, is equal to the square of its E. M. F. in volts, 
 divided by its resistance in ohms. 
 
 The ratio of the total to useful flux varies in different 
 machines between 1.2 to 2.1. 
 
 The flux density that can be employed without unduly 
 increasing the reluctivity of the circuit is about 7.5 kilo- 
 gausses in cast iron, and up to IT kilogausses in wrought 
 iron or soft cast steel. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER. ~| 
 WEEKLY. 
 
 No. 18. OCTOBEK 13, 1894. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED 
 
 DYNAMO. 
 
 142. The commercial efficiency of a dynamo-electric 
 machine, like that of any other electric source, is 
 the ratio between the output and the intake, and varies, 
 in different sizes of generators, between, say, 0.5 for a 
 one KW. machine, to 0.98 for a generator of, say, 3,750 
 KW. In other words, the commercial efficiency of a 
 
 machine is Out P ut = Intake-Losses^ 
 Intake Intake 
 
 In order, therefore, to determine the efficiency of a 
 machine, the intake being known, it only remains to de- 
 termine the losses. 
 
 These are of three kinds ; namely, 
 
 (1.) Mechanical losses, such air churning, brush fric- 
 tion, and journal friction. 
 
 (2.) Electrical losses of the type $ r ; namely, losses 
 in the armature winding, and in the field magnet winding ; 
 and losses, due to eddy currents set up in the metal by 
 variations of flux. 
 
 (3.) Magnetic losses in the iron due to hysteresis. 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 203 Broadway, New York N. Y. 
 
 [Entered as second class matter'at the New York, N. Y., Post Office, June 14, 1894.] 
 
138 
 
 143. The mechanical losses, as a rule, are readily esti- 
 mated. The loss by air churning is usually small,, 
 and, in large, slowly revolving armatures, may be neg- 
 lected. Indeed, a small expenditure of energy in this 
 direction, is, to a certain extent, advantageous, and is 
 sometimes designedly incurred for the purpose of venti- 
 lating the armature, and, by consequent cooling, increas- 
 ing the possible output. Brush friction is usually a large 
 item of loss in very smill machines, and an insignifi- 
 cantly small item in large machines. Journal friction 
 can be readily estimated by the ordinary rules of me- 
 chanics, when the gravitational and magnetic forces, to- 
 gether with belt pulls, when such exist, are taken into 
 account, together with the size of the shaft and length 
 of bearings. 
 
 The electrical losses of the type i 2 r, are of 
 three kinds : 
 
 First, those due to the passage of the armature cur- 
 rent through its resistance, and of the field exciting 
 current through the resistance of the field magnets. 
 
 Second, those due to the energy expended by waste- 
 ful currents in loops of conducting wire on the armature, 
 when short-circuited by the action of the brushes on the 
 commutator; and, 
 
 Third, those due to energy expended in the iron of 
 the armature or pole-pieces, or in the copper wire on the 
 armature, in setting up induction currents in them. 
 
 145. If the resistance of the armature of a 100 KW. 
 
 machine be 0.05 ohm, and the E. M. F. of the ma- 
 
 chine be 500 volts, the current delivered by the machine 
 
 will be 200 amperes. The electrical loss of energy in 
 
139 
 
 the armature will, therefore, be 40,000 x 0.05 = 2,000 
 watts or 2 KW. 2 per cent, of the output. 
 
 146. If the armature core were a solid mass of soft 
 iron, then, from the variations of the magnetic 
 
 flux produced in this mass during its revolution through 
 the field, E. M. F.'S would be induced in it, which, acting 
 through the very low resistance of so large a mass of 
 metal, would generate powerful and wasteful currents. 
 By laminating the substance of the core, in planes 
 parallel to the magnetic flux, the E. M. F. in each lamina 
 is reduced, and also the available cross-section for the 
 action of the E. M. F. By thus building up the armature 
 core of sheets of thin iron, the eddy current loss is 
 brought down to very small limits. For the same reason 
 the conducting wire on the surface of the armature, 
 when of comparatively large size, needs also to be lami- 
 nated by stranding. It is not usually necessary to insu- 
 late the separate strands from each other, as the E. M. F. 
 in any particular cross-section of the wire is so small 
 that the superficial layer of oxide of copper will inter- 
 pose an effectual barrier to the passage of eddy currents. 
 When the conductors are buried below the surface of 
 the armature, as in grooved or toothed armatures, lami- 
 nation of the conductor is not necessary, since the flux 
 is almost entirely carried by the iron on one side or other 
 of the conductor, and the transition is effected without 
 cutting the substance of the conductor. 
 
 147. The third source of loss in the generator is 
 purely magnetic, and is termed loss by hysteresis. 
 
 Hysteresis, meaning a lagging behind, is the lagging of 
 the magnetism in a magnetic metal behind the_niagiietiz- 
 
140 
 
 ing flux which produces it. Thus, on the reversal of the 
 magnetizing flux exerted on a piece of iron, the zero of 
 magnetism is reached at an instant of time sensibly later 
 than the zero of magnetizing flux. This entails an ex- 
 penditure of energy in the iron which takes the form of 
 heat. 
 
 148. If an electric current be sent through a con- 
 ducting loop, magnetic flux is produced through 
 the loop, and, during the time the current strength 
 is rising to its full value the rate at which flux 
 is entering the loop will induce around the loop an 
 E. M. F. of the type e volts. This E. M. F. is oppositely 
 directed to the current i, which establishes it, and con- 
 sequently the current does work upon the E. M. F. with 
 an activity of e i watts. This energy is stored away in 
 the air and the ether, as magnetic energy of the type 
 
 /ng 
 
 ergs per cubic centimetre. On withdrawing the cur- 
 
 8 7T 
 
 rent and emptying the loop of flux, which occurs 
 during the time the current is waning, an opposite 
 E. M. F. is produced, aiding the current, doing work on 
 the current and restoring the energy from the magnetic 
 flux into the circuit. This interchange of energy from 
 the circuit to the ether surrounding it, and thence back 
 to the circuit is, so far as is known, apart from electro- 
 magnetic radiation unaccompanied by loss of energy. 
 If, however, a bar of iron, or other magnetic material, be 
 introduced into the loop, then the magnetizing flux due 
 to the current passing through the loop, produces, as 
 before, a magnetic flux through the loop, but this mag- 
 netizing flux acting on the iron, produces by the align- 
 ment of its molecules a powerful M. M. F. and flux in its 
 
141 
 
 own direction. As before, the prime flux produces a 
 counter-electromotive force, 0, in the loop absorbing 
 energy of the type e i, joules per second. The flux 
 passing through the iron and loop also produces a more 
 powerful E. M. F., E) volts, absorbing energy from the 
 current at the rate E i, watts. This energy is stored in 
 the magnetic circuit of the iron. The total counter- 
 electromotive force produced will be E + 0, volts, and 
 the work expended 
 
 rT 
 
 I (E -\~ e) i dt joules. 
 <J o 
 
 On the withdrawal of the magnetizing current, the 
 prime flux is withdrawn at the same rate as before, but 
 the magnetic flux in the bar lags behind ; i.e. 9 tends to 
 persist, so that, although the current in the loop may be 
 made to disappear entirely, the flux in the aero-ferric cir- 
 cuit does not totally disappear. Consequently, the rate 
 at which the flux is poured out is less than that at 
 which it was poured in, and the smaller E. M. F. thereby 
 induced, restores to the circuit only a portion of the 
 energy stored in the iron. That is to say, the lagging 
 behind, or hysteresis, of the magnetism in the bar has 
 caused energy to disappear from the electric circuit, or 
 to be lost to it. 
 
 149. Let us now enquire what has become of the 
 energy thus lost, to the circuit. When, under the 
 influence of the prime magnetizing flux, an alignment 
 of the molecules of the iron has been produced, energy 
 is stored in them. On the withdrawal of the prime 
 magnetizing flux, the aligned molecules do not immedi- 
 ately break up or lose their alignment, but tend to re- 
 main fixed until the prime magnetic flux is sufficiently 
 
142 
 
 far withdrawn to render tlieir position untenable. They 
 then suddenly break up their alignment and fall swiftly 
 into new groups, but without uniform alignment. In 
 
 ETLUX 
 
 (GAUSSES) DENSITY 
 
 FIG. 59. 
 
 Hysteretic Diagram of Charcoal Iron Rings and of Hard Cast Steel. 
 
 Charcoal Iron: Full line to indicated scale. From observations of Kennelly. 
 JC 6, OJ 10,600. 
 
 Hard Cast Steel: Broken line, to 10 times indicated scale. From observations of 
 Steinmetz. 5C 82, (ft 11,500. 
 
143 
 
 this sudden relapse to the unmagnetized state, the mole- 
 cules, in swinging around, acquire momentum which 
 carries them past their new positions of equilibrium, thus 
 causing them to oscillate to-and-fro about that position, 
 and to dissipate their energy in the form of heat. 
 
 150. The magnetic changes which take place in their 
 relation to magnetizing flux may be diagrammati- 
 
 cally represented as in Fig. 59, which shows a hystere- 
 tic cycle for a soft iron ring. 
 
 151. At every reversal of the magnetization of the 
 iron there is, therefore, an expenditure of energy 
 
 in the iron. This is proportional in amount to the area 
 of the hysteretic loop or the energy expended in the 
 cycle. As the limits of flux density during the reversal 
 are increased, the energy expended in the iron increases. 
 If the iron be carried from an intensity of (B = -\- 5,00( > 
 gausses to (B = 5,000 gausses, the range of reversal 
 will be 10,000 gausses. If now the range be doubled, or 
 increased to 20 kilogausses, the energy expended in the 
 iron per cycle will be approximately trebled. The en- 
 ergy expended in a cubic centimetre of iron undergoing 
 periodical reversals of magnetism is approximately ex- 
 pressed by the equation W = /? (B 1 - 6 ergs per c. c., where 
 r h is a coefficient which varies from 0.002 for very soft 
 iron to 0.080 in the hardest steels. 
 
 When, therefore, the core of an armature of soft iron 
 having a total volume of, say, 8,000 c. c. makes 12 re- 
 volutions per second in a bipolar flux from (B = -|- 5,000 
 to 5,000 gausses, it will undergo one complete cycle 
 or double reversal for each revolution. Consequently 
 the expenditure of energy in the core by hysteresis, per 
 
144: 
 
 revolution of the armature, will be 0.002 X SjOOO 1 - 6 = 
 0.002 X 828,600 = 1,657 ergs per c. c.; or 8,000 X 1,657 
 = 13,256,000 ergs 1.3256 joules per revolution, and 
 at 12 revolutions per second a total hysteretic activity in 
 the armature of 15.907 joules per second = 15.907 
 watts. For this reason the intensity in the armature is 
 preferably kept much below saturation, in order to avoid 
 the rapid increase in hysteretic loss at high densities ac- 
 cording to the above rule. 
 
 152. If the three classes of loss of energy in a gene- 
 rator be summed, their total subtracted from the 
 intake, is equal to the output, and this divided by the 
 intake gives the commercial efficiency of the machine. 
 
 SYLLABUS. 
 
 The losses in a dynamo-electric machine are three ; 
 namely, mechanical, electrical and magnetic. 
 
 By hysteresis is meant the lagging of the magnetiza- 
 tion behind the magnetizing force. 
 
 The loss of energy in a magnetic metal undergoing re- 
 versals increases approximately as the 1.6th power of 
 the limiting flux density. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER. 1 
 WEEKLY. 
 
 No. 19. OCTOBER 20, 1894. 
 
 Electrical Engineering Leaflets, 
 
 BY 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED 
 
 THE DYNAMO 
 
 153. The limitations to the output of a dynamo are 
 
 of three kinds ; namely, limitations by excessive 
 
 drop or fall of pressure in the armature ; limitations by 
 
 excessive heatin g; and, limitations by excessive sparking. 
 
 When a powerful current passes through the armature 
 of a generator, the fall of pressure, or drop in the re- 
 sistance of the machine, may be so great that the limit- 
 ing E. M. F. developed by the machine may not be capable 
 of supplying at its terminals, the pressure required to 
 operate the external circuit. This limitation exists only 
 in the case of small machines ; for, provided that their 
 normal E. M. F. has been correctly apportioned, large 
 machines find their limitations in other directions. 
 
 Limitations due to excessive heating are reached when 
 the temperature of the machine acquires a certain limit- 
 ing or critical value. The heat is chiefly developed in 
 the armature, where friction, hysteresis, eddy currents 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 203 Broadway, New Vork N. Y. 
 
 [Entered as second-class matter at the New York, N. Y., Post Office, June 14, 1894.] 
 
146 
 
 and resistance losses, that is, I 2 7?, losses in the winding, 
 due to the load current, are all active. ^ . 
 
 154. In all properly drawn contracts for installing 
 generators, the specifications require a certain 
 limiting temperature elevation, which the machine shall 
 not exceed after a certain duration of continuous, full 
 load. The object of this limitation is mainly to prevent 
 such a rise of temperature, on any part of the machine, 
 as may endanger the insulation of its winding. 
 
 Cotton begins to char, or undergoes slow thermolysis, 
 at a temperature slightly above the boiling point of 
 water. It would, therefore, be theoretically safe to 
 operate a generator at continuous full load with the 
 copper wire at 100 C. Taking 25 C. as the normal 
 temperature of the external air, this would represent a 
 temperature elevation of 75 C. Supposing the limiting 
 current of a generator were adopted so as to produce, 
 after continuous full load run, a temperature elevation 
 of 75 C. in the factory in cases where the dynamo 
 happened to operate in a hotter room, say, at 40 C., the 
 same full load current would, probably, raise its tempera- 
 ture tP 115 C., and an overload under such circum- 
 stances of, say, 10 per cent, might raise it to 125 C. 
 It is evident, therefore, that a due regard to the safety 
 of the insulation of a dynamo requires that the tempera- 
 ture elevation should be considerably less than 75 C. 
 The temperature elevation frequently met in conserva- 
 tive specifications is 40 C. ; in special cases where the 
 generator has to work in a hot room, as low as 30 C. 
 
 155. The heat developed in the armature of a gene- 
 rator is dissipated by conduction, radiation and 
 convection. The usual allowance of free surface in 
 
14T 
 
 armatures is 0.15 watt per square centimetre, but when 
 the armature is specially ventilated, so that air passes 
 through its substance as well as over its surface, this may 
 be increased to as much as 0.45 watt per square centi- 
 metre. 
 
 156. Sparking at the brushes is in all cases the result 
 
 of inductance. That is to say, to the effect of an 
 
 E. M. F. produced in that coil or section of winding 
 
 which is leaving contact, through its commutator seg- 
 
 A 
 c 
 
 EUc.Engineer 
 
 FIG. 60. FIG. 61. 
 
 Commutation of segments on the Voltaic circuit made up of single-volt 
 
 Gramme -ring armature. cells. Analogous to dynamo armature 
 
 Brushes at A A', 15 volts ; BB', 13 volts; 
 C c', ii volts. 
 
 ment, with the brush. If, as is represented in Fig. 60, 
 the brush H, be in contact with the commutator bar , 
 the current 2 /, flowing through the brush, will be made 
 up of two currents each equal to ./, flowing through the 
 adjacent coils, as represented by the arrows. If the arma- 
 ture revolves counter-clockwise, as shown by the arrow, 
 then the relative motion of the brush is clockwise, or in the 
 opposite direction. If the width of the brush be w cms., 
 and the width of the gap between the adjacent bars be g 
 
148 
 
 cms., then the distance through which short-circuit will 
 be maintained between two bars will be w g cms. If 
 a be the radius of the commutator, its circumference will 
 be 2 TT 0, and the time occupied in the transfer of the 
 
 brush from any bar to the next will be s- seconds. 
 
 2 ii n a 
 
 It is evident, therefore, that the current in the winding 
 section, H, must be stopped and reversed in this fraction 
 of time if there is to be no E. 11. r. between J and H, 
 when H is transferred to <?, and taken up the position A. 
 If the current 7, in the segment, B, produces indepen- 
 dently of the flux from the field magnets a flux <#, 
 through its convolutions, and if there are v 9 convolutions 
 in this section, the total flux linked with the section due 
 to its own current will be v 0, and when the current is 
 reversed to /the total linked flux will be reversed to 
 - v ^ ; the total change will be 2 v <P, and the time in 
 
 which this change is effected w ^ seconds, so that the 
 
 2 n na 
 
 average E. M. F. established in the coil during the change 
 
 is 47rnav x 10- 8 volts. If there are 20 turns of 
 w g 
 
 wire in the section and (P = 10 kilowebers, a = 15 cms., 
 n = 12 revolutions per second, w g = 1 cm., the 
 average E. M. r. would be : 
 
 12.57 X 12 X 15 X 20 X 10,000 XlO~ 8 volts=4.525 volts. 
 If the change were not at a uniform rate during the 
 period of transfer, the E. M. F. in the last stages would 
 be augmented, and might rise to 50 volts or more. 
 
 157. It is evident that <#, depends upon the output, 
 
 while V) depends, for a given machine, upon the 
 
 number of commutator bars, so that v 4>, is reduced by 
 
149 
 
 increasing the number of bars in the commutator. In- 
 creasing this number up to a certain limit diminishes the 
 E. M. F., or sectional E. M. F.. and, therefore, diminishes 
 the tendency to spark. On the other hand, after a cer- 
 tain limit is readied, the cost of construction and connec- 
 tion of the commutator increases rapidly with the 
 number of bars. In order to supply the E. M. F. neces- 
 sary to comply with the relations indicated, and to reverse 
 the current in the short-circuited segment, it is usual to 
 
 PIG. 62. 
 
 give the brushes a lead, that is to say, to move them for- 
 ward in the direction in which the commutator is rotat- 
 ing. The lead has to be increased as the load increases, 
 By this means the coil under commutation is brought 
 within a portion of the flux from the field magnets 
 whose variation through the coil supplies the E. M. F. re- 
 quired to reverse the current during the period of short- 
 circuiting. 
 
 Two consequences follow a lead of the brushes : 
 
150 
 
 First, the reduction of the E. M. r. of the armature 
 owing to the position and consequent neutralization of 
 some of the $. M. F. generated, as shown in Fig. 01. 
 
 Second, a tendency to oppose and neutralize the con- 
 trolling flux through the field magnets at the pole corner 
 nearest the brush, as shown in Fig. 62. 
 
 In this figure the normal condition of the flux through 
 the pole-pieces of the armature of a four-pole generator 
 is shown at the quadrant A, when no current flows 
 through the armature, the direction of rotation being 
 indicated by the large arrow. At the quadrant, B, the 
 figure represents, diagrammatically, the flux set up by 
 the M. M. F. of the armature winding, in the quadrant 
 under A, when no current flows through the same. This 
 M. M. F. increases with the load. 
 
 At the quadrant c, the effect of combining or super- 
 posing these two conditions is similarly represented, and 
 indicates the consequences of what is called armature 
 reaction in the generator under load. It will be seen 
 that the flux is crowded together, i.e., its intensity is in- 
 creased at the edge of the pole edge 6, and diminished 
 under the edge 5. 
 
 158. The magnitude of the armature M. M. F. will be 
 1.25T / N gilberts, where JT is the number of 
 conductors covered by a pole-face, and 7, the current in 
 the winding, and this will be almost entirely distributed 
 in the two air-gaps, 3 and 4, or 5 and 6, since the path 
 through the iron of the pole-pieces and armature is com- 
 paratively short. The difference of maximum difference 
 of magnetic potential across each of these air-gaps will 
 
 be - _ gilberts ; and, if the entrefer or length of 
 
151 
 
 path between the iron and iron, be f cms., the maximum 
 possible flux density, due to this difference of magnetic 
 
 1 257 I N 
 potential will be - gausses. This intensity is 
 
 opposed to the controlling intensity in the entwefer from 
 the field magnets at the edge 5, and added to it at the 
 edge 6. When this armature intensity is equal to the 
 intensity from the field magnets, they will neutralize and 
 leave no intensity at the edge 5, while the intensity 
 under the edge 6, will be doubled. When the neutrali- 
 
 Elec.Engineer ' 
 
 FIG. 63. 
 
 Section of one Quadrant of a 4-pole Generator with Tooth-cored Armature. 
 
 zatioii is effected, no amount of lead can be of any ser- 
 vice in checking sparking, since the flux whose variation 
 should induce a controlling E. M. r. in the short-circuited 
 segment, lias been removed. The load current which, in 
 the case of smooth-cored armatures, can be sustained 
 without sparking, is, therefore, less than that which makes 
 
 p equal to the intensity in the gap, when no cur- 
 2 / 
 
 rent flows through the armature, and, in practice, only 
 about half this limiting current strength can be allowed. 
 
152 
 
 159. In the case of toothed core armatures, such as 
 shown diagrammatically in one quadrant by Fig. 
 63, the same general results occur, but if the cross-sec- 
 tion of the teeth be properly designed, they will suffice 
 to carry a normal intensity as at A, in Fig. 62, without 
 saturation of the iron, although the intensity in them 
 under this action may be high. When, however, owing 
 to the effect of the M. M. F. in the armature, a crowding 
 of the flux takes place towards the edge, A, this tendency 
 to increase the intensity saturates the iron, and enor- 
 mously increases its reluctivity in the teeth, thereby in- 
 terposing a barrier to the distortion of the flux, and 
 bringing about a more uniform distribution with less 
 reduction of flux at the corner B. 
 
 For this reason toothed-core armatures can be made 
 to sustain greater loads than prescribed by the sparking 
 limitations of smooth-core armatures. 
 
 SYLLABUS. 
 
 The limitations of a dynamo arise from the drop in its 
 armature, from excessive heating, or from excessive 
 sparking. 
 
 The limitation of temperature in the armature of a 
 dynamo is imposed in order to prevent the possibility of 
 endangering the insulation of the armature by excessive 
 heating. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 No. 20. : OCTOBEB 87, 1894. 
 
 Electrical Engineering Leaflets, 
 
 BY 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GRADE. 
 
 The Regulation of the Dynamo. 
 
 160. In all cases where more than a single receptive 
 device is actuated bj a generator, some means are 
 
 necessary to accommodate, automatically, the output of 
 the machine to changes in the load. If the recep- 
 tive devices are connected to the circuit in series, and 
 are operated by a constant current, it is necessary to in- 
 crease the E. M. F. of the generator in proportion to the 
 number of devices thrown into the circuit. Such are 
 series-arc-light generators (see Fig. 64). If the devices 
 are connected in parallel, and are operated by constant 
 current, the voltage at each device must be maintained 
 uniform, and the current and pressure of the machine 
 varied to suit this requirement. Most continuous cur- 
 rent incandescent generators, are of this type (see Fig. 65). 
 
 161. When a series-arc-light generator is running at 
 a constant speed, and with a fixed number of 
 
 turns on its armature, the E. M. F. developed by the ma- 
 chine can only be varied either by altering the quantity of 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 203~Broadway, New York, N. Y. 
 
 l[Entered as second-class matter at the New York, N. Y., Post Office, Tune 14, 1894.] 
 
154 
 
 flux passing through the armature, or by varying the posi- 
 tion of the brushes on the commutator. Fig. 61 indicates 
 how the E. M. F. of a generator can be varied by chang- 
 ing the lead of the brushes ; except that, whereas, in the 
 voltaic analogue represented, the coils are indicated as 
 having the same E. M. F., the coils on the armature of the 
 generator have, in reality, different E. M. F.'S existing on 
 opposite sides in pairs. 
 
 162. In most arc-light dynamos, the field magnets 
 
 are connected in series with the armature which 
 
 supplies a practically constant current, and, therefore, 
 
 4- SUPPLY MAIN 
 
 -I- SUPPLY MAIN 
 
 Elec. Engineer' 
 
 FIG. 64. 
 
 Series-wound generator. 
 
 SUPPLY MAIN Elec.Engiv 
 
 FIG. 65. 
 
 Shunt-wound generator. 
 
 the M. M. F. in the main magnetic circuit is practically 
 constant, and the entire variation of E. M. F., say, from 
 50 to 3,000 volts, is provided for by varying the posi- 
 tion of the brushes on the diameter of commutation 
 from the diameter of minimum E. M. F. to the diameter 
 of maximum E. M. F. The machines are so designed 
 that the M. M. F. from the armature winding is sufti- 
 
 C5 
 
 ciently powerful to neutralize, by the flux it produces, 
 the field flux through that portion of the air-gap and 
 armature-surface in which the coils undergoing com- 
 
155 
 
 mutation are situated, in the manner already described 
 in Section 156, so that the commutation is practically 
 sparkless in all positions of the brushes within regulat- 
 ing limits. If this balance between armature and field 
 M. M. F.'S and flux, were not maintained throughout this 
 range, violent sparking would occur, especially as arc 
 light machines reach such high pressures, and the num- 
 ber of volts per bar in the commutator is large. 
 
 163. "When a generator running at a constant speed 
 has to supply a varying current under an E. M. F. 
 
 which is automatically maintained constant, either at its 
 own terminals, or at the terminals of delivery, a com- 
 paratively large range of current variation has to be 
 provided for, with a definite but much smaller range of 
 E. M. F. variation. Thus a 100 KW. generator, intended 
 to supply 125 volts at its terminals, must automatically 
 maintain a pressure of 125 volts practically constant 
 under all conditions of load, from no current to 800 am- 
 peres, the E. M. F. which the machine must generate 
 being in one case 125 volts, and in the other, say, 130. 
 This variation of E. M. F. of five volts must accompany 
 the increase in output in due proportion. In such cases 
 the variation of E. M. F. is obtained, not by changing the 
 position of the brushes on the commutator, but by 
 changing the M. M. F. of the field magnets. 
 
 164. If the magnetic circuits of a dynamo, including 
 the leakage- or air-paths, be considered as analog- 
 ous to a corresponding system of voltaic circuits, as re- 
 presented, for example, in Figs. 35, 42, 43 and 44, each 
 branch reluctance in the system has a value of the type 
 
 - (a -\- b JC), where , is the virtual or real length of the 
 
156 
 
 branch in cms.; s, its virtual or real cross-section in sq. 
 cms. ; and (a + I 5C) its reluctivity at the prime flux 
 density 3C, which in its turn may be considered as the 
 average magnetic potential difference per cm. of length, 
 through the branch, or, if 37l b , be the total magnetic 
 
 p. D. between branch terminals - b = mean OC. Under 
 
 these conditions it can be shown that the flux a , pass- 
 ing through the armature will be 
 
 d> -= = _ ^ 
 a ~~ (R a ~~ di + bi 9fTl ' 
 
 so that the apparent reluctance of the magnetic circuit, 
 considered as having no leakage or shunt paths, is a 
 linear function of the M. M. F. in which a^ and 5 1? are con- 
 stants depending for their magnitude upon the qualities 
 of the iron in the dynamo, and on the configuration of 
 the magnetic system. This relation is known as 
 Frolich's law, and is a consequence of the experiment- 
 ally observed fact that the reluctance of any branch is 
 constant for a path through air, and of the form 
 
 for a path through iron. 
 
 In computing the reluctance in the magnetic circuit of 
 a dynamo, a slight addition, strictly speaking, is necessary 
 on account of the reluctance of such joints as may exist. 
 It has been found by measurement that the reluctance 
 of a joint between two smooth surfaces of wrought iron 
 is equal to the reluctance of an air-gap varying from 
 0.0026 to 0.0043 cm. according to the intensity in the 
 iron and other circumstances. The reluctance of a well 
 
157 
 
 fitted joint between smooth surfaces of soft iron, may, 
 therefore, be estimated as 0.003 oersted divided by the 
 area of the joint in sq. cms. This reluctance will usually 
 be a negligibly small fraction of the total reluctance of 
 the circuit. The reluctance of a badly fitted joint be- 
 tween soft iron surfaces may however be considerable. 
 
 165. When a generator has its load increased from 
 no load to full current load of 7, amperes, the 
 pressure at its terminals under constant M. M. F., diminishes 
 by I R volts, 7?, being the resistance of the generator. 
 If, in addition to this, a lead has to be given to the brushes 
 to maintain sparklessness at the commutator, the E. M. F. of 
 the armature will be diminished by an amount 0, volts, 
 which can be estimated from the distribution of E. M. F. 
 in the coils around the armature, but which is almost im- 
 possible to compute accurately. The lead of the brushes 
 also introduces a certain small counter M. M. F., from the 
 armature acting through the main magnetic circuit of 
 the field coils, thus reducing the main circuit flux and 
 the armature E. M. F. by a certain small amount e i9 volts. 
 The problem in designing an automatic constant poten- 
 tial generator, is, therefore, to cause the increase of cur- 
 rent 7, amperes, which tends to diminish the terminal 
 pressure by the amount (7 R + + <?i) volts, increase 
 the M. M. F. of the field magnets to the extent necessary 
 to increase the armature flux and generated E. M. F. by 
 this amount. 
 
 If the constants a v and 5 1? in the Frolich equation 
 
 i + f>i 3ft 
 were known, the change, A 2flt, necessary to introduce in 
 
158 
 
 3fft, for the required change in a , would be immediately 
 determined, and this change could be effected by causing 
 the load current /, to make such a number of turns t, 
 around the field magnets in aiding the shunt-winding, as 
 would make 1.257 1 t = A 971. The machine would 
 then be compound- wound and self-regulating; i.e.^ would 
 maintain a constant M. M. F. through a shunt-winding 
 connected to its constant potential terminals, and would 
 develop a M.M. r. through a short stout winding in series 
 with its armature. This auxiliary M. M. F. would be 
 zero, at no load, and at full load, would reach a maxi- 
 mum capable of compensating for the tendency of the 
 E. M. F. to fall. 
 
 166. In practical dynamo magnetic circuits, however, 
 owing to the complexity of the means for com- 
 puting the value of the constants a, and b ly it is prefer- 
 able to arrive at the same result by a synthetic process, 
 as follows : Having given a total fall of pressure at ter- 
 minals due to full load under a constant M. M. F., the in- 
 crease over the flux through the armature at no load, 
 necessary to recoup this loss, is immediately determined. 
 The intensity in the armature will, consequently, be in- 
 creased thereby from (B a to, say, & A , and the reluctance 
 of the armature from 
 
 CR, = A / _* \ to (R A = / __ ^L^ oersteds, 
 ' 
 
 , = A / _* \ to (R A = A / 
 * a \l b&J' s a \l 
 
 a and 5, being constants for the quality of the iron in the 
 armature. The constant reluctance (R. K , of the leakage 
 paths, placed in parallel with the armature, is supposed 
 to be known from the type of machine, from previous 
 
159 
 
 data, or from direct computation, and the joint reluc- 
 tance of the armature and leakage paths will be 
 
 (ft, = ^^ oersteds. 
 (R A + (R K 
 
 The total flux to be supplied through the field coil or 
 coils must, therefore, be 
 
 and the density in the iron of the field magnets becomes 
 
 <* = 4, 
 
 *M 
 
 so that the reluctance of the field cores will be 
 - l * 
 
 -~ 
 
 the total reluctance in the circuit will, therefore, be 
 
 (R = (RK + CR,, 
 
 and the M. M. F. required will be 
 371 </> M (R. 
 
 In order to economize the extra M. M. F. required to 
 maintain the pressure of the generator, it is necessary to 
 keep the densities (B A and (B VI , well below the limits of 
 saturation. 
 
 167. It is sometimes required to maintain the pres- 
 sure constant, not at the terminals at the gene- 
 rator, but at the terminals of supply, which may be a 
 mile or more distant, and situated at a real or virtual 
 electrical distance r, from the generator, so that the 
 drop in the armature and supply circuit together will be 
 [7 (R -\- y) -f- e + e?J volts. This case falls iiumedi- 
 
160 
 
 ately into the preceding treatment by supposing the re- 
 sistance of the armature increased by /, except that the 
 shunt-winding is no longer maintained at uniform ex- 
 citation, but slightly increases in excitation with the 
 load. 
 
 In order to make up for any deficiencies in design of 
 compound-wound generators so as to permit of over- 
 compounding, resistances called compensating coils are 
 sometimes connected, or left ready to connect, in parallel 
 with the series-winding on the magnets, so as to increase 
 or diminish their effect. 
 
 SYLLABUS. 
 
 Automatic regulation in generators is employed in 
 practice to maintain a uniform current under varying 
 E. M. F. or a uniform E. M. F. under varying current. 
 
 Constant-current generators are usually regulated by 
 shifting the brushes. 
 
 Constant-potential generators are usually regulated by 
 compound-winding, that is, by automatically varying the 
 flux. 
 
 Over-compounded generators, are generators whose 
 compound winding is designed to maintain automatically 
 a constant pressure at the terminals of delivery, instead 
 of at the terminals of the generator. 
 
 Laboratory of Houston & Keimelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELHCTRICAL ENGINEER.] 
 WEEKLY. 
 
 No. 21. NOVEMBEK 3, 1894. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED C F? A D E . 
 
 ELECTRODYNAMICS. 
 
 168. Electrodynamics is tliat branch of electromag- 
 netic science which treats of the apparent mutual 
 
 attractions and repulsions between electric currents, or 
 between electric currents and magnets. The apparent 
 mutual attraction or repulsion between magnets, although 
 frequently classed under electrodynamics more properly 
 belongs to the separate branch of imagnetodynamics. 
 
 When a conductor, situated in a magnetic flux, has a 
 current passed through it, the conductor tends to move. 
 This tendency to motion is the result of the mutual in- 
 teraction between the flux in which the wire is situated, 
 and the flux produced by the current in the wire. 
 
 169. When a wire of length /, cms., Fig. 66, situated 
 in a uniform flux of intensity (B gausses, carries a 
 
 current of strength i, c. G. s. units, the flux surrounding the 
 wire will no longer be represented by a uniform fleld, but 
 the flux above the wire will be increased in intensity, and 
 the flux below the wire decreased. Under these circum- 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 20 1 Broadway, New York, N. V. 
 
 [Entered as second-class matter at the New York. N T . Y., Post Office, Tune 14, 
 
162 
 
 stances the wire will be forced mechanically towards the 
 side on which the flux is weakest, and, since the difference 
 of intensity above and beneath the wire depends upon 
 the current strength through the wire, the electrodynamic 
 force with which the wire is acted upon will depend 
 upon the current strength. The value of the force ex- 
 erted on the wire will be f = i (B I dynes. It is evident 
 that if in obedience to this force, the wire is moved down- 
 wards through the flux with a velocity v cms. per second, 
 the E. M. F. generated in the wire will be e = v <B / 
 
 u 
 
 FIG. 67. 
 
 Diagram of rectangle of active con- 
 ductor A B c D, situated in a uniform mag- 
 netic flux. 
 
 c. a. s. units, as already shown in Sec. 124 ; and, since 
 the current will be opposed to this E. M. F., the current 
 will do work upon it, and energy from the source of 
 current will be expended in the wire at the rate e i ergs 
 per second. But the mechanical activity expended on 
 the wire, in dynes, will be the force on the wire multi- 
 plied by its velocity in cms. per second, so that if/", be 
 the force, then 
 
 f i) e i ergs per second, 
 
 or,/ = 1* dynes = v (&U ---- i & I dynes. 
 
163 
 
 The force exerted upon the wire will, therefore, de- 
 pend upon the current strength through the wire in c. G. s. 
 units, (of 10 amperes each), on the intensity of the flux, 
 and on the length of wire in that intensity. It will be 
 moved oppositely to the direction of motion which would 
 be necessary to give to the wire, in order to set up a cur- 
 rent in the direction of *, by induction from the flux. 
 
 170. Fleming's hand rule is frequently useful for 
 determining the direction of the force in such 
 
 cases. But it must be remembered that the left hand 
 is employed in the case of motors, and the right hand in 
 the case of dynamos. The motor rule may be phrased 
 as follows. If the hand be held as shown in Fig. 67, 
 then the /breflnger represents the direction of the /lux, 
 the im'ddle linger represents the direction of the current 
 ?", and the thumb points out the direction of the motion, 
 or tendency to motion, produced by the force. 
 
 171. We have seen that the mechanical force exerted 
 upon an active conductor in a flux is a consequence 
 
 of the law of the induction of E. M. F. in such a wire, 
 together with the law of the conservation of energy. In 
 order that a conductor may carry a current, it must form 
 part of a complete loop or circuit, and the total mechan- 
 ical force exerted on a conducting loop is the sum of all 
 the elementary mechanical forces exerted around the 
 loop in different positions, and, perhaps, in different in- 
 tensities of flux. If a loop carrying a current of strength 
 ?', c. G. s. units, moves under mechanical forces in any 
 manner, so that the flux linked with it is 0, at any mo- 
 ment, the E. M. F. generated in the loop will be =" e, 
 
 dt 
 
164 
 
 c. G. s. units, and the work done on that E. M. F. will be 
 e i ergs per second. This will be the mechanical activity 
 expended upon the loop by the system of forces at work 
 upon it. The total work done on the loop from the 
 initial position it occupied, to its final position will be 
 
 C e idt = C^ idt = rid<P = i<P ergs. 
 Jo Jo dt J <P 
 
 That is to say, the total work will be the total increase 
 of flux linked with the circuit multiplied by the current 
 strength in that circuit, or the total increase of linked 
 current-flux ; and this work is independent of the velocity 
 at any stage of the process, or of the manner in which 
 the motion has been brought about. The capability, 
 therefore, of a loop to do work by motion, depends only 
 on the total flux it can add to its contents, and on the 
 strength of the current it carries, assuming the current 
 strength to have remained constant. 
 
 172. It is evident that an active loop always endeavors 
 to move so as to add as much flux to its contents 
 as possible, and will remain in stable electromagnetic 
 equilibrium only when no excursion that it ca make will 
 increase the flu x that it contains. The fundamental reason, 
 therefore, for the mechanical force exerted upon an 
 active loop is, that the electromagnetic energy in 
 the ether within the loop tends to a maximum. That 
 
 (B 3 
 
 energy is expressed as we have seen in Sec. 93 by - 
 
 8 x 
 
 ergs per cubic centimetre, and this energy in the space 
 within the loop can only become a maximum by 
 making a maximum, and, therefore, by uniting the 
 direction of the external or prime flux, with the direction 
 
165 
 
 of the flux produced in the local magnetic circuit of the 
 active loop, so that an active loop will tend to move until 
 its own flux is parallel to the external or prime flux, i.e., 
 the flux producing the motion. 
 
 173. The key to all the phenomena of electro- 
 dynamics may be expressed as follows : the ten- 
 dency of the electromagnetic energy in the ether to a 
 maximum, and, consequently the tendency of fluxes to 
 become parallel. For example, consider a single loop of 
 wire A B c D, such as might be wound on a drum arma- 
 ture of the bi-polar electromagnetic motor shown in Fig. 
 66. Here the loop contains a flux of its own, owing to the 
 driving current supplied to the motor, and this flux passes 
 upwards through the loop as shown by the small arrows. 
 The loop immediately tends to move into the vertical 
 position in which it will hold the maximum possible 
 amount of flux. 
 
 The amount of work which will be performed by the 
 loop electrodynamically, during any small angular move- 
 ment d /?, is i d ergs, where d is the small increase of 
 flux admitted into the loop during the angular movement 
 d /9. This work can also be expressed as r d ft where r 
 is the torque exerted on the loop about its axis, so 
 that, equating the two expressions for the same amount of 
 
 work, r d ft = i d <P, or r = i -^-^. The torque ex- 
 
 d p 
 
 erted by the loop is therefore proportional to the rate at 
 which a small angular movement will increase the bi- 
 polar flux enclosed by the loop, and, if this loop existed 
 on an armature alone, the motion would cease as soon 
 as the loop reached the vertical, where the flux linked 
 with the loop is a maximum. If we assume that at some 
 
166 
 
 point in the plane of the loop A B c D, the flux due to the 
 M. M. F. of the loop is represented in magnitude and 
 direction by the line B o, Fig. 68, and the external flux, 
 by the line A B ; then at this point the resultant flux is 
 A c, or A K. When, however, the loop revolves into the 
 vertical position, B c is brought to B D, in line with A B, 
 and the resultant flux density at the point is A D. The 
 voluminal energy in a cubic centimetre of space at this 
 point being proportional to the square of the density, the 
 increase owing to the re volution of the loop is proportional 
 to the excess of the area A F G D over the area A E H K. 
 
 r Uc.Engineer 
 
 FIG. 68. 
 
 Diagram representing the increase of voluminal magnetic energy in space effected 
 by the alignment of two independent magnetic fluxes. 
 
 If now another loop be added to the armature at right 
 angles to the former, and also traversed by the driving cur- 
 rent, this loop will be at its position of maximum torque 
 when the first loop is devoid of torque, and, if, as in practice, 
 the number of loops occupying various angular positions 
 be placed on the armature, a continuous rotation will be 
 effected. Any loop reaching the vertical position abed, 
 has the maximum flux linked with it, and would tend to 
 resist onward movement in the same direction, that is, it 
 
16T 
 
 would oppose any decrease in the amount of flux it em- 
 braces. Where a number of loops are placed on an 
 armature, in order to. render the motion continuous in the 
 case just supposed, it is necessary to reverse the direction 
 of the current in each of the loops when they have 
 reached the vertical position. This is effected by means, 
 of a commutator. 
 
 174. The torque of a motor is the moment of the 
 rotating forces about the axis, and is equal to the 
 virtual tangential force exerted at unit radius. Thus, if 
 the force of f dynes, has to be exerted tangentially at a 
 radius of d cms. from the axis of a motor, in order to 
 just keep it from moving, the starting torque of the 
 motor is F d cm.-dynes ; if also during rotation the motor 
 exerts a tangential force, say, at its pulley, of 500 Ibs. 
 weight, and the radius of the pulley is 1.5 feet, the run- 
 ning torque of the motor will be 750 foot-pounds. 
 
 Since the torque exerted by a motor armature depends 
 upon the intensity of the flux passing through its loops, 
 it is evident that doubling the intensity of the flux will 
 double the torque; consequently the object of iron in 
 the armature, is to enable a powerful flux and flux in- 
 tensity to be maintained through the armature, from the 
 M. M. F. in the magnetic circuit of the Held magnets. 
 
 SYLLABUS. 
 
 The cause of the movement, or tendency to movement, 
 between active neighboring conductors, or between active 
 neighboring conductors and magnets, or between neigh- 
 boring magnets, is a tendency of voluminal electro- 
 
 (B 2 
 magnetic energy in ether, of the type ergs per cubic 
 
 8 7T 
 
168 
 
 centimetre to a maximum, within the substance of mag- 
 nets, and within the interior of coils. 
 
 In order to produce a maximum voluminal electro- 
 magnetic energy in ether, fluxes tend to associate and 
 unite in direction, and the motion or tendency to motion ; 
 i.e., the force, ceases, when parallelism of flux is attained. 
 
 An active conductor of any shape tends to alter its 
 shape in such a manner as to increase the flux linked 
 with it, i.e. the magnetic energy of its environment, and 
 the force so exerted ceases when the flux linked with the 
 circuit is a maximum. 
 
 Loops tend to become circles, and coils tend to shorten, 
 magnets to approach or recede, and magnet systems to 
 align themselves, in obedience to these laws. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 No. 22. NOVEMBER 10, 1894. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GRADE. 
 
 THK ELKCTRIC MOTOR 
 
 (CONTINUOUS CURRENT TYPE.) 
 
 175. We have seen that when loops of wire on an 
 armature are moved through a magnetic flux, 
 supplied, for example, by field magnets, there will be 
 E. M. F. generated in the loops of wire. 
 
 We have also seen that when the same loops of wire 
 carrying a current are placed in a magnetic flux, there 
 will be electrodynamic forces exerted upon the loops. 
 
 In all dynamo-electric machines, whether dynamos or 
 motors, both these conditions necessarily coexist; that is, 
 in the dynamo, the generation of E. M. F. is necessarily 
 accompanied by the generation of electro-dynamic forces 
 as soon as the E. M. F. drives a current through its 
 circuit; and, in the motor, the generation of electro- 
 dynamic forces is necessarily accompanied by the gene- 
 ration of electromotive forces. In the dynamo, the 
 direction of the electrodynamic force is opposed to the 
 direction of the force mechanically exerted on the ma- 
 chine in producing its E. M. F., while in the motor, the 
 
 Published by 
 THE ELECTRICAL ENGINEER, 
 
 203 Broadway, New York, N. V. --f f TV 1 T* T IH ' 
 
 [Entered as second-class matter at the New York, N. Y., Post fftee,- Jtirlfc ij, lift.]* 
 
 QW THIS 
 
170 
 
 direction of the E. M. F., generated by the motion of the 
 armature, is opposed to the direction of the driving cur- 
 rent. The E. M. F. of the motor is, therefore, called its 
 counter E. M. F. (abbreviated c. E. M. F.) ; and, in the same 
 way, the electrodynamic force of a dynamo may be called 
 its counter electrodynamic force. 
 
 1 76. The direct E. M. F. (abbreviated D. E. M. F.) of a 
 generator and the c. E. M. F. of a motor, being 
 
 similarly produced, are subject to the same laws ; conse- 
 quently the c. E. M. F. of a motor is expressed by, 
 
 e = n w c. GL s. units, 
 
 the same equation as in the case of a generator, where 
 <P, is the total useful flux passing through one pole into 
 the armature in webers ; n, is the number of revolutions 
 of the armature per second ; and w, is the number of 
 conductors lying on the surface of the armature, counted 
 once entirely around. 
 
 From the identity of this E. M. F. equation for motors 
 and dynamos, it is evident that if a motor were driven 
 by externally applied force at its speed n, revolutions 
 per second, but without receiving any driving current, 
 its E. M. F. as a dynamo, would be equal to its c. E. M. F. 
 
 177. The work absorbed by a motor from the driv- 
 ing circuit will be e i, ergs per second, where *, 
 
 the strength of the driving current in c. G. s. units of 
 10 amperes each = i (l> n w, so that the work absorbed 
 by the armature during each revolution will be i w 9 ergs. 
 
 178. The preceding considerations render manifest 
 the reversibility of all continuous-current dynamo 
 
 electric machines, in regard to their generation of current 
 by motion, or their generation of motion by current. 
 
171 
 
 It is in fact well known, that any motor, when driven, 
 will act as a generator, and produce current, provided 
 its field magnets are capable of self -excitation, or are 
 separately excited ; and, similarly, that any dynamo, 
 when properly supplied by a current, will act as a motor 
 and exert mechanical force. 
 
 179. All motors are required to produce a certain 
 amount of mechanical activity, but the circum- 
 stances under which this activity is required will vary 
 greatly in different cases. These different cases may be 
 classed as follows ; namely, where the requisites are, 
 
 (1.) Constant torque and constant speed. 
 
 (2.) Constant torque and variable speed. 
 
 (3.) Variable torque and constant speed. 
 
 (4) Variable torque and variable speed. 
 
 The torque and the speed of a motor are its essential 
 features, its activity being the product of the two. It 
 will be necessary, therefore, to examine the conditions 
 which determine both of these quantities. If r, be the 
 torque of the motor, and a>, its angular velocity, the 
 activity of the motor will be 
 
 r a) ergs per second. 
 
 The angular velocity is the number of unit angles, or 
 radians, described by the armature per second, and since 
 there are ^ TT, radians in each complete revolution, 
 
 co = 2 TT n\ 
 
 so that, the activity of the motor is, 2 n n r ergs per 
 second. 
 
 180. "We have already pointed out that the torque is 
 the mechanical couple exerted by or on a motor, or, 
 
 its tangential force at unit radius, and in c. G. s. units at a 
 
172 
 
 radius of one centimetre, so that if r, dynes be exerted 
 at the periphery of a motor shaft, whose radius is 1 cm., 
 the work done in one complete revolution of the shaft 
 will be 2 TT r, ergs, and if the shaft make n, revolutions 
 per second, the work per second, or activity, will be 
 2 TT n r, ergs per second, as before. 
 
 For example, if the 4-pole shunt-wound machine repre- 
 sented in Fig. 58, be employed as a motor, instead of 
 as a generator, its activity will be, say 100 KW., and its 
 commercial efficiency, 0.9. Then the electrical activity, 
 absorbed by the machine at its terminals, will be J^-- 
 111.1 KW. at, say, 500 volts pressure and 222.2 amperes, 
 of which, say, 218 amperes pass through the armature, 
 and 4.2 amperes through the field. If the useful flux 
 through each pole be 55 megawebers, the number of 
 wires on the surface of the armature 200, and the resist- 
 ance of the armature 0.05 ohm, the drop of pressure in 
 the armature at full load will be i r = 218 X 0.05 = 
 10.9 volts, so that the c. E. M. F. generated in the arma- 
 ture will be 500 1 0.9 = 489.1 volts. Since e= 4> nw, 
 
 the speed . = = 
 
 per second, or 266.7 revs, per minute, or an angular 
 velocity of 4.445 X 6.283 = 27.93 radians per second. 
 The torque of the motor at full load will be 
 
 r- P 
 
 } 
 
 CO 
 
 where P = the mechanical activity of the motor in 
 ergs per second. In this case P = 100,000 watts; and 
 
 one watt being 10 7 ergs per second, r = = 3.58 X 
 
 27.93 
 
 10 10 dyne-cms. = 3.58 x 1.0203 X 10 10 = 3.653 X 10 10 
 
milligrammes weight (at Washington) 3.653 X 10 4 kilo- 
 grammes weight, at a radius of one centimetre. 
 
 If the diameter of. the pulley were 30", and the thick- 
 ness of the belt driven by the pulley f", the effective 
 radius of transmission ISf^" or 46.2 cms., so that the 
 effective pull exerted by the belt 
 
 = 3 ' 653 t x 1Q4 = Y90.7 kilograinmes=1743 Ibs. weight. 
 46.2 
 
 181. When a continuous-current shunt-motor of re- 
 sistance /, ohms with separately-excited field, and 
 whose armature is ready to move, is connected to a 
 source of constant E. M. F., E, volts, a current will now 
 through the armature of the motor on closing its circuit. 
 The strength of this current will be determined not 
 merely by Ohm's law, that is by the resistance and the 
 E. M. F. in the circuit, but also by the inductance of the 
 circuit, which tends to check the first rush of current. 
 The initial strength of current, will, therefore be, either 
 equal to, or less than 
 
 /* 
 
 T 
 
 The torque set up in the motor by this current will be 
 
 1 4> w 
 
 ^r' 
 
 and if this torque is sufficient to set the armature in 
 motion against its load, the armature will immediately 
 start, and the c. E. M. F., generated by its motion will 
 reduce the current to some value *, expressed by 
 
 " 
 
 r 
 Under the influence of the driving current, the motor 
 
will continue to accelerate until the working speed is 
 arrived at, which satisfies both equations of energy and 
 of E. M. F.; for, it is necessary, that: 
 
 First, the intake is equal to the total work performed, 
 or that e i = speed X torque. This torque includes 
 not only the mechanical torque usefully exerted, but also 
 the f rictional torque due to eddy currents, hysteresis and 
 journal friction. 
 
 In well designed armatures, employing properly lami- 
 nated and insulated cores, the loss of power in eddy cur- 
 rents, and the torque exerted against their elect rodynamic 
 force, are comparatively small. The torque exerted against 
 journal and brush frictions may be approximately deter- 
 mined, when the motor is disconnected from its circuit, 
 by ascertaining the smallest weight which suspended by 
 a cord over the pulley, will maintain the armature in 
 motion. This weight in pounds, multiplied by the effec- 
 tive radius of the pulley, gives the observed frictiorial 
 torque in pounds-feet. A torque of 1 pound-foot = 13,825 
 gramme-cms. = 13,550,000 dyne-cms. (Washington.) 
 
 As soon as the field magnets of the motor are sepa- 
 rately excited, the torque resisting motion, observed in 
 this way, will be found to have considerably increased. 
 If v, be the volume of iron in the armature core in cubic 
 centimetres and 37, its hysteresis coefficient, (Sec. 151), (&, 
 its maximum intensity, p, the number of field magnet 
 poles, the energy expended in hysteresis per revolution 
 
 of the armature will be approximately -JL-L -- ergs, 
 
 2 
 
 and the torque due to hysteresis corresponding to this 
 
 expenditure of work will be - dyne-cms. Thus, 
 
 4: It 
 
175 
 
 an armature of a 4-pole machine (generator or motor) 
 containing 120,000 c.c. of soft iron of which the hyster- 
 esis coefficient is 0.002, magnetizing the armature at 
 full load to a density of 10 kilogausses in each direction, 
 would exert a hysteresis torque resisting motion, of 
 
 180,000 X4X 0.008X10,000" = mg x 10 , dylMMang . 
 12.5 1 
 
 = 14.15 lbs.-feet. 
 
 182. Second, the pressure at the terminals must be 
 equal to the c. E. M. F. plus the drop in the arma- 
 ture; or, that^= e-\- ir. The speed and current, there- 
 fore, co-operate to satisfy these two conditions, and these 
 will determine the normal condition of operation in the 
 motor for constant excitation, constant pressure, and 
 constant load, the total activity absorbed by the armature 
 being E i^ watts. If now, the load on the motor, i.e., the 
 mechanical torque, be increased, the speed will diminish 
 and witli it the o. E. M. F. until the current strength in- 
 creases to a value, which satisfies both the energy and 
 pressure equations. 
 
 The speed at which the motor runs is, in conformity 
 with these conditions, always expressed by the formula 
 
 revs, per second. 
 
 - 
 
 w W w* 
 
 The first term gives the speed at which the armature 
 would run if it had no drop, and the second term gives 
 
 the rein eta nee due to drop. 
 
 ^y^-^^j-JLU-^ff^ 
 183. It is evident, therefore, that when a motor is 
 
 prevented from moving by excessive torque, it 
 can perform no useful work, because its c. E. M. F. would 
 be zero. On the other hand, if all torque could be re- 
 
1Y6 
 
 moved from the machine its speed would be a maximum, 
 because the current it would take would be zero, the 
 maximum activity of the motor existing midway between 
 these two conditions ; namely, when its counter E. M. F. 
 is half that of the pressure at terminals or equal to the 
 drop. This would be represented by a commercial effi- 
 ciency of less than 0.5. In practice, however, the activ- 
 ity of all motors of any considerable size must be 
 considerably greater than 0.5, for the reason that if they 
 were to expend internally half the energy they receive, 
 they would become violently overheated. 
 
 SYLLABUS. 
 
 In all continuous current dynamo-electric machines, 
 whether dynamos or motors, E. M. r/s and electrodyna- 
 mic forces are developed. In dynamos there isacounter- 
 electrodynamic force and a direct E. M. F. In motors 
 there is a counter E. M. F. and a direct electrodynamic 
 force. 
 
 Dynamos and motors are reversible machines when 
 the lield magnets are capable of seif-excitation. In dy- 
 namos the E. M. F. is greater than the pressure at the ter- 
 minals, and in motors, the c. E. M. F. is less than the 
 pressure at the terminals, by the amount of the drop in 
 the machine. 
 
 The controlling factors in the activity of motors are 
 the torque and the speed. 
 
 A torque of one pound-foot is 0.13825 kgm.-metre, or 
 13.55 megadyne-cms. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 No. 23. NOVEMB.E IT, 1894. g*^^ Cent*. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GRADE. 
 
 THK ELKCTRIC MOTOR 
 
 (CONTINUOUS CURRENT TYPE.) 
 
 184. When a motor, connected to constant potential 
 mains, is loaded witli a constant torque, there are 
 
 three possible ways of varying its speed ; viz., 
 
 (1.) By shifting the brushes on the commutator, thus 
 altering the amount of c. E. M. F. available in the motor 
 circuit. 
 
 (2.) By inserting a resistance in the armature circuit, 
 thus producing a drop of pressure in the circuit of the 
 motor, and thereby lowering the pressure at its ter- 
 minals. 
 
 (3.) By varying the M. M. r. of the field magnets of 
 the motor, so as to induce a varying c. E. M. F. in the 
 armature, forcing it to alter its speed in order to main- 
 tain a constant c. E. M. F. 
 
 185. The method of varying the speed of a motor by 
 shifting its brushes is not practically employed ; 
 
 since, unless efficiency be intentionally sacrificed in the 
 design of the motor, for the purpose of permitting such 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 901 Broadway, New York, N. Y. 
 
 [.Entered as second-class matter at the New York, N. Y M Post Office, Juo 14, 1894.] 
 
1Y8 
 
 shifting, violent sparking would be produced at the 
 brushes. 
 
 The method of inserting a resistance in the armature 
 circuit is frequently adopted, especially with small 
 motors. It is, however, a wasteful process. 
 
 We have seen that the torque exerted by a motor is 
 
 cm.-dynes, (including torque against friction) so 
 
 2 7t 
 
 that, the torque remaining constant, the value of the 
 driving current is determined. If now, the speed re- 
 quired of the motor is such that the c. E. M. F. (0 n w) 
 is small, the difference between this c. E. M. F., and the 
 pressure in the mains must be made up of drop in re- 
 sistance i r, and this drop, when considerable, will 
 have to be almost entirely produced in external resist- 
 ance. Calling this drop <?, the activity lost in heating 
 the external resistance will be e i watts, which will be 
 large when the motor is running slowly, and small when 
 it runs at nearly full speed. Moreover, when the cur- 
 rent *, is powerful, and the drop 0, is large, the resistance 
 must be constructed in such a manner as to liberate a 
 large amount of energy without overheating, and this 
 necessitates bulky, cumbersome and expensive rheostats. 
 
 186. The third method for varying the speed of a 
 motor under constant torque, namely, that of 
 varying the M. M. F. of the iield magnets of the motor, 
 though frequently employed, is necessarily limited in 
 range. Shunt motors can have their M. M. F. controlled 
 by means of resistance inserted in the circuit of their 
 magnets. The range of variation of speed, obtained 
 in this way, generally amounts to about 25 per cent. 
 If the M. M. F. of the magnets be reduced beyond a 
 
179 
 
 certain point, the armature current, which has to be 
 increased in order to maintain a constant torque, will so 
 far increase the M. M. F. of the armature, as to destroy 
 largely or even to overpower the field flux, and thus 
 give rise to violent sparking at the brushes. 
 
 187. In series motors the variation of M. M. F., re- 
 quired for varying the speed, is usually obtained 
 
 by commuting the field coils ; that is, by arranging the 
 field-winding into a certain convenient number of coils, 
 and connecting these coils, by a suitable device, in 
 series or parallel. When the coils are all in parallel, 
 their united M. M. F. is a minimum, and the speed of 
 the armature is consequently highest. While, when 
 the coils are all in series, their M. M. F. is a maximum, 
 and the speed of the armature consequently least. It 
 is undesirable to commute the field coils of shunt ma- 
 chines, owing to their large inductance, and the high 
 pressures that may be excited in them when the current 
 strength is suddenly altered by commutation. 
 
 188. It is possible, under extraordinary conditions, to 
 obtain a shunt motor, of say, 30 KW. capacity, 
 
 which by inserting resistance in the field circuit, and 
 thus varying the M. M. F., will vary its speed under con- 
 stant torque and constant terminal pressure in the ratio 
 of 3 to 1. Under usual conditions, however, the speed 
 cannot be altered in this way in a higher ratio than 1.25. 
 Series- wound motors can be controlled in speed by com- 
 muting their field-coils in a ratio of from 1.25 to 2.0, 
 depending upon the amount of torque exerted by the 
 motor; that is, upon the current through the machine, 
 and the reluctivity of the iron at the existing M. M. F. 
 
180 
 
 189. The condition of variable torque and constant 
 speed is commonly met with in operating machin- 
 ery, especially machine tools, where varying loads have 
 to he encountered at constant speeds. A series motor, 
 unless specially controlled, is unable to maintain these 
 conditions, since the M. M. F. is constantly varying with 
 changes in the load. 
 
 A shunt motor would maintain a constant speed under 
 variable torque, up to full load, disregarding the modifi- 
 cations induced into the magnetic circuit by armature 
 reactions, if there were no drop in the armature resist- 
 ance. In motors of between 3 and 50 KW. capacity, the 
 armature drop averages about 4 per cent, at full load, 
 and the speed will, therefore, alter in the ratio of about 
 1.04 between light and full loads. This is usually a suffi- 
 ciently close regulation of speed, but it is possible to 
 employ a compound-wound motor, having the same con- 
 nections as a compound-wound generator, and, therefore, 
 so arranged that the armature current slightly weakens 
 the M. M. F. of the magnets, thus forcing upon the arma- 
 ture a constant speed under all loads. 
 
 190. The fourth condition, viz., that of variable tor- 
 que and variable speed, is best exemplified in the 
 
 case of the electric railroad motor. This condition is 
 practically met both by the insertion of resistance in the 
 armature circuit, and by varying the M. M. F., of the field 
 magnets, which are usually of the series wound type. Such 
 methods, however, while they may satisfy ordinary re- 
 quirements, are far from being a complete solution of 
 the problem, and no method has yet been introduced, 
 which can accurately control, within a wide range, under 
 variable torque, the speed of a motor on a constant po- 
 
181 
 
 tential circuit. In this direction the capabilities of the 
 electromagnetic motor appear to least advantage. 
 
 191. When a shunt-wound motor has to be started 
 from rest, and, therefore, from a condition of 
 
 zero c. E. M. F., it is necessary, since the resistance of a 
 large motor armature is very small, that the terminals 
 of the armature should not be directly connected to the 
 mains, inasmuch as such an armature connection would 
 practically constitute a short circuit to the mains, for the 
 tirst rush of current passing through the armature before 
 its inertia can be overcome, and its c. E. M. F. generated, 
 may be sufficient to destroy the armature winding 1 , or to 
 injure seriously its mechanical construction. 
 
 In order to avoid this danger it is usual to introduce a 
 resistance called a starting resistance into the armature 
 circuit, by the drop of pressure in which, the- pressure at 
 the armature terminals may be correspondingly reduced. 
 As soon as the armature is sufficiently accelerated to pro- 
 duce a suitable c. E. M. F., this resistance is gradually cut 
 out of circuit, thereby causing the motor to still further 
 accelerate, until its full speed and c. E. M. F. are attained, 
 when the resistance is entirely removed. 
 
 192. In consequence of the reversibility of a gene- 
 rator and motor, it might be supposed that the 
 
 output of a dynamo-electric machine would be the same, 
 whether employed as a dynamo or as a motor. This, 
 however, is not the case, since in a generator the fric- 
 tion losses are supplied directly from the engine, while 
 in a motor they have to be supplied from the driving 
 current. Suppose, for example, that a generator, sup- 
 plies 100 amperes at 100 volts terminal -pressure, or 10 
 
182 
 
 KW. When running at full load, its loss, expended in 
 friction, of say 2 KW., is supplied from the engine, which 
 delivers 12 KW. to the generator pulley. If the machine 
 be driven by the same full load current of 100 amperes 
 as a motor, and with the same terminal pressure of 100 
 volts, its intake will be 10 KW. and its output say 8 KW. 
 
 :oo 
 
 WATTS. INTAKE 
 
 FIG 69. 
 
 Curves showing Expenditure of Power in a Half- Horse-Power Series Wound Motor 
 wound for 500 volts. 
 
 Owing to this cause, a one KW. generator will be, say, a 
 0.75 KW. 'motor, or practically one H. p., but a large gene- 
 rator of, say, 175 KW., might be a 160 KW. motor. 
 
 198. Figs. 69 and 70 give curves taken from actual 
 
 tests of a well known type of motor ; Fig. t>9, 
 
 being a test of a series-wound H. p. motor, and Fig. JO 
 
183 
 
 a corresponding test of a shunt-wound machine of the 
 same make and power. The characteristic properties of 
 shunt and series-winding, in regard to speed and effici- 
 ency, are clearly shown. The loss of energy taking 
 place at all activities up to full load is shown, for the 
 Held as magnetizing energy (*' 2 /'), for the armature as 
 drop (i 2 r) and for friction of eddy-current, hysteretic 
 
 100 
 
 WATTS. INTAKE 
 
 FIG. 80 
 
 Curves showing Expenditure of Power in a Half-Horse-Power, Shunt-Wound Motor 
 wound for 500 volts. 
 
 and mechanical types combined. Thus, at an output of 
 850 watts, the shunt motor is seen to have absorbed 640 
 watts, of which 82 were expended in magnetizing the 
 field, 50 in heating the armature, and the remaining 158 
 in frictions, representing a commercial efficiency of 54.0 
 per cent.; while, at the same output with the series ma- 
 chine, the intake was 620 watts, with 57 in the field 
 
184 
 
 magnets, 70 in the armature, and the remainder of 143 
 in frictions, representing a commercial efficiency of 56.4 
 per cent. The speed of the series machine drops from 
 38.5 revolutions per second at no load, to 21 revolutions 
 per second at full load, while the speed of the shunt 
 machine drops from 29.2 revolutions per second at no 
 load, to 25 at full load. The series machine is somewhat 
 cheaper to construct, since its field magnets are wound 
 with a few turns of coarse wire instead of many turns 
 of finer and more expensive wire, but the regulation in 
 speed of the shunt motor is much closer. 
 
 SYLLABUS. 
 
 The regulation of speed in a motor under constant 
 torque, connected to constant potential mains may be 
 obtained either by inserting resistance in the armature 
 circuit, or by altering the M. M. F. of the tield magnets. 
 This variation of speed is practically limited in range, 
 and constitutes the principal disadvantage of the electric 
 motor. 
 
 The uniform regulation of speed in a motor under 
 variable torque, when connected to constant potential 
 mains, is readily obtained either by shunt winding, or still 
 more closely, by compound winding. 
 
 The regulation in speed in a motor under variable tor- 
 que, when a wide range of speed and torque have to be 
 maintained, is accomplished by the insertion of resist- 
 ance in the armature circuit and by varying the M. M. F. 
 of the n'eld magnets, whiclr are usually series-wound. 
 
 Dynamo-electric machines have, other things being 
 equal, a greater output when employed as generators 
 than as motors. 
 Laboratory of 'Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 Nn 94 "NViv^MRTTR 94- 18Q4- Price, - 10 Cents. 
 
 S J4, 1 M. Subscription, $3.00. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GRADE. 
 
 ELECTRIC MOTOR, 
 
 (CONTINUOUS CURRENT TYPE.) 
 
 194. Motor armatures, like dynamo armatures, are 
 either smooth-cored or toothed-cored. The 
 toothed-cored armature was one of the earliest forms 
 devised. Latterly, however, owing to its mechanical and 
 electrical ad vantages, the toothed-cored armature has again 
 come into almost universal favor. In a smooth-cored 
 armature the electrodynamic force is mainly exerted upon 
 the wires on its surface and, therefore, unless these 
 wires are very carefully bound and secured, they are 
 liable to be dislodged. In the toothed-cored armature, 
 not only are the wires more completely protected from 
 injury and in a position more favorable to complete in- 
 sulation, but the electrodynamic force is no longer ex- 
 erted upon the substance of the copper, but on the mass 
 of the iron in the teeth. The M. M. F. of the current in 
 the wires, affects the distribution of flux from the M. M. F. 
 of the field magnets through the armature core, and 
 produces a distortion of flux density which serves to 
 
 Published by 
 THE ELECTRICAL ENGINEER, 
 
 203 Broadway, New York, N. Y. 
 
 [Entered as second-class matter at the New York, N. Y., Post Office, June 14, 1894.] 
 
186 
 
 rotate the armature according to the law of tractive 
 force, ( dynes per sq. cm.) as already explained. 
 
 \8 7T / 
 
 Moreover, eddy currents are avoided in the substance of 
 the conductor; for the flux no longer penetrates the 
 wires themselves, but is deflected by the surrounding 
 iron either to one side or to the other. This effect does 
 not alter the E. M. F. produced in such imbedded wires, 
 since the rate of linking flux with them remains equally 
 effective ; and, although the electrodynamic force set up 
 by currents in the wires changes its point of application, 
 yet its amount is unaltered. 
 
 195. The effect of armature reaction, in a motor, is 
 the same as in a dynamo, except that its relative 
 direction is reversed ; that is to say, the polar edge which 
 is weakened is the trailing pole, or the pole that is left, 
 and the pole which is strengthened, is the leading pole 
 or the pole that is approached. This is evidently owing 
 to the fact that, other things being equal, the current in 
 the armature is in the reverse direction to that produced 
 when it is operating as a dynamo, and, consequently, the 
 direction of the armature M. M. F. is reversed. 
 
 Since the rotation of a motor is produced by electro- 
 dynamic force, the leading pole requires to have its flux 
 density strengthened by armature reaction, and the fol- 
 lowing, or trailing pole, must be correspondingly weak- 
 
 (B 2 
 ened. That is to say, the distribution of - , is such as 
 
 8 7T 
 
 to increase at the leading polar edge, in accordance with 
 the principles described in Section 116, so that the arma- 
 ture is pulled around in the direction of the denser flux. 
 In a generator, however, the armature has to be moved 
 
by mechanical force away from the denser flux, at the 
 
 (B 2 
 strengthened pole-piece where the distribution of 
 
 is greater, and, therefore, the trailing polar edge is 
 strengthened by armature reaction. Consequently, the 
 fact that the direction of both armature reaction and 
 armature M. M. F. must be opposite in a motor to that 
 which exists in a dynamo, is the fundamental law under- 
 lying all considerations of direction of relative rotation 
 in motors and generators. 
 
 196. As a consequence of the preceding fundamental 
 law, it will be seen, that in order to preserve the 
 same direction of rotation of the armature as a motor 
 that it possesses as a generator, the direction of current 
 through the armature must be reversed, unless the direc- 
 tion of the current in the field magnets is also reversed. 
 That is to say, the relative direction of M. M. r. between 
 field magnets and armature must be reversed. 
 
 (1.) Shunt-wound machines will preserve their direc- 
 tion of rotation as motors, either when the current 
 through them retains the same direction, or when the 
 E. M. F. at their terminals retains the same direction, as 
 in their condition as generators. 
 
 (2.) Series- wound machines will reverse their direction 
 of rotation as motors, either when the current through 
 them retains the same direction, or when the E. M. F. at 
 their terminals retains the same direction, as in their 
 condition as generators. 
 
 (3.) In order to reverse the direction of rotation of a 
 motor it is necessary to change the M. M. F. in either field 
 or armature ; i.e., to reverse the direction of either the 
 field or armature. Merely reversing the direction of pres- 
 
188 
 
 sure at the motor terminals ; or, what is the same thing, re- 
 versing the direction of current through the entire motor, 
 
 DIRECTION OF 
 TERMINAL CURRENT PRESERVEI 
 
 DIRECTION OF 
 TERMINAL E. M. r. PRESERVED 
 
 GENERATORS 
 
 Elec.Engin.eer 
 
 FIG. 71. 
 
 Showing Relative Direction of Rotation in Generators and Motors. 
 
 does not change its direction of rotation unless the ma- 
 chine be separately-excited. These relations are indi- 
 
189 
 
 cated diagram matically in Fig. 71, where the uppermost 
 row of machines are separately excited, the middle row 
 are shunt-wound, and the lowest row series-wound. The 
 large arrows point out the directions of M. M. F. in field 
 and armature, and the curved arrows the direction of 
 armature rotation. It is evident that in order to retain 
 as a motor the direction of rotation possessed as a dyna- 
 mo, a relative reversal of M. M. F.'S in field and armature 
 must be effected. 
 
 197. When a motor is connected with an E. M. F., 
 current flows through the motor, and electrody- 
 namic force is set up, as we have seen, between the 
 armature and field fluxes. Under the action of this 
 force, the motor accelerates until its c. E. M. F. is suffi- 
 cient to limit the current strength it receives to the amount 
 required for the performance of the total work expended 
 in and by the motor at the speed which it must main- 
 tain to develop that c. E. M. F. When, however, two 
 motors are connected in series, they will tend to accele- 
 rate, until, by their united c. E. M. F.'S, the current they 
 receive is limited to the total work they absorb; but 
 since by varying their relative speeds the same amount 
 of c. E. M. F., and the same amount of work, may be 
 distributed between them in an indefinitely great num- 
 ber of ways, it is clear that their relative speeds will be 
 indeterminate. For, as an example of such instability, 
 consider two similar, separately-excited motors A and B, 
 to be connected in series, and each loaded by indepen- 
 dent, equal and uniform torques, such as by weights sus- 
 pended over their pulleys. Then, for a given current 
 strength passing through the armatures, by symmetry, 
 the two motors will run at equal speeds, dividing the 
 
190 
 
 total voltage equally between them, and exerting equal 
 activities. But any slight accidental increase in the tor- 
 que imposed on one motor, say A, instead of automatically 
 causing an increased current strength from the mains to 
 overcome the extra load, might be met by the absolute 
 stoppage of A, with a doubled speed on the part of its 
 neighbor B. The same current strength would continue 
 to flow through the armatures, but one motor would do 
 all the work and generate the entire c. E. M. F. 
 
 198. For the same reason, motors which are oper- 
 ated in series arc circuits, are difficult to con- 
 trol in speed unless their torque increases with the 
 speed, as in the case of fan motors, or unless some 
 speed governing mechanism is employed to vary the 
 torque in relation to the speed. Few motors of any con- 
 siderable size are, therefore, operated upon series circuits. 
 
 It is often necessary in practice to reverse the direction 
 of a motor. For this purpose it is only necessary to re- 
 verse the M. M. F. either of the field or of the armature. 
 It is customary in such cases to reverse the connections 
 of the armature. Care lias to be taken, however, not to 
 apply too powerful an F,. M. F. at the brushes, immedi- 
 ately after such reversal ; for, the c. E. M. F. of the arma- 
 ture, which will be still revolving by its momentum in 
 the original direction, will now be an E. M. F. in the 
 same direction as the driving current, and will, therefore, 
 aid in producing a very powerful current through the 
 armature, which may act as a short circuit on the mains. 
 
 199. Whatever may be the importance of small 
 weight in the case of stationary electric motors, 
 
 there can be no doubt that, in the case of electric loco- 
 
191 
 
 motors, it is desirable to reduce their weight for a given 
 output as much as possible. For a given output the 
 torque required may vary within wide limits, and is in- 
 versely as the maximum speed the motor has to main- 
 tain. When a motor can produce a given output, it is 
 evident that any torque can be theoretically obtained from 
 it by sufficiently increasing or reducing the speed of rota- 
 tion through the necessary gearing. In practice, however, 
 such gearing is frequently objectionable from the fric- 
 tion, noise and wearing introduced by it. Thus, street- 
 car motors as first employed, reduced their speed of 
 rotation by double gearing from 12 to 25 times, accord- 
 ing to the type and power of motor employed. They 
 now usually reduce their speed by single gearing from 
 four to five times, requiring, however, a slower armature 
 speed and a greater corresponding torque for the same 
 output ; or, in other words, a more powerful motor. By 
 employing cast steel, multipolar, field magnets, and by 
 economy in weight, street car motors are built which de- 
 velop at their armature shafts a torque of 133,000 dyne- 
 cms., per ampere, per kilogramme, that is 0.00448 or 
 212-5 pound-foot, per ampere, per pound of total motor 
 weight, not including the weight of gearing ; so that at 
 this rate, a 500-volt motor weighing 223 pounds, and 
 supplied with one ampere, would exert a torque of one 
 pound-foot. A 500-volt stationary motor of about the 
 same size (15 H. p.) usually exerts a torque at its arma- 
 ture shaft, of about 0.001 to 0.0015 pound-foot per am- 
 pere, per pound of weight, so that street-car motors are 
 usually about four times more powerful than stationary 
 motors in reference to their weight. 
 
 > Of 
 
 UNIVERSITY 
 
192 
 
 SYLLABUS. 
 
 In smooth-cored armatures, the electrodynamic force 
 is largely exerted upon the substance of the conductors 
 wound upon its surface, but in toothed-cored armatures, 
 the armature is sheltered from both eddy currents and 
 from electrodynamic force by the surrounding iron. 
 
 In a generator, the leading polar edge is weakened, 
 while in a motor it is strengthened by armature M. M. F. 
 and reaction ; consequently, the M. M. r. in a motor arma 
 ture must, for the same direction of rotation be reversed 
 in direction to that which existed in a generator. 
 
 Motors operated in series, are unstable in speed unless 
 their torques are either maintained in uniformity, or in- 
 creased at a greater ratio than their speeds. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 No. 25. DECEMBEK 1, 1894. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED CRADE. 
 
 ELKCTRIC HBATINQ. 
 
 200. When an electric current of strength i, ex- 
 pressed in c. G. s. units, passes steadily through a 
 
 resistance of r c. G. s. units, a c. E. M. r. of e = i r c. G. s. 
 units is developed in the resistance, while energy is ex- 
 pended by the current against this c. E. M. F., at the rate of 
 e i = i 2 r ergs per second, and appears in the resistance 
 as heat. Transformed into practical units, a current of i 
 amperes, passing steadily through a resistance of r ohms, 
 develops a c. E. M. r. of i r volts, and does work at the 
 rate of one joule per second (10 megergs), or with an 
 activity of one watt, as heat in the resistance. 
 
 201. The scientific unit of heat generally employed 
 is the amount of heat required to raise the tem- 
 perature of a gramme of water from 3 to 4 C. This 
 unit is indifferently called the lesser calorie, the therm, 
 the gramme-calorie, or the water-gramme-degrce-centi- 
 grade. 
 
 Since the calorie is not a c. G. s. unit, it is more con- 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 303 Broadway, New York, N. Y. 
 
 [Entered as second-class matter at the New York, N. Y., Post Office, June 14, 1894.] 
 
194 
 
 venient, in electrical engineering, to employ as the prac- 
 tteal unit of heat, its mechanical equivalent ; namely, the 
 joule, or 10 megergs. The joule is equivalent to 0.23D 
 therifi ; or, in other words, 4.18 joules approximately are 
 required to be expended in heat to raise the temperature 
 of one gramme of water one degree C. (One British 
 Thermal Unit, or B. T. u., that is, 1 pound of water raised 
 from 68 to 69 F., requires an expenditure of 1053 
 joules, so that, roughly, 1 B. T. u. = 1 kilojoule). 
 
 Heat produced in resistance by electrical currents is 
 either purposely developed, as in electric heaters or elec- 
 tric furnaces, or incidentally and unavoidably developed, 
 as in dynamo machinery and wires conveying currents. 
 
 202. The flow of heat through a conductor follows 
 the same law as that which determines the flow of 
 electricity through a conductor, i. e., Ohm's law. If 6, 
 be the difference of temperature in degrees Centigrade, 
 between two parallel plane surfaces of the conductor, 
 and xS r , the thermal resistance of this portion of the con- 
 ductor, then H, the strength of the thermal current, in 
 joules per second, will be 
 
 $, is determined as follows ; viz., if y, be the thermal re- 
 sistivity, Z, the length of the conductor in cms., and , 
 its cross-sectional area in square centimetres, then 
 
 #=*-. 
 a 
 
 The thermal resistivity of a substance is the reciprocal 
 of its thermal conductivity, and may be defined as being 
 equal to the reciprocal of the amount of heat, expressed 
 
195 
 
 in joules, which will traverse a cube of the material one 
 cin. in length of edge, in one second of time, with 1 C. 
 difference of temperature between two opposed faces. 
 
 Thus, if a wire had a resistance when heated to 100 
 C. of 1.41 ohms, and was enclosed in a cubical box 
 whose internal edge was 10 cms. in length, with walls 
 composed of felt and 1 cm. thick, the external surface 
 being zinc lined, and maintained by immersion in 
 water, at a temperature of 20 C., then if the wire were 
 so disposed within the interior that its temperature 
 was immediately communicated to the internal surface 
 of the walls, these would each have a cross-section of 
 100 sq. cms. and a difference of temperature of 80 C. 
 between the inner and outer surfaces. The thermal re- 
 sistivity of felt, expressed in c. o. s. units, according to 
 the above notation is about 2750, so that the resistance 
 
 1 V 2750 
 
 of each wall Avould be - : = 27.5, and since the 
 
 1UO 
 
 box has six walls, the total thermal resistance would be 
 ^2. = 4.583. The flow of heat would, therefore, be 
 
 80 
 
 = 17.46 joules, and the current strength which 
 4.583 
 
 would have to be sent through the wire to maintain its 
 temperature, with that of the interior walls, at 100 C., 
 would be 1.41 X i 2 17.46, or i = 3.52 amperes. 
 
 The preceding relations form the basis for determining 
 the amount of energy required to be expended in obtain- 
 ing a fixed temperature in a closed electric stove of given 
 dimensions and material, after due allowance has been 
 made for the thermal capacity of the contents ; i.e., of 
 the amount of heat required to be expended in such 
 
196 
 
 contents in order to raise them initially to the required 
 temperature. 
 
 203. The following is a list of thermal resistivities 
 for a few substances. These values can only be 
 regarded as approximations. Comparatively few obser- 
 vations have been made, and the thermal resistivity of a 
 substance, like its electric resistivity, varies both with its 
 physical condition and with its temperature. 
 
 Like electric resistivities, it would seem that good 
 thermal conductors conduct better, and good thermal 
 insulators insulate better at low temperatures. 
 
 THERMAL RESISTIVITIES IN JOULEAN UNITS. 
 
 THERMAL CONDUCTORS. 
 
 Silver 0.17 
 
 Copper 0.225 
 
 Zinc 0.81 
 
 Brass 0.83 
 
 Iron 1.52 
 
 Lead 1.95 
 
 German Silver 2.29 
 
 THERMAL INSULATORS. 
 
 Stone 50 
 
 Chalk. . 100 
 
 Glass ..................... 100 
 
 Sand ..................... 300 
 
 Gutta-percha ............. 500 
 
 Caoutchouc .............. 600 
 
 Clay ..................... 800 
 
 Sawdust .................. 2000 
 
 Wool ...... - .............. 2100 
 
 Paper ................... 2200 
 
 Vulcanized Indiarubber. ... 2700 
 
 Felt. 
 
 2750 
 
 204. In general, heat developed in a conductor by 
 the passage of an electric current is dissipated by 
 conduction, radiation and convection. The conduction 
 losses, as we have seen, depend both upon the dimen- 
 sions and thermal resistivity of the conducting substance, 
 and the difference of temperature at opposing surfaces. 
 The loss of heat by radiation follows less simple laws, 
 and the loss of heat by convection is still more complex. 
 
197 
 
 205. Radiant heat is believed to be a purely electro- 
 magnetic phenomenon, and its laws are not yet 
 
 accurately known. The rule commonly employed in com- 
 puting the amount of radiation from a hot body is an 
 empirical rule determined by Dulong and Petit from a 
 large number of practical observations : The loss by 
 radiation is proportional to the surface of the heated 
 body, to the nature of the surfaces of surrounding bodies, 
 arid is in geometrical proportion to the absolute tempera- 
 ture of the surfaces. The loss of heat from a body by 
 convection depends upon the temperature of the surface 
 of the body, the nature, and density of the surrounding 
 medium, the normal amount of motion in the medium 
 (for instance, wind in the case of air) and the form of 
 the body, with the friction which its surface offers to 
 the motion of the medium. The result is a complex 
 thermodynamical and hydrodynamical problem which 
 has only been reduced to quantitative results in a very 
 few cases. 
 
 206. Although radiation from the surface of the hot 
 wire takes place in geometrical proportion to its 
 
 temperature elevation, yet it is usually sufficient, within 
 the range of ordinary temperatures, to take a mean 
 value of the radiation in direct proportion to the rise of 
 temperature. 
 
 One sq. cm. of bright copper radiates 0.0006 watt per 
 C temp, elevation (approximately). 
 
 One sq. cm. of blackened copper radiates 0.001 i watt 
 per C temp, elevation (approximately). 
 
 For practical purposes the convective loss of heat 
 from a wire supported horizontally in still air, may be 
 taken as independent of the diameter, and as equal to 
 
198 
 
 0.00175 watt per linear cm. of the wire per C. of temp, 
 elevation (0.0533 watt per foot). In moving air, as for 
 example, in ordinary weather out of doors, the convec- 
 tive loss is usually many times greater. 
 
 20Y. The temperature elevation of a wire, for a 
 given current strength, depends upon its resistivity, 
 diameter, covering and environment. A bare wire is 
 best cooled by supporting it on insulators in the open 
 air, where any breeze or other motion of the air that 
 may exist, will carry off its heat convectively. A 
 covering of, say, cotton, rubber, or other electric non- 
 conductor will, up to a certain thickness, serve to cool 
 the wire by increasing its surface, even although the 
 thermal resistivity of such materials is very high. A 
 buried, insulated w r ire is usually kept much cooler, 
 by conduction through the substance of the soil, than 
 the same wire suspended in quiescent air; while an 
 insulated wire, submerged in water, is maintained still 
 cooler, by reason of rapid convection of heat through 
 the water together with its large thermal capacity. 
 
 The following table gives the diameter of copper 
 wire, required to carry the various current strengths, 
 with an elevation of 20 0. in temperature, as deduced 
 from actual measurements of the heating of wire under 
 different conditions. If the normal temperature of a 
 wire be 30 C., the continued passage of the tabulated 
 current strength will cause the wire to approximately 
 attain the temperature of 50^ C., which will enable 
 the wire to be held in the hand without pain, and 
 such a temperature may be considered as a safe limiting 
 temperature. Fire insurance rules both in the United 
 States and in Great Britain require a lower temperature 
 
109 
 
 elevation and limiting current-strength in order to pro- 
 vide a margin of safety, namely, what is equivalent to 
 an elevation of 10 C. at full load, or about 33 per cent, 
 less current strength. 
 
 TABLE OF DIAMETERS OF COPPER WIRE, OF CONDUCTIVITY 98 PER 
 CENT. MATTHIESSEN'S STANDARD, ELEVATED 20 C. BY VARIOUS 
 CURRENT STRENGTHS ix AMPERES (ALTERNATING OR CON- 
 TINUOUS). 
 
 Effective 
 Current 
 Strength 
 Amperes. 
 
 Covered Wire 
 in Wooden 
 Moulding. 
 
 Bare Wire Suspended 
 Horizontally in Still Air 
 Within Doors. 
 
 Bright. Blackened. 
 
 Bare Wire Suspended 
 Horizontally in Calm 
 Weather Out of Doors. 
 
 Bright. Blackened. 
 
 
 Inches. 
 
 Inches. 
 
 Inches. Inches. 
 
 Inches. 
 
 5 
 
 O.020 
 
 0.015 
 
 0.014 o.on 
 
 010 
 
 10 
 
 0.036 
 
 o 030 
 
 O.O28 O.O22 
 
 0.020 
 
 15 
 
 O.OJ2 
 
 0.045 
 
 0.042 0.032 
 
 0.030 
 
 20 
 
 0.069 
 
 0.060 
 
 0.057 0.042 
 
 0.039 
 
 25 
 
 0.085 
 
 0.075 
 
 0.068 0.052 
 
 0.049 
 
 3 
 
 O.IOO 
 
 0.090 
 
 0.080 0.061 
 
 0.038 
 
 35 
 
 0.114 
 
 0.103 
 
 0.092 0.070 
 
 0.066 
 
 40 
 
 0.127 
 
 0.115 
 
 0.105 0079 
 
 0074 
 
 45 
 
 0.140 
 
 0.128 
 
 0.117 0.087 
 
 0.082 
 
 So 
 
 0.152 0.140 
 
 0.130 0.094 
 
 0.089 
 
 60 
 
 o 175 
 
 o.i 68 
 
 o 152 0.108 
 
 o 103 
 
 70 
 
 0.197 
 
 0.190 
 
 0.171 O.I22 
 
 olu6 
 
 So 
 
 2l8 
 
 O.2I2 
 
 O.I92 
 
 0.134 
 
 0.128 
 
 9 
 
 0.236 
 
 0.2 3 5 
 
 O.2iO 
 
 0.146 
 
 o 140 
 
 100 
 
 .-<54 
 
 0257 
 
 0.227 
 
 0-157 
 
 0.151 
 
 I2 5 
 
 O.2Q2 
 
 0.307 
 
 0.265 
 
 0.183 
 
 0.175 
 
 150 
 
 0.326 
 
 -3 6 5 
 
 0.308 
 
 O.21O 
 
 O.2O2 
 
 175 
 
 -357 
 
 0.410 
 
 o-347 
 
 0.234 
 
 o 227 
 
 200 
 
 0.386 
 
 0.450 
 
 0-385 
 
 0.256 
 
 0.248 
 
 2 5 
 
 0.440 
 
 0.520 
 
 0-455 
 
 0.299 
 
 O.2yO 
 
 3 00 
 
 
 0.615 
 
 0.518 
 
 0-339 
 
 0-330. 
 
 400 
 
 
 0.765 
 
 0.640 
 
 0.418 
 
 0.406 
 
 500 
 
 
 
 o 910 
 
 0.750 
 
 0.488 
 
 0.471 
 
 600 
 
 
 .... 
 
 0.857 
 
 0-550 
 
 0-533 
 
 700 
 
 
 .... 
 
 0.958 
 
 o.6n 
 
 o-593 
 
 800 
 
 .... 
 
 .... 
 
 
 0.671 
 
 0.650 
 
 goo 
 
 .... 
 
 .... 
 
 .... 
 
 0.717- 
 
 0.693 
 
 IOOO 
 
 
 .... 
 
 
 0.782 
 
 0-745 
 
200 
 
 208. The rapid elevation of temperature in an over- 
 loaded conductor is practically employed in safety 
 fuses which are formed of high resistivity conductors 
 with a small surface per unit length and a low melting 
 point, so that an excess of current strength above their 
 rated capacity readily fuses them. The heat developed 
 in a safety fuse depends upon its resistivity at the work- 
 ing temperature, on the current strength, and on the 
 length of the fuse. As the current strength, and con- 
 sequently the temperature, increases, the resistivity of 
 the metal increases, the energy expended in unit length 
 increases, and the rate of dissipation of the energy by 
 conduction, radiation and convection also increase until 
 the melting temperature is attained. Except in fuse 
 wires of very small diameter, the predetermination of 
 their melting current becomes very complex and differ- 
 ent under different circumstances, such as the inclination 
 of the fuse, its surface, condition, etc. With large fuses 
 the capacity for heat may be such that an enormous over- 
 load may be safely carried for a very brief interval, the 
 energy being expended in raising the temperature of the 
 metal while a much smaller steady increase of load 
 would certainly melt them. 
 
 SYLLABUS. 
 
 Heat escapes from a hot body by conduction, radiation 
 and convection. Conduction follows a law similar to 
 Ohm's law. Radiation is believed to be a purely elec- 
 tromagnetic function of the ether and follows laws not 
 yet fully ascertained. Convection is a still more com- 
 plex function depending upon the material environment 
 of the body. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 No 2fi DT?mr\rRT?p 8 1 8Q4- Price ' 10 Cents. 
 
 ^ X ** Subscnption, $3.00. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GRADE. 
 
 LIGHTING 
 
 209. AVhen a substance is lieated to the temperature 
 of incandescence, it imparts energy, by wave mo- 
 tion or radiation, to the surrounding ether. This wave 
 motion comprises a great variety of vibration frequencies. 
 All waves of frequencies lying between the limits of ap- 
 proximately 390 trillions and 760 trillions per second, are 
 capable of affecting the eye as light. All radiations 
 whose frequencies lie outside these limits, since they fail 
 to affect the eye are called non-luminous or obscure radi- 
 ations. Of the radiant energy emitted by a body, only 
 a certain quantity consists therefore of luminous energy. 
 
 210. If w, be the activity of radiation per unit dif- 
 ference of frequency, the total luminous activity 
 
 can be expressed as, 
 
 760,000,000,000,000 
 
 y- 
 w dn watts, 
 
 390,000,000,000,000 
 
 where n, is the frequency. This is shown in Fig. 72, 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 203 Broadway, New York, N. Y. 
 
 [Entered as second-class matter at the New York, N. Y., Post Office, June 14, 1894.] 
 
202 
 
 which roughly represents the distribution of radiant 
 activity with reference to the frequency of vibration in 
 an ordinary incandescent lamp. The frequencies com- 
 prised between the ordinates e Jc and g h, are luminous 
 frequencies. The shaded area e f g h #, comprised be- 
 tween the curve and base, between these limits, repre- 
 sents the number of watts expended by the lamp in 
 luminous radiation. The unshaded areas represent the 
 non-luminous activity. The ratio of the shaded to the 
 unshaded area is about 0.03. 
 
 X10 
 
 FlG. 72 
 
 Distribution of radiant energy from incandescent filament with respect to vibration 
 frequency. 
 
 Area, e f g h k = luminous activity in watts. 
 Curve, A B c = physiological coefficient of illuminating power referred to standard 
 
 frequency as unity. 
 Area, E F G H K = effective physiological illuminating power. 
 
 The total flux of radiation activity emitted by a fila- 
 ment of surface-area, S sq. cms. at an absolute temperature 
 T, is expressed by 
 
 P = TcSTe aT watts, 
 
 where k, is a constant depending upon the nature of the 
 filament, and a = 0.0043. 
 
 The luminous effect produced on the average normal 
 eye by a given quantity of radiation activity, say one 
 watt, is not the same in different parts of the spectrum ; 
 
203 
 
 that is, at different frequencies. For the average eye, 
 the maximum effect is produced in the yellow, at a fre- 
 quency of about 500 trillions per second. The amount 
 of illuminating power in a given source of light cannot 
 therefore be determined from the total activity of radia- 
 tion. It becomes necessary to determine the illuminating 
 values of one watt of activity at all frequencies within 
 visual limits. If this physiological coefficient of illumi- 
 nation be expressed by z, in suitably chosen units, or, as in 
 Fig. 72, by reference to the physiological effect B D, at some 
 standard frequency, taken as unity, then the illuminat- 
 ing value of any quantity of energy w dn, covering a 
 small range of frequency dn, will be z w dn, and we 
 obtain by the application of the coefficient z, a new 
 curve E F G H K, whose area is 
 
 7.6 XlO 14 
 
 w dn 
 
 3.9 XlO 14 
 
 units of physiologically effective illumination. For this 
 reason it is impossible to compare accurately the illumi- 
 nating power of two different sources of light, such as a 
 candle and an arc light, unless the physiological coeffi- 
 cient 2, at present undetermined, be known for all parts 
 of the spectrum, as well as the distribution of activity in 
 the spectra of the two sources. 
 
 211. The most efficient source of light, if it could 
 be produced, would be that in which all the en- 
 ergy radiated possessed a frequency within visual limits. 
 Considering illuminating power alone, that particular 
 frequency near which 2, is a maximum, that is some- 
 
 <2*Ui r &^T^ 
 
 where near the ^cHow of the spectrum, would be the 
 most advantageous frequency the source could possess, 
 
204 
 
 but, considered with reference to fitness for agreeable 
 illumination and the distinction of colors, that distribu- 
 tion of frequencies would be the most desirable which 
 best agreed with the distribution in sunlight. 
 
 212. The frequencies which are predominant in the 
 radiation of bodies heated to incandescence, are 
 non-luminous frequencies. Consequently, in all artifical 
 sources of illumination, the larger proportion of the en- 
 ergy radiated is of a useless character. It has been found 
 that, in the neighborhood of 1 ,000 C., as the temperature 
 of a luminous body increases, the luminous radiation 
 rapidly increases, so that the attainment of a very high 
 temperature is essential for a successful artificial illumi- 
 nant. A high refractory power is necessary, therefore, 
 to sustain the high temperature required, and carbon is 
 the only common substance which has yet fully met 
 this requirement. An illustration of the importance of 
 a high temperature, and the efficiency of luminous radi- 
 ation, is seen in the case of the arc and incandescent 
 lamps, each of which employ incandescent carbon as a 
 source of radiant energy, but in the arc lamp the tem- 
 perature attained, being that of the volatilization of car- 
 bon, is higher than that which the incandescent filament 
 can safely and continuously sustain. The amount of 
 energy expended in an arc lamp is usually about 450 
 watts, and of this about eight per cent, is expended in 
 luminous radiation, the balance being non-luminous, while 
 in incandescent lamps the percentage of luminous radia- 
 tion is about three. Moreover, the distribution of energy 
 differs in these two sources of light, the average physio- 
 logical coefficient being greater in the spectrum of the 
 arc lamp, than in the spectrum of the incandescent lamp. 
 
205 
 
 213. The object in the commercial incandescent lamp 
 is to produce an electrically heated incandescent 
 surface at the highest practical temperature ; for, as we 
 have seen, such a temperature will produce the best effi- 
 ciency of luminous radiation and a fair approximation 
 to the character of sunlight. 
 
 The high temperature necessary for the proper work- 
 ing of an incandescent lamp must be uniformly main- 
 tained over the entire surface of the filament, and, to 
 insure this, the resistance of the filament must necessarily 
 l)e uniform .per unit of length, since, otherwise, on the 
 passage of a steady current through it, different parts 
 would glow with unequal brightness and the parts un- 
 duly heated would be rapidly destroyed, or, if preserved 
 at the safe temperature, the rest of the filament would be 
 insufficiently heated. 
 
 214-. The standard of physiological effective luminous 
 radiation, or, as it is ordinarily called, the standard 
 of light, differs in different countries. In the United 
 States and in Great Britain it is the standard candle 
 burning 2 grains (0.1296 gramme) per minute ; in France, 
 a Carcel lamp of definite dimensions, burning 42 grammes 
 of colza oil per hour ; in Germany, a Hefner- AltenecJc 
 lamp of definite dimensions burning amyl-acetate with a 
 flame four cms. high. The light emitted from one square 
 centimetre of platinum at a definite high temperature is 
 also employed as a standard in Germany under the name 
 of the Reichsanstalt Unit. In France the Violle lamp 
 of molten platinum was adopted by the International 
 Paris Conference of 1881, but has not come into general 
 use. 
 
 According to the best determinations one standard 
 
206 
 
 British candle = 0.0506 Violle, = 0.1053 carcel, = 1.14 
 Hefner Alteneck. 
 
 215. The illumination received by any surface is the 
 quantity of light (the physiologically effective flux 
 
 of light) received by its surface per unit area. Thus, if 
 the standard candle be regarded as the unit point-source 
 of light, the total quantity of light it emits is 4 TT, units 
 of luminous flux, and one unit of luminous flux received 
 per square centimetre would constitute unit illumination. 
 No name or unit of illumination has, however, yet been 
 adopted, but common expressions of illumination refer to 
 the candle-foot, or the carcel-metre as unit, these being 
 respectively the illumination produced, on a perpendicu- 
 lar surface by a candle at a distance of one foot, and by 
 a carcel at a distance of one metre. These intensities 
 of illumination are nearly equal, one candle-foot being 
 greater than one carcel-metre in the approximate ratio of 
 1.133. 
 
 216. The proper lighting of a room depends upon its 
 dimensions, and upon the character of its interior 
 
 surface. Highly diffusive wall surfaces require a smaller 
 amount of light to produce the same general degree of 
 illumination. The character of the illumination will 
 also depend upon the amount of light and upon its dis- 
 tribution. A single source of light will usually produce 
 the greatest local and the lowest average illumination, 
 while the same total quantity of light from numerous 
 distributed sources will produce the opposite results. In 
 the case of incandescent lamps, an illumination upon the 
 surface of a book, equivalent to one carcel-metre, is suf- 
 ficient for the purposes of easy reading. This is usually 
 obtained in a room by allowing 1 candle power to the 
 
207 
 
 square foot of floor space, or one 16 c. P. lamp to 50 sq. 
 feet, while rooms not devoted to reading purposes, unless 
 darkly papered, will be amply illumined by one 16 c. P. 
 lamp per 100 sq. feet of floor space. The intensity of 
 illumination from a single point-source of light is inversely 
 as the square of the distance from tlie^ source, so that a 
 room with a high ceiling, lighted by incandescent lamps 
 placed on the ceiling, would receive on a desk or table a 
 lesser degree of illumination than if the lamp were lower, 
 and, in any case, the illumination on the surface of the 
 desk or table is ordinarily greater than on the surface of 
 the floor. In determining, therefore, the number of in- 
 candescent lamps required for the proper illumination of 
 a room, reference must be had not only to the character 
 of the illumination but to the parts of the room where 
 such illumination is specially required. 
 
 217. The number of watts that have to be supplied to 
 an incandescent lamp per candle power that it 
 
 yields is frequently called the efficiency of the lamp, but 
 could more accurately be called the inefficiency of the 
 lamp or its specific activity r , since the greater the number 
 of watts supplied per candle obtained, the lower the ef- 
 fective physiological efficiency of the lamp. 
 
 The true efficiency of the lamp, or its specific illumi- 
 nating power, is the reciprocal of this, or the number of 
 candles obtained from the lamp per watt supplied to it. 
 The efficiency at which new lamps are usually operated, 
 ranges between -i- and ^ candles per watt. 
 
 218. The higher the temperature at which a lamp is 
 operated the greater its efficiency, but the shorter 
 
 its probable duration of life. 
 
208 
 
 When an incandescent lamp is steadily operated at 
 constant pressure, the light it emits steadily decreases, 
 that is, its efficiency becomes reduced. This is owing to 
 two causes consequent upon the disintegration of the fil- 
 ament. First, to the deposition of the disintegrated 
 material as an opaque coating on the walls of the lamp 
 globe, thereby reducing the amount of light emitted, and 
 second, to the reduction in the cross-section of the tila- 
 ment by the disintegration and the consequent increase 
 in resistance, whereby less energy is absorbed by the 
 lamp. .- 
 
 SYLLABUS. 
 
 The physiological effect on the retina of different re- 
 lative frequencies within visible limits is different ; gener- 
 ally, therefore, the physiological effect of a given quantity 
 of luminous activity varies with different sources of light. 
 
 The illumination required on a well lighted table in 
 an ordinary room is about one carcel-rnetre, or usually, 
 two sixteen candle power lamps for every 100 square 
 feet of floor space. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 No. 27. DECEMBER 15, 1894. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GRADE. 
 
 INCANDESCENT LIGHTINQ 
 
 219. When a new incandescent lamp is connected 
 to mains which supply it uniformly with the 
 pressure for which it was designed, say, for example, a 
 pressure of 110 volts, the lamp having an initial resist- 
 ance when hot of 252 ohms, the current through the 
 lamp will be 0.4364 ampere, and the activity in the 
 lamp will be 48 watts ; or, if the lamp supplies 16 c. P., 
 an efficiency of | candle per watt. The first effect of 
 the high temperature upon the filament, may be to re- 
 duce its resistance by a coking or carbonizing process 
 sustained by heating in a vacuum. The current, 
 therefore, which passes through the lamp, together with 
 the activity of the lamp, will increase in corresponding 
 measure, thereby increasing the temperature of the 
 filament, and the candle-power as well as the efficiency 
 of the lamp. Tiiis diminution in resistance, which, 
 however, does not occur in all lamps, soon ceases, and, 
 after say twenty hours, the resistance of the filament 
 begins to increase. 
 
 Published by 
 THE ELECTRICAL ENGINEER, 
 
 203 Broadway, New York, N. Y, 
 
 [.Entered as second-class matter at the New York, N. Y., Post Office, June 14, 189}.] 
 
210 
 
 The candle-power of the lamp attains its maximum 
 with the minimum resistance of the filament. 
 
 220. The temperature of the filament in incandes- 
 cent lamps, operated at an efficiency of J candle 
 
 per watt, is estimated to be about 1345 C.; at | candle 
 per watt about 1310 C.; and at * T candle per watt 
 about 1290 C. An increase of one per cent, in the 
 activity of a glowing lamp, i.e., in the number of watts 
 it absorbs, is believed to increase the temperature of its 
 filament about 2 C. and its candle-power or its total 
 flux of light about three per cent. 
 
 221. The progressive increase in the resistance of the 
 filament during use, is due to the reduction in the 
 
 diameter and cross-sectional area of the filament. This 
 reduction in the diameter of the filament is brought about 
 *by one or all of the following causes ; namely, 
 
 (^.) Mechanical, by the explosive evolution of occluded 
 gases in the surface layers of the filament. 
 
 (2.) Chemical, by the removal of the surface layers 
 of the filament through chemical combination with some 
 of the constituents of the residual gases in the globe. 
 
 (3.) Physical, by electrical evaporation of the surface 
 layers under the influence of high temperature and elec- 
 trification. 
 
 222. Not only is the diameter of the filament de- 
 creased and its resistance thereby increased, but 
 
 the emissivity of the surface is considerably increased. 
 
 The temperature of the filament is thus lowered dur- 
 ing the use of the lamp for two reasons ; first, because 
 the emissivity of the surface increases by reason of the 
 surface change, thus enabling the same quantity of activ- 
 
ity per unit surface to be radiated at a lower tempera- 
 ture, and secondly, because the diminished conductance 
 of the filament causes it to take less activity from the 
 mains in the same proportion. There is thus less activ- 
 ity in the lamp and also less temperature elevation re- 
 quired to radiate the activity that remains. 
 
 223. The carbon which is thus removed from the 
 surface of the filament is slowly deposited on the 
 
 inside of the lamp globe in a dark semi-opaque layer, 
 cutting off some of the light emitted by the filament 
 and, therefore, tending to reduce the efficiency of the 
 lamp. Each of these three causes ; namely, increased 
 resistance, increased emissivity, and increased opacity, 
 decreases the efficiency of the lamp to approximately 
 the same degree. As a consequence, new lamps starting 
 at an efficiency of ^ candle per watt, steadily decrease 
 in their efficiency after the first few hours, until an 
 efficiency even lower than ^ candle per watt may be ulti- 
 mately reached. 
 
 224. The physiologically effective luminous radiation 
 from a lamp increases rapidly with the current, 
 
 between the fifth and sixth powers of the current strength. 
 Since at incandescent temperatures, the temperature 
 coefficient of variation in the resistivity of the filament 
 is small, and a small change of temperature is accom- 
 panied by a great change in candle power, it follows that 
 the candle-power of a lamp varies with the terminal 
 voltage between its fifth and sixth powers, and therefore 
 approximately as the cube of the intake in. watts. 
 
 Since the efficiency of a lamp steadily decreases with 
 its continued use, there must come a time when even if 
 
212 
 
 the filament does not break, the light emitted becomes 
 so small in proportion to the power consumed, that it 
 may be more economical to destroy the lamp and replace 
 it by a new one, than to continue its use at such low 
 efficiency. The length of time during which it will 
 be advantageous to continue the use of such a lamp will 
 depend on the cost of electrical energy and on the cost 
 of new lamps. Although this may be determined on a 
 large scale of operation, as in central station lighting, it 
 is practically impossible to lay down an inflexible rule 
 for the economical breaking point of any lamp, since it 
 is evidently economical to retain a lamp in employment 
 so long as it supplies sufficient light to meet the purposes 
 required of it. 
 
 225. In large cities in the United States, practical 
 experience in central station work shows that the 
 
 maximum load is approximately 50 per cent, of the total 
 number of lamps connected with the system, that the 
 average load is approximately 27 per cent, of the maxi- 
 mum load and the minimum load from 10 to 20 per cent, 
 of the maximum load. 
 
 226. Attempts have been made at different times to 
 produce a lamp capable of being regulated in 
 
 candle power, when supplied from constant potential 
 mains, thus corresponding to the gradual turning off at 
 the key in a gas burner. This has been accomplished in 
 the case of the incandescent lamp in two ways; first, by 
 introducing additional resistance into the lamp circuit 
 and, second, by reducing the time during which, in 
 periodic contacts, the iilament is in connection with the 
 mains. Both methods result in a considerable reduction 
 
213 
 
 of efficiency in the lamp, and a diminished temperature 
 of the filament, so that the light is not only more expen- 
 sively produced but also becomes duller in color. 
 
 227. In large installations where the number of lights 
 required is great and the distance from the supply 
 
 centre not excessive, incandescent lamps are almost in- 
 variably connected to the supply mains in parallel. The 
 parallel connection method of distribution is both simple 
 and economical. But where the district to be lighted is 
 scattered, necessitating long circuits on which the density 
 of lighting is not great, this method becomes very ex- 
 pensive in all cases where a comparatively small drop is 
 to be maintained on the supply mains. In such cases it 
 is more economical to employ a high tension system ; 
 that is, either a series-connected system ; or, as is more 
 common, an alternating current system in connection 
 with transformers. In a series incandescent system, the 
 lamps are connected to the circuit in series. The resist- 
 ance of series incandescent lamps is usually compara- 
 tively small and the current they take greater than in 
 multiple incandescent lamps. In many cases incandes- 
 cent lamps are connected in series arc circuits, and, there- 
 fore, require to be operated by the current generally 
 employed in such circuits, namely, about 10 amperes. 
 
 228. The rupture of a filament, which merely ex- 
 tinguishes the lamp in a multiple-connected cir- 
 cuit, in a series circuit extinguishes all the lamps in that 
 circuit, unless a device be employed to cut out the im- 
 perfect lamp. This is frequently accomplished by means 
 of a film cut-out. Fig. 73 shows a series incandescent 
 lamp and a film cut-out arranged in the lamp base. This 
 
cut-out consists of a film of paper which insulates per- 
 fectly at a pressure of 20 volts, but breaks down com- 
 pletely under a pressure approaching that of the full 
 pressure in the circuit, so that the two contact points 
 separated by the film become welded together as soon 
 as the lamp breaks. This cut out is placed either in the 
 base of the lamp or in the socket. 
 
 529. Since one per cent, change in the pressure sup- 
 plied to the terminals of an incandescent lamp, 
 above or below the normal pressure, produces about 5 
 
 FIG 73. 
 
 Series Incandescent Lamp with Film Cut-Out. 
 
 per cent, change in the amount of light supplied by the 
 lamp, it is necessary to ensure that the drop of pressure 
 in the mains supplying different lamps shall not be ex- 
 cessive. Where a large number of lamps have to be 
 supplied in parallel from a network of mains, the pres- 
 sure will be lowest at the most distant lamps. If when 
 all the lamps are lighted, the maximum drop of the 
 most distant lamps amounts to, say, 10 per cent, of the 
 pressure of the dynamos, then it is desirable to make 
 the average pressure for the whola system, the normal 
 
215 
 
 pressure for which the lamps are designed. In this case 
 the distant lamps will be operated at 5 per cent, below 
 pressure, while those nearest to the dynamo will be oper- 
 ated at 5 per cent, above pressure. This will -reduce 
 the average life of the nearest lamps in a very marked 
 degree, while the distant lamps, will be below candle- 
 power by an amount which depends upon their normal 
 efficiency. The usual range of drop permitted in the 
 wiring of buildings supplied by their own dynamos is 
 from 2 to 5 per cent, of the pressure at the dynamo ter- 
 minals, according to the size of the building, i.e., from 
 1 to 2^ per cent, above or below the normal mean. So 
 that, allowing 5 per cent, drop, if the normal voltage of 
 the lamps be 110, the dynamo pressure would be 112.8 
 and the pressure at the lowest lamp 107.2 volts. The 
 lamps nearest the dynamos would, therefore, give say 19 
 candles initially and the lamps furthest from the dynamo 
 13.5 candles. 
 
 230. The difficulty arising from drop experienced in 
 the lightiLg of a single building, is greatly in- 
 creased when the lighting has to be extended over a 
 large area, in a city, from a single central station. In 
 such cases excessive drop may be avoided by the use of 
 suitably located and proportional feeders. A feeder is a 
 conductor, one end of which is connected to the bus- 
 bars at the station, and the other end is connected to 
 some point on the mains, there being no lamps connected 
 directly to the feeders, so that the mains supply the 
 lamps, while the feeders supply the mains. In this way 
 it is possible to maintain say 110 volts at a very distant 
 lamp, with a drop of perhaps three volts in the mains, 
 making 113 volts at the feeding point, but with a drop 
 
 or 
 
216 
 
 of 17 volts in the feeder or feeders, and a pressure of 
 130 volts at the central station. In other words, it is 
 possible to have 15 or 20 per cent, drop in the feeders 
 and only a very small range of drop in the mains and 
 house wires. 
 
 The number and size of feeders employed in distrib- 
 uting currents from a central station depends upon the 
 cost of the power which has to be expended in the drop 
 under existing conditions of load, upon the cost of the 
 various sizes of feeder, upon the facility with which the 
 pressure can be maintained uniform at feeder terminals 
 and its effect upon the average 'life time and proper 
 operation of lamps. Feeders have to be so selected that 
 the total cost, including these items, together with depre- 
 ciation shall be a minimum. 
 
 SYLLABUS. 
 
 The resistance of an incandescent lamp increases with 
 its use. 
 
 This increase is due to a decrease in its diameter that 
 may be produced by mechanical, chemical and physical 
 causes. 
 
 The effect of the decrease of the diameter of the fila- 
 ment is not only accompanied by an increase in its re- 
 sistance, but also by an increase in the emissivity of its 
 filament and by a blackening of the globe. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 NY> 9S "n-uwc'Ttni-E'i? 99 1 SQJ. Price, - 10 Cents. 
 
 ,EMBEK JJ, 1 *k. Subscnption, $3.00. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED CF?AE>E 
 
 ARC LlQHTINQ. 
 
 23 1 . The voltaic carbon arc consists of a bow-shaped 
 cloud of volatilized carbon, formed between the 
 points of two carbon electrodes by the passage of an 
 electric current. In order to produce this current, a 
 pressure of from 30 to 55 volts has to be maintained 
 between the carbon electrodes. This pressure is 
 required by reason of resistances in the arc, and partly 
 by a c. E. M. F. The c. E. M. F. depends upon the quality 
 of the carbons employed and the temperature attained. 
 When the arc is very short, the temperature is compara- 
 tively low, and the c. E. M. F. comparatively small, but 
 for arcs of -J in. or more, the c. E. M. F. varies from 35 to 
 40 volts, and the drop due to resistances increases with 
 the length of arc, being about 50 to 75 volts per inch, 
 (20 to 30 volt per cm.), of distance between the elec- 
 trodes. The current strength employed varies from 3 
 to 200 amperes, according to the size and nature of the 
 carbons. Consequently, the activity in the carbon voltaic 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 03 Broadway, New York, N. Y. 
 
 [Entered as second-class matter at the New York, N. Y., Post Office, June 14, 1804.] 
 
218 
 
 arc may have a very wide range. The ordinary com- 
 mercial arc lamp takes about 10 amperes at 45 volts 
 pressure between lamp terminals, and, therefore, has an 
 activity of about 450 watts. Such an arc lamp is some- 
 times described as a 450-watt arc lamp, but is more pre- 
 cisely described as a 450-watt 45-volt arc lamp. 
 
 232. Of the E. M. F. in the arc lamp, about 38 to 
 40 volts are usually developed at the surface of the 
 
 positive electrode, 4 to 6 volts in the arc proper, and the 
 remainder in the carbon rods and the electromagnetic 
 apparatus. The activity is, therefore, about 400 watts 
 at the surface of the positive carbon, 40 to 60 watts in 
 the arc proper, and the remainder in the substance of 
 the carbons and conductors. So large a proportion of the 
 activity at the positive carbon surface, necessitates the 
 development there of an exceedingly high temperature, 
 and, consequently, this is the principal source of light in 
 the voltaic arc, about 85 per cent, of all the light being 
 emitted from the glowing surface of the positive carbon, 
 about 10 per cent, from the arc proper, and about five 
 per cent, from the surface of the negative carbon. 
 
 233. The high value of the c. E. M. F., developed at the 
 positive surface, is analagous to the c. E. M. F. de- 
 veloped at the surface of the electrode in an electrolytic 
 cell. In this case, however, the work is not expended 
 in freeing ions from molecular combinations, but in vola- 
 tilizing carbon, and the high temperature is accompanied 
 by intense radiation. Consequently, all the volatilization 
 occurs at the end of the positive carbon, which is thereby 
 hollowed out in the form of a minute crater, the principal 
 source of light in the arc. The character of the lumin- 
 
ous radiation will depend on the quality of the carbon 
 electrodes and their distance apart ; but, with the same 
 material, the distance being maintained constant, the 
 temperature at the surface of the positive carbon will be 
 uniform if the current strength is adequately main- 
 tained.- Carbon having, like other substances under 
 fixed conditions, a fixed temperature of volatilization, 
 (estimated at 3,500 C.), the temperature at the posi- 
 tive carbon, and consequently the intensity of radiation, 
 are thereby determined. It has been found that the 
 brightness of the positive crater amounts to about 16,000 
 British standard candles per square centimetre, or, 
 roughly, 100,000 candles per square inch. 
 
 The negative carbon is at a temperature sufficiently 
 below that of the positive to permit the volatilized car- 
 bon to be condensed upon its surface in the shape of a 
 small mound or nipple of graphite. 
 
 234. The temperature of volatilization of carbon 
 being so much greater than that at which carbon 
 
 monoxide forms, is probably above the dissociation tem- 
 perature of carbon and oxygen, so that the carbon vapor 
 can only oxydize at the external surface when the tem- 
 perature suddenly falls. This accounts for the coating 
 of flame which surrounds the arc itself, and for the com- 
 paratively slow rate of carbon consumption. 
 
 235. With the carbons arranged as is usual in street 
 lamps with both carbons in the same vertical 
 
 line the positive above the negative, the amount of 
 light given off from the arc varies in different angular 
 positions. This difference in the intensity of the emitted 
 light is due to the following circumstances : 
 
220 
 
 (1.) The positive crater, the main source of light, is not 
 a plane surface, but is concave ; the principal distribution 
 of its radiant flux is, consequently, downwards. 
 
 (2.) The crater being surrounded by a wall of opaque 
 carbon, the horizontal intensity of the emitted light is 
 comparatively small, and, since the edges of the wall are 
 irregular, the horizontal intensity varies in different 
 azimuths. 
 
 (3.) However closely the axis of the two carbon elec- 
 trodes may be aligned, the arc will rarely remain long at 
 
 Elec. Engineer 
 
 FIG. 74. 
 
 Diagram Indicating Luminous Intensity of an Arc Lamp in Different Directions. 
 
 the centre, but tends to travel around the edges of the 
 positive carbons, thereby causing the crater to appear on 
 the side of the arc, and tending to increase the illumina- 
 tion on that side. 
 
 (4.) The arc is usually accompanied by some flame of 
 a reddish color surrounding the arc proper, like a lum- 
 inous cloud, and the light from this source is of an 
 unstable flickering nature, shifting irregularly. 
 
 5. Even the smallest mechanical irregularity or chemi- 
 cal impurities, liable to be present in the best carbons, 
 develop fluctuations in the intensity of the light. 
 
221 
 
 Fig. 74 represents graphically, in polar co-ordinates, the 
 relative distribution of luminous intensity from an ordi- 
 nary 500-watt, 50- volt arc lamp. It will be seen that the 
 maximum intensity is developed at an angle which is ap- 
 proximately 50 below the horizontal plane. The hori- 
 zontal intensity is usually only about 10 to 20 per cent, 
 of the maximum intensity, and, in the actual example 
 here represented, o B, or o G is only about 11 per cent, of 
 o c, or o F. The horizontal intensity is subject, owing to 
 the causes above mentioned, to much greater fluctuations 
 than the maximum intensity. The mean spherical can- 
 dle power is the average intensity measured in candle- 
 power for all directions. The mean spherical candle- 
 power is usually about 30 to 40 per cent, of the maxi- 
 mum intensity and from 2 to 4 times greater than the 
 horizontal intensity. In Fig. 74 the radius o j is, in 
 length, 30 per cent, of the radius o c, or o F. The ordi- 
 nary empirical formula which fairly expresses the ob- 
 served relationship between the spherical and maximum 
 intensities is, 
 Mean spherical intensity = 
 
 Mean horizontal intensity , Maximum intensity. 
 
 HP ~T~ 
 
 It is evident that the total quantity of light emitted 
 will be 4 TT X mean spherical intensity in units of lu- 
 minous flux. 
 
 236. The nominal intensity of an arc lamp, as for ex- 
 ample, that of a 2,000 candle-power arc, means the 
 maximum intensity of the arc under favorable conditions 
 of carbons and operation. A preferable rating, however, 
 would be either by the total luminous flux of the arc 
 lamp or its mean spherical candle-power. 
 
The greater the current strength through an arc lamp 
 the greater the surface which becomes elevated in tem- 
 perature. If the carbons are too small, this will be ac- 
 accompanied by flaming disintegration, and other dis- 
 turbances, but if the carbons be suitably increased in 
 diameter, the increase in total luminous flux will be 
 safely obtained. For a given arc lamp of 48 volts pres- 
 sure, it has been observed that an empirical relation exists 
 between the intensity of the current strength fairly ex- 
 pressed by the formula, 
 
 Maximum luminous intensity = 190 i -f- 4 i z , 
 where * = current strength in amperes. 
 
 So that a 480-watt, 10-ampere arc lamp gives under 
 favorable conditions a maximum intensity of 2,300 
 candles. 
 
 237. A great difficulty exists in accurately measuring 
 the candle power of an arc-lamp by the use of 
 any of the ordinary standards of light. This difficulty 
 is due not only to the rapid fluctuations constantly occur- 
 in the arc, but also to the difference in the character be- 
 tween the light of the arc and that of the ordinary 
 standards with which it is compared. An arc lamp is 
 particularly rich in waves of high frequency ; namely, 
 those near the violet end of the spectrum, and the eye is 
 unable fairly to match intensities between lights of es- 
 sentially different colors. This difficulty has led to the 
 proposal of a special standard for arc lamp photometry, 
 based on the relation which has been found to exist be- 
 tween the amount of light emitted per unit surface of the 
 crater in the positive carbon. 
 
 The arc lamp whose luminous intensity is to be meas- 
 ured is compared in the photometer with what might be 
 
223 
 
 called a unit-arc-light crater-intensity, which consists 
 of a standard arc lamp whose crater is exposed to the 
 photometer through an opening of standard dimensions 
 in an opaque and artificially cooled screen. 
 
 Most arc light carbons, in use in the United States, 
 are provided with a thin metallic coating of copper, 
 electrolytically deposited. The effect of this coat- 
 ing is not only to decrease the resistance of the rods, 
 but also to prevent irregular burning and disintegration. 
 Carbons so protected are more apt to burn with com- 
 paratively blunt ends, and, therefore, to last longer. 
 Unprotected carbons are apt to burn in points, and thus 
 seriously interfere with the proper feeding of the 
 carbons, that is, their automatic adjustment as to distance. 
 
 238. During use, the carbons consume unequally. 
 The positive carbon consuming roughly twice as 
 rapidly as the negative carbon. The more rapid con- 
 sumption of the positive carbon is due not only to the 
 higher temperature but also to the fact that it is volatil- 
 ized. For this reason the positive carbon is generally 
 made about twice as long as the negative carbon. 
 Attempts have been made to prolong the duration of 
 the carbons by increasing their diameter, but whenever 
 the diameter of the carbon exceeds a certain limit, de- 
 pending upon the strength of the current, the light be- 
 comes unsteady, owing to the tendency of the arc to 
 travel around the edges of the larger cross section 
 offered. Less objection is experienced to increasing the 
 diameter of the negative carbon, alone, but even here, 
 the increased duration is accompanied by increased fluc- 
 tuations in the light. 
 
 The average length of the positive carbons employed 
 
224 
 
 in systems of street lighting does not usually exceed 12 
 inches, the length of the negative carbon being about 
 seven inches. Such a pair of carbons will ordinarily 
 last about 7 hours when T \- in. in diameter, and 
 about 9 hours when in. in diameter. Consequently, 
 during prolonged runs, such as are necessitated during 
 winter, a lamp provided with but a single pair of such 
 carbons would require re-carboning during the night. In 
 order to avoid this, various expedients have been adopted, 
 such as an increase in the diameter of carbons already 
 alluded to. The method in general use is that of employ- 
 ing two pairs of carbons side by side, so arranged that one 
 pair of carbons is first consumed and the second pair is 
 then automatically switched into the circuit. Such a lamp 
 is commonly called a dou~ble-carbcm,, or all-night lamp. 
 
 SYLLABBUS. 
 
 The c. E. M. F. of a carbon voltaic arc is principally 
 resident at the surface of the carbon electrode or crater. 
 
 It is commonly considered that a 450-watt 45-volt arc- 
 lamp gives a maximum of 2,000 candle-power, but this 
 is only true under the most favorable conditions. 
 
 An arc light differs principally from the light of 
 candles, incandescent lamps and other luminous sources, 
 in being richly provided with luminous waves of high 
 frequency. 
 
 The mean horizontal intensity of an arc lamp is much 
 more variable than its maximum intensity, but is com- 
 monly about 15 per cent, of the maximum intensity. 
 
 The mean spherical intensity of an arc lamp is about 
 35 per cent, of its maximum intensity. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 No. 29. DECEMBER 29, 1894. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED CF?ADE 
 
 ARC LIOHTINO. 
 
 239. On constant current circuits, arc lamps are 
 generally operated in series and are then supplied 
 by special generators known as arc-light dynamos. 
 These generators are always series-wound. The number 
 of lamps operated in series is commonly about 50, 
 though occasionally it reaches about 100, and in rare in- 
 stances 200. The largest arc generator yet constructed 
 being for 200 lamps, a pressure of about 10,000 volts exists 
 between machine terminals. Since the number of arc 
 lights in a circuit is seldom constant, the generator 
 must maintain a constant current under all conditions 
 and must be able to vary the E. M. F. it generates. 
 
 When a series arc-light circuit, Fig. 750, containing say 
 10 lamps, and having a total pressure at machine termin- 
 als of 500 volts, is perfectly insulated from the ground, 
 there will, by symmetry, be a difference of potential be- 
 tween the positive brush and the ground of 250 volts, 
 and a difference of potential between the negative brush 
 
 Published by 
 
 THE ELECTRICAL ENGINE 
 203 Broadway, New York, N. 
 
 [Entered as second-class matter at the New York, N. Y M 
 
226 
 
 and the ground of an equal amount, while a point B, in the 
 circuit, situated electrically midway between the termi- 
 nals, will be at zero potential, and could, therefore, be con- 
 nected to the ground without in any way disturbing the 
 pressures or current strengths in the circuit. If, however, 
 instead of connecting the circuit to ground at its central 
 point, the ground connection were made at any other 
 point, such, for example, as at the positive terminal of 
 the generator, D, Fig. 75&, that point would be reduced 
 
 1-200 
 
 O.-HOO 
 
 I 
 
 o 
 
 -100 
 -200? 
 --300Q 
 -400 > 
 -500 
 
 -t-400 
 H- 300' 
 ^+200 
 >+lOO 
 
 Elec.Engineer 
 
 FIG. 75. 
 
 Distribution of Electric Potential in Continuous Current Series Arc Circuit. 
 
 to zero potential, the symmetry of pressure at the 
 dynamo terminals would be disturbed and the potential 
 of the negative terminal would become 500 volts. Sim- 
 ilarly, if the ground connection, instead of being made 
 at D, were made at G, Fig. 75tf, the potential at that point 
 would be reduced to zero, producing the distribution 
 of potential shown. There would, however, be no 
 permanent flow of current from the circuit through the 
 ground connection while the insulation of the rest of the 
 
227 
 
 circuit is preserved. If, however, a second ground con- 
 nection occur, then a current would flow through both 
 ground connections of a strength determined by the 
 resistance of the ground connections and the difference 
 of potential between the points of contact. 
 
 Thus if, Fig. 75c, a slight leak to ground were at- 
 tached at the point H, the E. M. F. tending to send a cur- 
 rent through the leak to ground would be the difference 
 of potential between H and the ground, or 250 volts. A 
 man standing on the ground at H and coming in contact 
 with the wire would be subjected to a pressure of 250 
 volts. 
 
 240. Arc lights are sometimes operated on constant- 
 potential circuits, usually at from 110 or 220 volts 
 pressure. In Fig.. 75 ten arc lamps are represented as 
 being connected in series, and the extremities of the cir- 
 cuit are assumed to be connected to a generator directly. 
 The advantage of the series arc-circuit is a high pressure 
 and the small diameter of conductor which may be em- 
 ployed for conveying the total strength of current, usu- 
 ally 10 amperes, and this, in a district of street lighting 
 covering an extended area, is a matter of considerable 
 importance. The advantage of multiple-arc lighting is 
 found in the combination of arc lamps with incandescent 
 lamps, from the same circuit, without additional wires or 
 generators. In many cases it is more economical to place 
 arc lights on already existing incandescent circuits, rather 
 than establish entirely separate series-circuits and a spe- 
 cial generator, even though the amount of copper re- 
 quired in the circuits be considerably increased. This is 
 partly on account of the increased simplicity of the sys- 
 tem, the reduced space and cost of generators, and partly 
 
228 
 
 on account of the greater efficiency of incandescent genera- 
 tors. But the conditions under which economy exists in 
 the use of constant potential arc lamps are limited, and 
 each case must be determined on its own merits. 
 
 Two lamps are generally operated in series on a 110 
 volt circuit, and four lamps in series on 220 volt cir- 
 cuit. A small resistance is usually inserted in the circuit 
 of each lamp to assist in its regulation. The usual cur- 
 rent strength employed in constant-potential lamps is 
 from 4 to 10 amperes. The best results are obtained 
 with a cored carbon, for the positive electrode. With 
 the usual twelve inch positive and seven inch negative 
 carbons, of ^ inch diameter, a lamp with a current of 
 nine amperes will last nearly nine hours. 
 
 241. Arc lamps are sometimes operated from special 
 generators on alternating current circuits. In 
 such cases, since the carbons are alternately positive and 
 negative, neither crater nor nipple forms on the car- 
 bons, which burn with comparatively blunt points. In the 
 alternating current arc, the temperature is evenly distri- 
 buted; consequently, the horizontal candle-power does 
 not differ so markedly in intensity from the maximum, 
 and there are two directions of maxima, one upwards 
 and one downwards, as shown in Fig. 76, which repre- 
 sents in polar co-ordinates the distribution of light in a 
 particular case. The distribution varies considerably 
 with different current strengths and characters of carbon. 
 Alternating current arcs are usually operated from local 
 step-down transformers, by which a pressure of from 28 
 to 35 volts alternating is supplied directly to the 
 lamp terminals. The current in the main or primary cir- 
 
cuit of the generator is usually about 30 amperes, instead 
 of 9 or 10, as in the continuous-current circuit, by which 
 means a lower total pressure for a given number of arcs 
 can be obtained. 
 
 242. In the application of the voltaic arc to search- 
 lights, exceedingly powerful currents are em- 
 ployed with suitably proportioned carbons, so that a very 
 great intensity of light is obtained. In order to throw 
 
 FIG. 76. 
 
 Distribution of Light from an Alternating Current Are as measured in a particular case. 
 
 this into an approximately parallel beam, instead of dif- 
 fusing it in all directions, the carbon arc is formed at the 
 focus of a suitable projector. These projectors may be 
 catoptric, i. e., reflecting ; or, dioptric, that is, re- 
 fracting. 
 
 The usual form is, however, a reflector of the parabolic 
 or spherical type. Since large parabolic projectors are 
 very expensive, a spherical reflector is generally em- 
 
230 
 
 ployed. This consists of a lens-shaped mass of glass the 
 two sides of which have different radii of curvature, the 
 exterior surface being silvered. The light from the car- 
 bon arc, on entering the substance of the glass, suffers re- 
 fraction, and it is then reflected from the silvering at the 
 exterior surface again suffering refraction on issuing 
 from the glass into the air. The curvatures are so chosen 
 with regard to the index of refraction of the glass, that 
 the light emerges in a sensibly parallel beam. The car- 
 bons are usually tilted at such an angle that the crater 
 
 FIG. 77. 
 
 Speciment of MagiuTtiu. Reflector. Section through Axis. Dimensions in Centimetres. 
 
 is most effectively exposed towards the reflecting mechan- 
 ism. In many cases a small reflector is employed near 
 the arc to throw its light on the lens. 
 
 The beam of light issuing from a search light projector 
 being only approximately parallel, necessarily diverges 
 and lessens in intensity with the distance from the appa- 
 ratus. Beyond a distance of a few hundred feet, the illu- 
 mination produced by the beam approximately varies 
 inversely as the square of the distance. Neglecting, how- 
 
231 
 
 ever, the absorption of light by dust and fog in the at- 
 mosphere, the total flux of light in the beam remains 
 constant, so that the area of the beam increases after the 
 flrst few hundred feet approximately as the square of the 
 distance. 
 
 A Mangin reflector is represented in axial section in 
 Fig. 77. The arc being placed at the principal focus 
 A, which in this case is 38.3 cms. from the centre of 
 the inner surface, throws a beam parallel to p A, of dia- 
 meter D E, the surface B o.c, being silvered. 
 
 243. Carbon arc lights for street lighting are gener- 
 ally surrounded by globes, which may be clear or 
 ground. In either case a loss of light is thereby entailed, 
 but a more uniform diffusion of light obtained. This is 
 especially the case where the globe is ground or consists 
 of translucent glass or porcelain. The loss of light may 
 amount to as much as 60 per cent., but the general illu- 
 mination produced is better and shadows are avoided. 
 
 SYLLABUS. 
 
 Arc lights are generally operated commercially on 
 series circuits from specially designed dynamos, generat- 
 ing sufficient difference of potential to maintain the cur- 
 rent constant under all conditions. Arc lamps are some- 
 times operated on constant-potential circuits, with either 
 two or four lamps in series. 
 
 Arc lamps are sometimes operated on alternating-cur- 
 rent circuits from transformers. 
 
232 
 
 Alternating-current lamps have two maxima of light 
 intensity, one upwards and one downwards, no marked 
 crater being formed. 
 
 Reflectors are commonly used with large search lights. 
 
 Globes placed around arc lights, while useful for dif- 
 fusing the light, cut off from 10 to 60 per cent of the 
 total light emitted. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 No. 30. JANUARY 5, 1895. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GRADE. 
 
 Alternating Currents 
 
 The comprehension of the following definitions 
 is necessary to a clear understanding of alternat- 
 ting currents. 
 
 An alternating E. M. F. or current is an E. M. F. or cur- 
 rent which successively reverses its direction. 
 
 Fig. 78 is a graphical representation of an E. M. F. 
 or current which is alternating, for it successively changes 
 its sign, being, say, in the positive direction at a, and in 
 the negative direction at 0, while at b df h &, it has zero 
 value and no direction. 
 
 Aperiodic alternating E. M. F. or current, is an alter- 
 nating E. M. F. or current which not only periodically 
 reverses its direction, but also periodically repeats its 
 changes in magnitude. Figs. 79 to 84 represent periodic 
 alternating E. M. F.'S or currents. 
 
 The terms alternating E. M. F., or alternating current, 
 as ordinarily employed, designate periodic alternating 
 E. M. F. and current, respectively. 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 303 Broadway, New York, N. Y. 
 
 [Entered as second-class matter at the New York, N. Y., Post Office, June 14, 1804.] 
 
234 
 
 Each reversal of a periodic alternating E. M. F. or cur- 
 rent is called an alternation or semi-period. Thus in 
 Fig. 79, o a I c, or c d <?/*, orj k I m, each represent one 
 alternation or semi-period. 
 
 i i 
 
 Elec. Engineer 
 
 FIG. 78. 
 
 Graphical Representation of Non Periodically Alternating Current or E. M. F. 
 
 A complete doable alternation or double reversal is 
 called a cycle. Thus in Fig. 80, the curve oab cd efg A, 
 represents one double reversal or cycle. It is not neces- 
 sary, however, that the cycle commence at the zero point. 
 Thus cdefghjkl, mfghjkl mnp, each represent 
 one cycle. 
 
 The time occupied in executing a cycle is called a 
 period. Thus in Fig. 79, the period is 0.01 second. In 
 
 
 c 
 
 f 
 
 j 
 
 m |, 
 
 
 
 
 
 
 
 
 
 I e 
 
 ft 
 
 
 j 
 
 FIG. 79. 
 
 Periodic Alternating E. M. F. or Current. 
 Rectangular Type. 
 
 Elec. Engineer 
 
 FIG. 81. 
 
 Periodic Alternating E. M. F. or Current. 
 Zig-zag Type. 
 
 Fig. 80 the period is 0.1 second, and in Fig. 82, 0.004 
 second. 
 
 The number of periods described in one second, or 
 the reciprocal of the period, is called the frequency. 
 
23-5 
 
 245. Thus in Fig. 79, the frequency is 100 
 
 is, 100 periods per second ; in Fig. 80, 10 
 in Fig. 82, 250 ~. 
 
 that 
 and 
 
 FIG. 80. 
 
 Periodic Alternating E. M. F. or Current. Circular Type. 
 
 When the E. M. F. or current periodically reverses, it 
 may do so in an infinite variety of ways ; namely, 
 
 (1.) It may change suddenly from the positive maxi- 
 mum value to the negative maximum value, and vice 
 versa, as shown in Fig. 79. The graphical representation 
 of these reversals is a rectangular curve. 
 
 (2.) It may change gradually from the positive maxi- 
 mum value to the negative maximum value and vice 
 versa, as shown in Fig. 81. 
 
 (3.) It may change from the full positive value to the 
 full negative value according to a definite law, more 
 
 FIG. 82. 
 
 Periodic Alternaling E.M.F, 
 
 or Current. 
 Flat-Topped Curve. 
 
 FIG. 83. 
 
 Periodic Alternating E.M.F. 
 
 or Current. 
 Peaked Curve. 
 
 FlG. 84. 
 
 Periodic Alternating E.M F 
 
 or Current. 
 Sinusoidal Curve. 
 
 complex than either (1) or (2). Such changes are shown 
 in Figs. 78, 82, 83 and 84. Thus, Fig. 78 represents 
 graphically a circular variation or type of wave ; Fig. 
 
236 
 
 82, a flat-top type of wave ; Fig. 83, a peaked type of 
 wave and Fig. 84, a sinusoidal wave. 
 
 246. A sinusoidal E. M.F. or current is one whose suc- 
 cessive magnitudes with respect to time vary as the 
 sine of a quantity proportional to the time, or which 
 alternates in time according to a simple harmonic law. 
 
 .Elec.Eny tnvt>r 
 
 FIG. 85. 
 
 Graphical Representations of Simple Harmonic E. M. F.'S or Currents. 
 
 An example of a simple-harmonic motion (abbreviated 
 s. H. M.) is seen in the motion of a vertically falling shadow 
 projected upon a horizontal plane, from a point on a verti- 
 cal disc which is uniformly rotating about a horizontal 
 axis. Thus in Fig. 85, the disc Q K s, revolving uniformly 
 about its horizontal axis at o, has a pin p, whose shadow 
 
237 
 
 falling vertically upon a band of paper T v, lying in a 
 horizontal plane, produces an s. H. M. upon the paper. If, 
 therefore, the paper be moved in the direction of the 
 arrow in its own plane and in a direction at right angles 
 to the plane of the disc, the shadow will trace on the 
 paper a simple-harmonic or periodic curve, A B c D E F, 
 and this curve is called sinusoidal, because any ordinate, 
 such as o A, is proportional to the sine of the angle con- 
 tained between the radius of the pin and the vertical 
 plane through the axis of the disc. It is evident that 
 the outline of the sinusoidal curve so traced depends 
 upon the distance of the pin from the axis, and the 
 velocities of disc-rotation and paper-progression. Thus, 
 assuming the paper to move with the same velocity in 
 the four cases represented at A, B, (7 and D, respectively, 
 then the shape of the curve will only depend upon the 
 position of the pin and on the velocity of its rotation. 
 Thus, the pin is shown in the same position at A, and at 
 D, namely, near the edge of the disc ; but since the 
 velocity of rotation at D, is twice that at A, the cycle is 
 completed in half the time at J9, and the frequency of the 
 periodic motion is, therefore, twice as great at D, as at A. 
 At B arid (7, the pin is shown half way between the centre 
 and the edge of the disc, while (7, has twice the rotary 
 velocity of B. The amplitude or maximum ordinate 
 in B and C, is half that in A and D. The frequencies 
 in O and D are equal, and the frequencies in A and B, are 
 equal. The waves represented at A, B, 6 y , or D are, there- 
 fore, all sinusoidal waves in spite of their differences of 
 appearance, and any E. M. F.'S or currents, whose suc- 
 cessive changes in time are represented by such curves 
 are sinusoidal E. M. F.'S and currents. 
 
288 
 
 Calling , the time in seconds dating from the initial or 
 zero position, to, the angular velocity of the disc in radi- 
 ans per second, and Y, the amplitude, the y ordinate at 
 any instant is y = Y sin co t. 
 
 The angle contained between the radius vector o P, 
 and the initial ascending vertical radius o K, is called the 
 phase of the motion. Thus the phase of the point c, in 
 the curve of A 9 is 270, the phase of the point E, 90 and 
 of B and F, zero. 
 
 247. A coil of insulated wire, rotated with uniform 
 velocity about any diameter as axis in a uniform 
 
 magnetic flux, has generated in it a sinusoidal E. M. F." In 
 practice alternators, or dynamos for producing alternating 
 E. M. F.'S, never produce strictly sinusoidal E. M. F.'S, al- 
 though they frequently generate E. M. F.'S that are suf- 
 ficiently nearly sinusoidal to be considered as true sinu- 
 soids for purposes of computation. The E. M. F. gen- 
 erated by any practical alternator may be regarded as 
 lying between the flat-topped type of Fig. 82 and the 
 peaked type of 83. 
 
 248. Since an E. M. F. or current which is changing 
 its direction many times a second, has, at different 
 
 instants of time, all values comprised between its maximum 
 and zero, it becomes necessary to define conventionally 
 the numerical value of such an E. M. F. or current. If this 
 value were taken as being equal to the maximum, the 
 E. M. F. or current could only attain its nominal value twice 
 in each cycle. If the arithmetical mean value without re- 
 gard to sign be taken, the value so obtained is called 
 the mean E. M. F. or mean current but this value has 
 very little practical application. The value of an alter- 
 
nating E. M.F. or current is most conveniently defined 
 by reference to its heating power and this is the method 
 invariably adopted. If a given continuous-current pres- 
 sure maintains a given thermal activity in a fixed resist- 
 ance, then the alternating E. M. F., which will maintain 
 the same thermal activity in the resistance, will have the 
 same nominal val lie expressed in volts, so that this value, 
 which is called the effective value of the E. M. F., may be 
 regarded as the value of the continuous E. M. F. required 
 to produce the same thermal activity. Since, according 
 to Ohm's law, the thermal activity maintained in a re- 
 
 <? 2 
 sistance R, by an unvarying E. M. F. of ^ volts, is -^ 
 
 watts, the activity developed by a periodically varying 
 
 E. M. F., at any instant, will be similarly ^ watts, where 
 
 H 
 
 e, is the instantaneous value of the E. M. F. The value of 
 e\ if averaged over a sufficiently long time, will corres- 
 pond to the square of the effective E. M. F. e^ or in mathe- 
 matical language, if E, be the effective E. M. F., 
 
 where r, is the time occupied in any complete cycle. In 
 the case of a sinusoidal or simple harmonic E. M. F., the 
 effective E. M. F. is always the maximum E. M. F. in the 
 cycle divided by -v/2? so that the effective E. M. F. = 
 0.7071 maximum E. M. F. 
 
 SYLLABUS. 
 
 A sinusoidal E. M. F. or current is one whose successive 
 magnitudes with respect to time are represented by the 
 ordinates of a sinusoidal or simple-harmonic curve. 
 
240 
 
 ~No alternators generate strictly sinusoidal E. M. F.'S, 
 but many generate E. M. F.'S which are sufficiently nearly 
 sinusoidal to be regarded as such for purposes of com- 
 putation. 
 
 The effective value of an alternating E. M. F. or current 
 is the square root of the time average of its square. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINBBR.] 
 WEEKLY. 
 
 No. 31. JANUARY 12, 1895. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED CRADE. 
 
 Alternating Currents. 
 
 249. When two simple harmonic E. M. F.'S, of the 
 same frequency, are simultaneously impressed on 
 
 the same circuit in series, as, for example, when two 
 similar alternators are driven on the same shaft, the 
 effect produced will depend upon the relative phases of 
 the two E. M. F.'S ; for, if the two E. M. F.'S are in phase 
 their combined effect or resultant will be equivalent to 
 their arithmetical sum, or to that of a single source of 
 double E. M. F. If, however, the two E. M. F.'S are in 
 opposite phase, their resultant will be zero, and between 
 these two conditions there will be an infinite number of 
 possible intermediate resultants. In all cases, however, 
 the sum of their E. M. F.'S will be their vector or 
 geometrical sum. 
 
 250. In order to determine the value of the sum of two 
 or more vectors in a plane we proceed as follows. 
 
 Let A B, be a quantity whose magnitude and direction are 
 represented by the line A B, Fig. 86, and let o D, be a 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 203 Broadway, New York, N. Y. 
 
 [Entered as second-class matter atjthe] New York, N. Y., Post Office, June 14, 1804.] 
 
242 
 
 quantity whose magnitude and direction are represented 
 by the line c D ; then the vector sum of A B and c r>, 
 will be found by laying off from B, a line parallel to and 
 
 Elec.Engineer 
 
 FIG. 86. 
 
 equalto c D, so that the straight line A D, will be the 
 vector sum. If now A B, represents at some instant of 
 time the relative position of the sinusoidal E. M. F., of 
 say 1180 volts effective, a second sinusoidal E. M. F. 
 of say 820 volts effective, whose phase is 150 in rear 
 of A B; i.e., T 5 ^ of a complete revolution, or period, will 
 be represented by c D. For if the lines A B and c D, be 
 each set revolving counter-clockwise about the ex- 
 tremities A and c, respectively, with equal and uniform 
 angular velocities in the plane of the paper, then if c D, 
 lags 150 behind A B, when A B, reaches the position 
 shown CD, will also occupy the position indicated. Their 
 vector sum A D, will be the resultant or combined E. M. F. 
 of these two generators when placed in series at this de- 
 
 , K 
 
 PIG. 87. 
 
 finite phase relationship and will be represented by a 
 sinusoidal E. M. F. of 620 volts effective, 41 behind A B. 
 If, as represented in Fig. 87, two equal sinusoidal 
 
243 
 
 E. M. F.'S, each 1000 volts effective, are connected in 
 series at an angle of 60, or ^ period, their resultant will 
 be a sinusoidal E. M. F. of 1733 volts. T ^ period ahead of 
 E F, or y 1 ^ period behind F G. If the angular displace- 
 ment be J period, their resultant will be 1415 volts 
 effective, -J of a period later than j K ; while, if the 
 angular divergence be 150, their resultant will be 518 
 volts effective, 75 in advance of L M. 
 
 Any number of co-periodic simple harmonic E. M. F.'S 
 can be compounded into an equivalent single resultant by 
 finding their vector sum. 
 
 E 
 
 62 VOLTS 
 
 t 
 
 ^ 
 
 RESISTANCE 10 OHMS 
 
 FIG. 88. FIG 89. 
 
 The impressed E. M. F. at the terminals of an alternat- 
 ing current circuit is always equal to the geometrical 
 sum of the component c. E. M. F.'S in that circuit, that is 
 to say, if there be only resistance in the circuit, the im- 
 pressed E. M. F. will be expressed by the c. E. M. F., / R ; 
 or, if there be additional c. E. M. F.'S of the type 0, the 
 impressed E. M. F. will be expressed by the vector sum 
 Ifi + e. 
 
 This law applies to the continuous current circuit 
 where however the sum is merely arithmatical. 
 
 If, therefore, the drop / 7?, in the resistance, be laid 
 off on the line A B, Fig. 88 and the c. E. M. F., 0, due to 
 the variation of flux linkage be laid off by the line B c, 
 at right angles to A B, and 90 in advance of it, then A c, 
 
244 
 
 will be the vector sum of the c. E. M. F.'S, and this must 
 be equal to the impressed E. M. r. 
 
 251. Instead of considering the current produced in 
 an alternating-current circuit as being numerically 
 equal to the quotient of the resultant E. M. F. by the 
 ohmic resistance of the circuit, in accordance with Ohm's 
 law, it is frequently simpler to regard the impressed 
 E. M. F. as acting alone in the circuit, and that the resist- 
 ance of the circuit is altered to, what is called the impe- 
 dance of the circuit. For example, if the circuit 
 possesses a resistance a 5, Fig. 89 of say 10 ohms, and 
 the frequency of the E. M. F. be 100 ^, its angular 
 velocity will be 628.3 radians per second ; i.e. the angu- 
 lar velocity of the revolving line in the plane of 
 the paper will be 100 X 2 TT. If the inductance be 
 0.015 henry, the reactance I c, will be 0.015 X 628.3 = 
 9.425 ohms, 90 in advance of a &, and the impedance of 
 the circuit will be the geometrical sum of these two 
 components, or a c, 13.74 ohms, 43 18' in advance of 
 a b. We have, therefore, in an alternating current cir- 
 cuit, the vector relationships, 
 
 (1) Reactance of an Inductance L henrys = j 2 TT n L 
 ohms where n, is the frequency and j, is the symbol of 
 direction or V-- 1, indicating that the reactance is set 
 at right angles to the resistance. 
 
 (2) Impedance = Resistance -f- Reactance. Ohm's 
 
 T? 
 
 law applied to such a circuit becomes / = _ am- 
 
 J 
 
 peres, where /, is the vector impedance. In dividing 
 vectors, their lengths are divided numerically and their 
 angles subtracted. Thus, if p Q, and E s, Fig. 90 be two 
 vectors p Q, being 0.8 /60, and R s, 0.5 /270; or, 
 
245 
 
 0.5 \ 90, their arithmetical product will be 0.8 X 0.5 
 /270 + 60 = 0.4 /33Q' = 0.4 \30. While the 
 
 quotient of If = will be - 8 /60 270 = 1.6 / 210 
 R s 0.5 
 
 = 1.6 \ 210 = 1.6/150 as shown at T v, and v w, Fig. 
 90. If then, the resistance coil last considered, have 
 an impressed sinusoidal E. M. F. of say 52 volts, con- 
 nected to its terminals, the current in the circuit will be 
 
 M 3.785 
 
 13.74 ,/43 IS' : " /43 18' 
 
 as represented in Fig. 89, and the current will, there- 
 fore, lag 43 IS' behind the E. M. F. in phase. 
 
 252. The reactance of a condenser is the reciprocal 
 of the product of its capacity in farads and the 
 angular velocity of the impressed E. M. F. Thus, if a 
 condenser of 10 microfarads ; that if, 10~ 5 farad, be con- 
 nected directly with the terminals of the alternator of 
 100 ~, and 1100 volts effective, as measured at ter- 
 minals, the reactance of the condenser at this frequency 
 
 will be = 159.2 ohms ; but this reactance, 
 
 10- 5 X 628.3 
 
 while set off at right angles to ohmic resistance, is marked 
 in the opposite direction to inductance-reactance as shown 
 
246 
 
 at B G Fig. 91. This is for the reason that inductance 
 and capacity in a circuit tend to neutralize each others 
 influence, and, calling the inductance-reactance positive, 
 capacity-reactance is reckoned as negative. The current 
 through the condenser under these conditions will be 
 
 _ 6.91 /90. so that the current in this case 
 159.2 \ 90 
 
 leads the E. M. F. by a quarter period. The reactance of 
 
 a condenser of capacity c, farads is therefore j 
 
 ' .<? a) 
 
 ohms, where a) = 2 n n, the angular velocity. 
 
 II 
 
 FIG. 91. 
 
 The drop in a resistance in a continuous current cir- 
 cuit is 1 R, volts. The drop in the impedance of an 
 alternating current circuit is / /, volts. 
 
 Let for example, a coil of 50 ohms have an inductance 
 of 0.02 henry (20 milli-henrys) and be connected in 
 series with a condenser of 10 micro-farads capacity to 
 the terminals of a sinusoidal alternator delivering 
 1100 volts effective at a frequency of 100 ~. The re- 
 actance of the condenser will be 159.2 ohms as be- 
 fore. The reactance of the inductance in the coil will 
 be 628.3x0.02 = 125. 7 ohms, and the resultant reactance 
 33.5 ohms as shown in Fig. 92. The impedance, or 
 
247 
 
 resultant of the reactance and resistance, will, therefore, 
 be 60.2 ohms and the current in the circuit will be 
 
 . 18.27 /33 50' amperes, so that a cur- 
 60.2 \ 33 50' 
 
 rent of 18.27 amperes .effective, leads the E. M. F. by 
 approximately 34. 
 
 The drop at the terminals of the condenser will be 
 18.27 /33 50' X 159.2 \ 90 = 2909 \ 56 10' volts. 
 The drop in the inductance if it could be isolated ; that 
 
 "' 50 OHMS** 
 
 FIG. 92. 
 
 FIG. 93. 
 
 FIG. 94. 
 
 is, separated from the resistance in the coil would be 
 18.27 /33 50 X X 125.7 /90 = 2296 /123 50 r volts, 
 and tlie drop in the resistance 18,27 /33 50' X 50 = 
 913.5 /33 50 X volts. As, however, the inductance and 
 the resistance in a coil are inseparably united, the drop 
 can only be measured on the impedance of the coil, 
 which will be 50-|-125.7 > ; = 135.3 ohms, as shown in Fig. 
 
248 
 
 93, j, being the symbol of V 1 or an operator which 
 rotates 125.7 through a right angle, counter-clockwise 
 from the direction of the resistance. The drop at the 
 terminals of the coil will, therefore be 18.27 /33 50' X 
 135.3 /68 19 r = 2472 /1Q2 09', and as shown in Fig. 94 
 2472 /102 09 ; + 2909 \ 50 10' = 1100. 
 
 It is evident that by the combination of an induct- 
 ance with a condenser, the pressure at the terminals of a 
 condenser may exceed that of the impressed E. M. F. 
 The vector sum of the total c. E. M.'F.'S or drops in the 
 circuit must, however, be equal to the impressed E. M. F. 
 as shown in Fig. 94. 
 
 If the reactance of a condenser is equal to the react- 
 ance of the inductance in a circuit, the impedance of the 
 circuit is reduced to its simple resistance, so that an al- 
 ternating current circuit on a coil having a small resist- 
 ance but large inductance, in circuit with a properly 
 selected condenser may develop an exceedingly high 
 pressure at the condenser and at the coil terminals. Such 
 a circuit is said to be resonant. 
 
 SYLLABUS. 
 
 The sum or difference of two co-periodic, sinusoidal 
 E. M. F.'S is their geometrical or vector sum, or differ- 
 ence. 
 
 Laboratory of Houston & Keiinelly, 
 Philadelphia. 
 
[Copyright, 1894, by THE ELECTRICAL ENGINBBR.] 
 WEEKLY. 
 
 No. 32. JANTTAHV 19, 1895. l^tio" S3m 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED 
 
 Alternating Currents. 
 
 253. Since in an alternating-current circuit we have 
 
 Tf 1 
 
 the vector equation I = amperes = E .- .am- 
 
 J J 
 
 peres, we may write 1 = E A amperes, where the ad- 
 mittance A, is the reciprocal of the impedance, and is 
 expressed in mhos. In a continuous-current circuit, 
 
 7? 
 
 I = = E G amperes, where 6r, is the conductance in 
 R 
 
 mhos (Sec. 24), and the admittance A, degrades into a 
 simple conductance. 
 
 In a continuous-current circuit, the joint conductance 
 of a number of separate conductances in multiple is their 
 arithmetical sum. 
 
 In an alternating -current circuit, the joint admittance 
 of a number of separate admittances in multiple, is their 
 geometrical sum. For example, let two impedances be 
 connected to the terminals of an alternator delivering 
 1100 volts at coJJ.es tor rjpgs, with a frequency of 12S *v, 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 203 Broadway, New York, N. Y. 
 
 [Entered & second-clas matter at the New York, N. Y., Port Office, June 14, 1894. ] 
 
250 
 
 one of these impedances being offered by a coil of 30 
 ohms resistance and 0.2 henry inductance, and the 
 other impedance being that of a condenser of 10 micro- 
 farads capacity ; then the angular velocity of the E. M. F. is 
 785.4 radians per second. As shown in Fig. 95, the re- 
 actance of the inductance is 15 Y.I /90 ohms, and the 
 impedance C E, 159.9 /79 11' ohms. The reactance 
 
 it \ 
 i / 
 
 C 80 OHMS D 
 
 "0.002076 MHO 
 
 FIG. 95. 
 
 Illustrating the Combination of Impedances in Parallel. 
 
 of the condenser is 127.3 \ 90 ohms, and this, in the 
 absence of resistance in series with it, becomes its im- 
 pedance. The admittance of the coil is, therefore 
 
 159 9 /79 11' = - 006252 \ W H' raho, as repre- 
 sented by the line c d, to a convenient scale ; and the 
 admittance of the condenser is similarly ===^ 
 
 4.27.0 \ yo 
 
251 
 
 = 0.007854 /90 mho. The geometrical sum, or joint 
 admittance of a I and c d, is a d, 0.002076 /55 37' 
 mho. The joint impedance is, therefore 
 
 0.002076 
 
 \ 55 
 
 as represented by the line G H, to a suitable scale. The 
 current supplied from the alternator will, consequently 
 
 be - = = 2.284 /55 37' amperes, as shown 
 
 " 481.6 \ 55 37' 
 by the line N p. The current in the resistance coil will 
 
 be 159 9 7790 n/ = 6.877 \ 79 11' amperes, as repre- 
 sented by the line L M, and the current in the condenser 
 
 will be o = 8.641 /90 amperes, as shown by 
 \2ii.o \ 90 
 
 the line j K. The arithmetical sum of these two branch 
 currents would be 6.877 + 8.641 = 15.518 amperes, 
 whereas the current actually supplied is only 
 2.284 /55 37' amperes, and this is the vector sum of 
 6.879 /79 11' + 8.641 /90. 
 
 254. In a continuous-current circuit we have the con- 
 dition that the sum of tfre currents arriving at a 
 point in a network of conductors is equal to the sum of 
 the currents leaving that point (Sec. 50). This is true 
 in an alternating current circuit if we substitute the 
 geometrical sum for the arithmetical sum. 
 
 The multiplying power of a shunt (Sec. 37) in a con- 
 
 S7 I & 
 
 tinuous current circuit is - ' T* ' ? where G, is the re- 
 
 X3 
 
 sistance of the galvanometer or similar device, and /, 
 
252 
 
 the resistance of the shunt. In an alternating-current 
 circuit, the same ratio holds when the computation is 
 effected geometrically. Thus, suppose a galvanometer 
 applicable to an alternating-current circuit ; for instance, 
 an electro-dynamometer is placed in a circuit whose fre- 
 quency is 125 ~, and whose angular velocity is there- 
 fore, 785.4 radians per second, with a resistance of 6.19 
 ohms, and an inductance of 0.01 H. Its reactance, 
 therefore will be 7.854 ohms, and its impedance, as 
 shown in Fig. 90 of 10 /51 45' ohms. If this dynamo- 
 meter is shunted by a simple non-inductive resistance $, 
 of 10 ohms, and whose impedance is, therefore, 10 /0 
 
 100HM8. 
 
 FIG 96. 
 
 Illustrating the Multiplying Power of a Shunt. 
 
 ohms, then the vector sum G -\- $, is shown to be 
 17.99 /25^3 / ohms. This sum divided by 8, is clearly 
 1.799 /25 53', so that the readings of the dynamometer 
 would have to be multiplied by 1.799 in order to obtain 
 the total current strength. 
 
 255. In the same way it may be shown that all the 
 formulae, applying to continuous-current circuits^ 
 apply equally to sinusoidal-current circuits when the 
 proper impedances, are substituted for the various re- 
 sistances, and the computation is carried out vectorially. 
 
 In a continuous-current circuit, the activity is E 1 
 
253 
 
 watts, E I, being the numerical product. In a sinusoidal- 
 current circuit, the activity is E /watts, E 1, being in- 
 terpreted geometrically, and representing the co-directed 
 product ; or, if , be the angle included between E, and 
 /, the activity is E /cos a watts. 
 
 Thus, considering the case represented in Fig. 95, the 
 activity supplied to the condenser by the alternator of 
 1100 volts, will be 1100 X 8.641 X cos 90 = 0, (see 
 Fig. 97.) Such a current is sometimes called a wattless 
 current. 
 
 _ . ^A >- 
 
 ,100 VOLTS B, A,, 1100 VOLTS B w 
 
 2ec-Engineer 
 
 FIG. 97. 
 
 Illustrating Activity Relations. 
 
 Considering next the activity in the circuit of the coil, 
 we have 1100 X 6.877 X cos 79 IV = 1419 watts. 
 This energy is expended in heating the coil. 
 
 256. When the circuit embraces iron, there will be 
 hysteretic expenditure of energy in the iron at 
 each cycle (Sec. 148). The effect of the hysteresis will 
 be to apparently increase the resistance in the circuit, to 
 what may be termed its equivalent resistance. Thus, if 
 an E. M. F. of 100 volts at 130 ~ be impressed upon the 
 terminals of a coil embracing iron, having a resistance of 
 1.0 ohms (Fig. 98) and an inductance of 0.1 henry (sym- 
 bolically written 0.1 H\ the angular velocity being 
 
254 
 
 816.8 radians per second, the reactance of the coil will 
 be 81.68 /90 ohms, and the impedance of the coil will 
 be 82.31 /83 01' ohms. If, owing to the effect of 
 hysteresis, the 100 volts is opposed by a c. E. M. F. 20 
 /1 50 volts, as shown by the line E F, the resultant E. M. r. 
 will be D E + E F, or 83.28 /6 54' volts, and this re- 
 sultant E. M. F., considered as acting on the impedance of 
 
 83 28 
 ' 
 
 the coil, will produce a current 
 
 82 31 ,^go 01 / 
 
 \ 83 01' amperes, represented by the line d g, which 
 
 *k d \~i--- esi'^ 
 
 ' 83,%,' 76 07 / - 
 
 Elec.Engineer 
 
 FIG. 98. 
 
 Illustrating Equivalent Resistance, Reactance and Impedance. 
 
 will be 76 07' behind the impressed E. M. F. d 1 9 of 100 
 volts. The same result can, however, be obtained if we 
 consider the impressed E. M. F. as acting directly on a 
 circuit whose impedance is 98.8 /76 07' ohms, and whose 
 equivalent resistance and reactance are 23.7 ohms, and 
 95.96 /9^ ohms, respectively. 
 
 257. The ratio of the impedance to the ohmic resis- 
 
 tance in a conductor or circuit is called its im- 
 
 pedance factor. The ratio of the reactance to the ohmic 
 
255 
 
 resistance in a conductor or circuit is called its reactance 
 factor. The impedance factor is therefore the secant, 
 and the reactance factor the tangent, of the angle of lag. 
 
 258. When an alternating current in a primary circuit 
 
 is linked with a secondary circuit, through the 
 
 medium of a mutual inductance of L^ henrys, an E. M. F. 
 
 is set up in the secondary circuit, and a c. E. M. F. is set 
 
 up in the primary circuit under the influence of the cur- 
 
 I 
 
 RA 
 
 EQ. -RESISTANCE 45 OHMS 
 
 Site. Engineer 
 
 FIG. 99. 
 
 Illustrating Equivalent Resistance, Reactance and Impedances of Mutually Inductive 
 
 Circuits. 
 
 rent in the secondary circuit. Without, however, ana- 
 lyzing the direction and magnitude of these E. M. F.'S, it 
 is sufficient to modify the impedance of the primary cir- 
 cuit in order to determine the results produced. If 
 j?a, !*> e/aj represent respectively the resistance, reactance 
 and impedance of the primary circuit, r^ & b , and / b , the 
 corresponding quantities in the secondary circuit and 
 
 0) L 
 
 then fi^ has to be increased by n* r^ to J? 4 ; and K^ di- 
 
256 
 
 minished by n 2 K b to K^ ; when the impedance J = 72 A 
 + 7jT A , is the equivalent impedance of the primary circuit. 
 Thus, if a primary circuit of 20 ohms resistance and 
 100 ohms reactance have impressed upon its terminals a 
 sinusoidal E. M. r. of 100 volts, whose angular velocity 
 is 1000 radians -per second, and is linked through a mutual 
 inductance of 0.05 henry, with a secondary circuit of 
 resistance r b of 50 ohms, reactance & b , of 50 \ 90 ohms, 
 and, therefore, an impedance of 70.7 \ 45 ohms, as 
 
 shown in Fig. 99, then n = 100 X - 05 = 0.707 
 
 70.7 
 
 and n 2 = 0.5, so that the primary resistance has to be 
 increased by 0.5 X 50 = 25 ohms, and the secondary re- 
 actance diminished by 0.5 X 50 = 25, i. e., increased 
 by 25 ohms, so that the equivalent resistance 7? A , is 45 
 ohms, the equivalent reactance 7T A 125 /90 ohms, and 
 the equivalent impedance 132.8 /70 12'. The primary 
 
 current is, therefore 132 8 Q 12 / = 0.753 \ 70 12'. 
 
 The secondary E. M. F. is expressed by j to L^ 7 A = 
 
 to L 7 A \^W = 50 \TJO X 0.753 \~70~ 12 r = 37.65 
 
 \ 160 12 ; , and this secondary current 7 b will be 
 37.65 060^ m ^ 
 
 70.7 \ 45 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
[Copyright, 1894, by THH ELECTRICAL ENGINEER.] 
 WEEKLY. 
 
 oft i QQK rce, - en 
 
 2b, 1 Subscription, $3.00. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D! 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GRADE. 
 
 ALTBRN ATTORN. 
 
 259. The essential difference between an alternator 
 and a continuous-current generator is that the al- 
 ternator has to supply an alternating E. M. F. of definite 
 frequency and of definite wave character, whereas the 
 continuous-current generator has only to supply a con- 
 stant E. M. F. If p, be the number of poles, or the num- 
 ber of magnetic circuits in the alternator field, and if /?, 
 l>e the number of revolutions made by the armature per 
 
 second, the frequency will be & n periods per second, 
 
 except in the case of some inductor alternators whose 
 frequency is p n ~. Thus a bipolar machine, to produce 
 a frequency of 1.00 ~, would have to make 100 revolu- 
 tions per second, or 0000 revolutions per minute, a speed 
 only attained by steam turbines. Consequently, almost 
 all commercial alternators are multipolar machines, some 
 having as many as 112 poles. The lower the frequency 
 adopted on a circuit, the smaller the number of poles, or 
 the fewer the number of revolutions per minute. 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 203 Broadway, New York, N. Y. 
 
 [Entered as second class matter at the New York, N. Y., Pott Office, June 14, 1804.] 
 
258 
 
 260. The shape of the wave of E. M. F. produced by 
 an alternator depends primarily upon the rate 
 
 from instant to instant, at which flux is linked with the 
 armature-winding during revolution. It will, therefore, 
 vary with the shape of the poles and with the shape of 
 the winding on the armature. 
 
 The simplest form of wave that can be produced by 
 an alternator is a sinusoidal wave. As already men- 
 tioned, many alternators produce a close approximation 
 to the sinusoidal wave form, but, no matter how far the 
 wave may deviate from a strictly sinusoidal form, it may 
 always be considered as a combination of a number of 
 sinusoidal waves, or, in other words, as a complex sinu- 
 soidal wave. According to what is known as Fourier's 
 theorem, every periodic and single-valued wave of what- 
 ever complexity, may be resolved into a combination of 
 a single fundamental wave or simple sinusoid, having 
 the frequency of the complex wave, and a number of 
 shorter sinusoidal waves or harmonics, whose frequen- 
 cies are all some integral multiple of the fundamental 
 frequency. 
 
 261. The first harmonic has a frequency twice that 
 of the fundamental. The second harmonic three 
 
 times, and the nth harmonic, n-j-1 times that of the fun- 
 damental. In some forms of waves the complexity is so 
 great as to necessitate the resolution into an indefinitely 
 great number of harmonics superposed upon the funda- 
 mental, while for practical purposes, waves may usually 
 be considered as simply composed of a fundamental 
 together with the superposition of the second, fourth and 
 sixth harmonics, since beyond the sixth, the eifect of 
 higher harmonics becomes practically negligible. 
 
259 
 
 Fig. 100, represents at A, a fundamental wave of the 
 sinusoidal type ; B, its first harmonic ; c, its second ; D, 
 its third, and E, its fourth. Fig. 101 represents at s, 
 a fundamental sinusoidal E. M. F. of 800 volts amplitude, 
 i. e., 565.6 volts effective and 100 ~; at P, its first har- 
 monic of 400 volts amplitude, and at Q, its second har- 
 monic of 500 volts amplitude. If these E. M. F.'S were 
 
 FUNDAMENTAL 
 
 V V 
 
 vwww 
 
 Elec. Kngi 
 
 FIG. 100. 
 
 FIG. 101. 
 
 independently produced by three separate alternators, 
 which could be coupled rigidly together on the same 
 shaft, then when alternators P, and Q, were so connected, 
 starting together from the zero in the same direction, the 
 E. M. F. which would be produced is shown in Fig. 102. 
 If all three were connected together the resultant wave 
 type of E. M. F. is represented in Fig. 103. 
 
260 
 
 262. It is evident from an inspection of Figs. 102 anci 
 103, that no ordinary alternator could produce 
 such types of wave as are there represented, because the 
 positive waves are not geometrical inversions of the neg- 
 ative waves, with respect to the zero line. Thus the 
 negative wave D E F G H, should continue from D, to the 
 point as far below the zero line as A, is above it, in order 
 to represent the symmetry that must be developed in an 
 alternator where the various outlines of a positive wave 
 are repeated in due succession in the negative wave, with 
 mere alteration of direction. The discrepancy is due to 
 
 -Else. Engineer 
 
 FIG. 102. 
 
 Elec.Engineer 
 
 FIG. 103. 
 
 the introduction of the first harmonic. It can be shown, 
 that in order to maintain the symmetry referred to, only 
 the even harmonics, that is, second, fourth, sixth, etc., 
 can be present ; that is, those harmonics whose frequency 
 is an odd number of times that of the fundamental fre- 
 quency. Fig. 104 represents the combination of a fun- 
 damental sinusoidal wave of E. M. F. with its second 
 harmonic of 200 volts amplitude in two different cases 
 of phase relationship. At F -f- A, the fundamental F, 
 and second harmonic A, are united, while at F -f- B, the 
 same fundamental and B, are united. "It is evident, 
 
261 
 
 therefore, that the marked presence of a second harmonic 
 in an alternating-current wave may produce either a flat 
 topped or a peaked form of wave, according to the phase 
 of the harmonic, relatively to the fundamental. 
 
 Any alternating E. M. r. may, therefore, be expressed 
 by the formula, 
 
 e = E\ sin (cot + i) + E z sin (3 tot + 3 ) 
 
 sin (5 tot + 05) + volts 
 
 FUNDAMENTAL 
 
 - HARMONIC 
 
 FIG. 1C5. 
 
 FIG. 104. 
 
 where e, is the instantaneous value of the E. M. F., the 
 frequency, E^ E^ E 5 the amplitudes of the fundamental 
 and the second and fourth harmonics, and a 19 3 , 5 , the 
 respective phase angles. If it be required to eliminate 
 the phase angles, this may be done by resolving each 
 
262 
 
 successive wave into two sinusoidal components in quad- 
 rature, thus 
 e = E t sin cot + E' cos cot + E itl sin Scot -f- 
 
 E" cos 3 cot + EV sin 5 ^ -f ^ v cos 5 w tf, -f- 
 
 This equation is one expression of Fourier's theorem. 
 The same applies to any alternating current, if *', and /, 
 be substituted for e, and E, respectively. 
 
 263. When a complex-harmonic E. M. F.; that is, an 
 E. M. F. distinctly deviating from the simple-sinu- 
 soidal type, sends a current through a circuit containing 
 inductance, the reactance of the circuit to the harmonics 
 will be greater than to the fundamental E. M. F., and, 
 therefore, the impedance will be greater to the har- 
 monics. For this reason the components of harmonic cur- 
 rents are weakened relatively to the fundamental, and 
 the current tends to approach the sinusoidal form more 
 closely than the E. M. F. When, however, the circuit is 
 linked with iron, the presence of hysteresis will usually 
 introduce a greater amount of distorsion than the induct- 
 ance can compensate, so that the current supplied to al- 
 ternating current transformers, particularly on light 
 loads, are usually much distorted. 
 
 264. When two alternators are connected in series 
 and driven by independent sources of power, the 
 
 armatures tend to take up such a position that the E. M. F. 
 waves of one are in the opposite direction to the E. M. r. 
 waves of the other, so that no resultant E. M. F. is de- 
 veloped. For this reason, when alternators have to be 
 connected together, they are connected in parallel in- 
 stead of in series unless rigidly connected on the same 
 shaft. 
 
263 
 
 When two alternators are connected in parallel, they 
 must necessarily keep step, and their phase difference 
 must, therefore, be constant, within certain limits. Sup- 
 pose two alternators, of 1100 volts effective E. M. F., run- 
 ning independently, be suddenly connected together 
 at a time when their phase difference is, for example, as 
 represented in Fig. 105. The E. M. F. existing in the 
 circuit connecting the two armatures, whose E. M. F.'S, are 
 represented in magnitude and phase by o A, and o B, will, 
 therefore, be represented by the line A B, and this E. M. F. 
 tends to send a current through the armature, whose 
 effect \vill be to accelerate the lagging armature and re- 
 tard the leading armature, thus bringing the machines 
 into phase. On the other hand, by armature reaction, 
 the current will tend to produce a c. M. M. F. in the vari- 
 ous magnetic circuits, tending to weaken the E. M. F. of 
 the leading machine. The machines, will, therefore, rap- 
 idly fall into step, or out of step, according to which of 
 these influences preponderates. The smaller the phase 
 difference existing at the time of interconnection, the lesser 
 the liability of derangement in operation. The lower 
 the frequency and the smaller the armature reaction, the 
 more readily the interconnection can be brought about. 
 If this connection be made at an unfavorable moment, 
 the current in the armatures may reach unduly great 
 strengths, sufficient to blow the fuses, and the mechani- 
 cal strains brought to bear upon the machines are liable to 
 be excessive. For this reason with alternators at Ameri- 
 can frequencies in electric lighting, i. e., from 120 ~ to 
 135 ~~ parallel workings has not come into use. although 
 in Europe, where the frequencies are from 40 ~~ to 
 100 ~, parallel working is the general practice. In- 
 
264 
 
 struments called phase detectors are frequently employed 
 to ascertain the right moment at which to throw the 
 switch connecting two machines in parallel. 
 
 SYLLABUS. 
 
 Any single-valued, periodic function may be analyzed 
 into a sinusoidal wave, of the frequency of the function, 
 and a series of superposed harmonics. 
 
 The n\h harmonic has a frequency of n-\-\. times that 
 of the fundamental. 
 
 A complex E. M. F. acting upon a circuit of con- 
 siderable reactance tends to generate a current more 
 nearly sinusoidal in type. 
 
 Alternators connected in series, unless rigidly con- 
 nected together, tend to annul each other's E. M. F. 
 
 Alternators, when suddenly connected in parallel, may 
 either fall into step, or short circuit one another, accord- 
 ing to the nature of the machines, the armature reaction, 
 frequency, and the phase difference between them. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 

 [Copyright, 1894, bv THK ELECTRICAL 
 
 WEEKLY. 
 NY 34 FTTRT?TTAT?V 9 ISQPi Price, - 10 Cents. 
 
 BRUARY 2, 1 Subscription, $8.00. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED CRADE. 
 
 ALTKRNATORS. 
 
 265. A multiphase alternator, or multiphaser, as distin- 
 guished from a uniphase alternator, or uniphaser, 
 
 is a machine which generates two or more alternating 
 currents in definite phase relationship with each other. 
 Multiphase alternators are diphase when they produce 
 two separate alternating E. M. F.'S in quadrature, or sepa- 
 rated by a quarter cycle, and triphase when they pro- 
 duce three separate alternating E. M. F.'S separated by 
 one-third of a cycle. Multiphase generators are only 
 required for the purpose of operating alternating cur- 
 rent motors, which can start from rest at full torque ; 
 that is, induction motors. 
 
 266. Diphase generators employ on the armature 
 two sets of coils or windings so arranged that the 
 
 E. M. F.'S generated in them shall have the same magnitude, 
 frequency and wave type, but shall differ in phase by 
 90, or a quarter cycle, so that the diagram representing 
 such effective E. M. F.'S will be shown in Fig. 106. The 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 303 Broadway, New York, N. Y. 
 
 [Entered as second-class matter at the New York, N. Y., Post Office, June 14, 1894.] 
 
266 
 
 current produced by these two E. M. F.'S may be carried 
 in two independent circuits, necessitating four wires and 
 four collector rings, as in Fig. 107, or in two inter-con- 
 
 n 
 
 100 VOLT 8 ^ ^ XOJ ~\~\^ Jilec.n<jineer 
 
 Elec.Kngineer LJ 
 
 FIG. 106. FIG. 107. 
 
 Diagram of Diphase E. M. F.'S. Biphase Connections, Separate Circuits. 
 
 nected circuits, 1 with one common return requiring three 
 wires and three collector rings, as in Fig. 108. 
 
 The E. M. F. between the collector rings A and o, will 
 in the latter case, be the same as between B and o, while 
 the E. M. F. between the jings A and B, will be equal to 
 the length of the line B A, joining the extremities of o B 
 and o A, Fig. 106; or supposing o A and o B, to be each 
 equal to <?, the E. M. F., B A will be e V%. When the third 
 wire is employed as a common return circuit, as for ex- 
 ample, wire (2) in Fig. 108, the current it carries will be 
 
 Elec.Enyineer 
 
 FIG. 108. 
 
 Diphase Connections, Interconnected Circuits. 
 
 the sum of the two currents in circuits x and Y, which, be- 
 ing in quadrature, will be represented as in Fig. 109, and 
 will be i V%, where *, is the current strength in each circuit. 
 
267 
 
 The cross-section of wire (2) will, therefore, have to be 
 4:1 per cent, greater than that of either of the two other 
 wires in order to have the same drop of pressure when 
 the two circuits x and Y, are similar in all respects. 
 
 267. Triphase generators are wound in two ways ; that 
 
 is, the star winding and the triangular winding, 
 
 as shown in Figs. 110 and 111. A combination of the 
 
 two has also been introduced as shown in Fig. 112, but 
 
 owing to its greater complication it is seldom employed. 
 
 The winding of a triphase alternator may, therefore, 
 be effected by employing three separate sets of coils, 
 
 FIG. 109. 
 
 I Hagram of sum of two equal 
 Diphase Currents. 
 
 FIG. 110. 
 
 Star Triphase Winding. 
 
 FIG. 111. 
 
 Triangle Triphase 
 Winding. 
 
 each generating an E. M. F. of equal magnitude, frequency 
 and wave type, but differing in phase by | cycle. Or, 
 they may be made to differ by J cycle, so far as re- 
 gards their production in the armature, and, by reversing 
 the intermediate E. M. r. relatively to the external circuit, 
 the spacing is converted into J cycle, as shown in Fig. 
 113, where OA, OB and oc, represent three equal E. M. F.'S 
 of ^ cycle angular displacement. The E. M. F. of o B, 
 being reversed, with respect to the external circuit, be- 
 comes o B', when o A, o c, and o B', are three triphase 
 E. M. F.'S displaced by ^ cycle. 
 
268 
 
 (The E. M.F. of a tri phase alternator; that is, a triphaser, 
 is not measured from the common connection o, to the 
 terminals A B, or o, but between any pair of terminals 
 A B, B c or c A. The E. M. F. so measured will be repre- 
 sented by the lengths of the line A B, B c or c A, and if 
 the effective E. M. F. in each branch o A, o B or o c, be de- 
 noted by , the effective E. M. F. between any pair of 
 terminals will be e V$. 
 
 Elec. Engineer 
 
 FIG. 112. FIG, 113. FIG. 114. 
 
 Combination Triphase Diagram representing the trans- Triphase E. M. E. Dia- 
 Winding. formation of % cycle E. M.F. 's into gram. 
 
 External Triphase E. M. K.'S. 
 
 268. A triangular winding may be obtained in a bi- 
 polar machine by tapping the armature at three 
 points 120 apart, as shown in Fig. 114, when a tri phase 
 E. M. F., not usually sinusoidal, will be generated. 
 
 In multipolar triphase machines, the armature is wound 
 with three sets of coils which are subsequently connected 
 either in series, that is, triangularly ; or in parallel ; that 
 is, star-connected. If e be the effective E. M. F. of each 
 winding, the E. M. F. of a triangularly connected ma- 
 chine, between any pair of terminals, will be 0, and in a 
 star connected machine the E. M. F. between any pair of 
 
269 
 
 terminals, will be e 4/3. The out-put in both cases will 
 be the same ; for, if a triangular triphaser have a load 
 represented by a resistance r, connected to each pair of 
 terminals as shown in Fig. Ill, the current in each cir- 
 
 p 
 
 cuit will have the numerical strength - = i. amperes ; e, 
 
 r 
 
 being the pressure at machine terminals, so that the 
 output of the machine will be 3 e i watts. If, however, 
 a star-triphaser has a resistance R = 3 r, connected as a 
 load to each pair of terminals, the current *, in R, will be 
 
 1.732 e \30 
 
 \ 30 
 
 3 r Sr 1.T32 
 
 e e /60 C 
 
 similarly, the current in R will be * = 
 
 6 r 
 
 _ i /30 
 - . The current in the winding O A, will be the 
 
 J..7o<a 
 
 The external activity of this winding will, therefore, 
 be e i watts, and the total external activity of the ma- 
 chine 3 e i watts, as before. In order that the star-tri- 
 phaser shall have the same activity, as the triangular-tri- 
 phaser, its resistance must be 3 r, on each circuit ; that 
 is, its load must be J- of the load on the triangular tri- 
 phaser. The E. M. F. of the star triphaser is, therefore, 
 y8 times the E. M. F. of a triangular triphaser of the same 
 winding, but will carry -J of the current strength in 
 the external circuits that a triangular triphaser will sus- 
 tain. It is, therefore, necessary to reduce the number 
 of turns in a star-triphaser by about 43 per cent, in order 
 to produce the same E. M. F. at terminals as a triangular 
 
triphaser, and to utilize the winding space so gained for 
 an increased conductivity, in the proportion of 1.732. 
 The E. M. F. at the terminals of both machines will then 
 be the same, and the drops in each machine the same. 
 
 269. Fig. 115 represents a star-triphaser ABC, con- 
 nected to the star load A', B', c', the load of whish 
 may consist either of loaded transformers, of diphase 
 
 , E U C .n<rir 
 
 FIG. 115. 
 
 Diagram and Analysis of Tnphase Circuit. 
 
 motors, of lamps, etc. It is evident that the middle 
 points o and o', are, by symmetry, always at zero poten- 
 tial when the system is perfectly insulated, so that the 
 ground plates G, G, may be connected to this point at each 
 end of the line without altering the distribution of cur- 
 
371 
 
 rents and potentials, and, therefore, without carrying any 
 current through the ground ; for, if the loads on the 
 three circuits be equally balanced, the current in o A, will 
 be the vector sum of the currents in o B and o c. For 
 purposes of transmission, therefore, the circuits may- 
 be regarded as constituting three separate uniphase cir- 
 cuits o A" A"' o, o B" B o, and o c" c'" o, each employ- 
 ing a ground return circuit of zero resistance ; so that a 
 triphaser supplying 1000 volts at its terminals is equiva- 
 lent, in regard to pressure of delivery and economy in 
 conductor, to a uniphaser at 577.4 volts pressure with 
 
 V G 
 
 El: 
 
 FIG. 116. 
 
 Monocyclic E. M. F. Diagram. 
 
 ground return, or, to a uniphaser of 1155 volts employing 
 a simple return circuit. 
 
 270. A recent combination of uniphase and triphase 
 systems is called the wonocyclic system. 
 
 A monocyclic alternator is wound with two circuits, 
 one of which is the principal circuit and has the princi- 
 pal E. M. F., o A, Fig. 116, for uniphase transmission, 
 while the second circuit has a smaller wire of fewer 
 turns with an E. M. F., B c, in quadrature with A B, and 
 about J of the E. M. F., o A. The second winding is con- 
 nected to the middle of the main winding as shown. The 
 terminals o, A, are connected to the incandescent lighting 
 mains, and the E. M. F. between these terminals will be 
 
272 
 
 simply Uniphase. Where, however, induction motors 
 are required to be operated with full starting torque, a 
 third or power wire connected to the terminal B, is brought 
 into connection with the motor through two transformers 
 o c and c A, connected, as shown in Fig. 117. The 
 
 SECONDARY 
 Q'l 100 VOLTS 
 
 nfflflffltfRfflfflSW^ 
 
 \r\ 1154 Tr 119* I 
 
 | PRIMARY PRIMARY 
 
 Eltc.Engineer 
 
 FIG. 117. 
 
 Monocyclic Triphase Transformer 
 Connections. 
 
 Combination of Secondary Monocyclic 
 E. M. F. into Triphase System. 
 
 E. M. F.'S, suitably reduced by transformers, are o' c' and 
 c' A', Fig. 118, differing in phase by 60. By reversing 
 the secondary connections of the E. M. F., c' A', the 
 E.M. F.'S developed are o- c', c' A", and their sum o' A", 
 which are three triphase E. M. F.'S. and which may be 
 connected to the terminals of a triphase motor. 
 
 Laboratory of Houston & Kermelly, 
 Philadelphia. 
 
[Copyright, 1894, by THB ELECTRICAL ENGINEER.! 
 WEEKLY. 
 
 No. 35. FEBKUAKY 9, 1895. 
 
 Electrical Engineering Leaflets, 
 
 Prof. E. J. Houston, Ph. D. 
 
 AND 
 
 A. E. Kennelly, F. R. A. S. 
 
 ADVANCED GRADE. 
 
 Alternating Current Transformers, 
 
 271. An alternating-current transformer- is a device 
 for inducing an E. M. F. in a secondary circuit mag- 
 netically linked with a primary circuit, under the influ- 
 ence of an alternating current in the primary. 
 
 A transformer enables a powerful alternating current 
 to he developed in a local consumption circuit without 
 the necessity of conveying the current over a long dis- 
 tance, thus avoiding either the heavy loss of energy, or 
 the heavy expenditure in conductors, which would other- 
 wise he necessary. The energy may be transmitted over 
 the main circuit at high pressure with a small current 
 strength, and is transformed locally to a lower pressure 
 and correspondingly increased current strength. Such a 
 transformer is called a step-down transformer. On the 
 other hand, a transformer employed to raise the pressure 
 and diminish the current, is called a step-up transformer. 
 The ratio of transformation is the ratio of the effective 
 E. M. F. at secondarv terminals to the effective E, M. F. at 
 
 Published by 
 
 THE ELECTRICAL ENGINEER, 
 903 Broadway, New York, N. Y. 
 
 \ Entered as second-class matter at the New York, N. Y., Post Office, Juoe 14, 1894.] 
 
primary terminals on open circuit. The ratio of trans- 
 formation in a step-down transformer is, therefore, always 
 less than unity, and in a step-up transformer always 
 greater than unity. The transformers ordinarily em- 
 ployed in electric incandescent lighting usually step- 
 down, from a pressure of 1000 or 2000 volts in the prim- 
 ary mains, to 50 or 100 volts in consumption circuits, and, 
 therefore, have a ratio of transformation of from T ^ to ^ 
 If a ring of iron wire c c c, Fig. 119, be wrapped with 
 a primary coil p, of JV turns, and connected to an alter- 
 nating effective voltage ] the c. E. M. F. of self-induc- 
 tion added geometrically to the u drop" in the coil must 
 be equal to E. Since the drop in the primary coil of a 
 small transformer at full load would not exceed two per 
 cent., while in a large transformer it would be less than 
 one per cent., we may practically ignore the drop, and 
 consider that the c. E. M. F. produced by the transformer 
 must be equal and opposite to this impressed E. M. F. 
 Consequently, whatever be the wave form of the im- 
 pressed E. M. F., the wave form of the c. E. M. F. devel- 
 oped must be the same. The flux through the magnetic 
 circuit of the primary coil must, therefore, be such that 
 the rate of change in the flux-linkage, shall at every instant 
 be equal to the impressed E. M. F., in c. G. s. units. Ex- 
 pressed in symbols, if <0, considered as 4 a variable depend- 
 ent upon time, be the flux linkage in the primary cir- 
 cuit, expressed in weber-turns ; then neglecting drop, 
 
 SSt = e', where <?', is the instantaneous value of the ef- 
 dt 
 
 fective E. M. F. E, expressed in c. <;. s. units. 
 
 The current-strength, which will pass through the pri- 
 mary coil at each instant, is such that the M. M. F. it de- 
 velops in the coil shall maintain the flux linkage <#, 
 
275 
 
 As a simple example, suppose a primary coil of 500 
 turns, and 2 ohms resistance, to be wound on a magnetic 
 circuit of 0.002 oersted reluctance, and connected to a 
 sinusoidal E. M. F. of 1000 volts effective, with 800 radi- 
 ans per second angular velocity. Assuming the absence 
 of hysteresis and eddy currents, and that all the flux 
 passes through all the turns, the effective flux must be 
 250,000 webers, for the flux-linkage will be 250,000 X 
 500 = 125,000,000 weber turns, and the time variation 
 of this will be 800 X 125,000,000 = 10 11 c. o. s. units 
 of E. M. F. = 1000 volts. The effective M. M. F. required 
 to produce this flux will be 250,000 X 0.002 = 500 
 gilberts = 400 ampere-turns approximately, or 0.8 am- 
 pere effective through the coil. This is called the excit- 
 ing or magnetizing current. 
 
 Under all conditions of load in a transformer, the re- 
 sultant M. M. F. remains constant, when the drop in the 
 primary coil may be neglected. 
 
 272. If now the secondary coil s, of n turns, Fig. 119, 
 be wound on the ring, no change will take place 
 in the primary circuit, so long as the secondary coil is 
 open, but the flux pulsating through the magnetic cir- 
 cuit and the secondary coil, will set up an E. M. F. of e = 
 
 v 
 ^^TT , effective volts in the latter. 
 
 When the secondary coil has its circuit closed through 
 
 a total impedance </, a current of i amperes = - will 
 
 J 
 
 pass through the secondary circuit, and a M. M. F. of n i 
 effective ampere-turns will then be imposed upon the 
 magnetic circuit. If the secondary load be non-inductive, 
 say, a series of incandescent lamps, and if there existed no 
 
276 
 
 leakage flux in the transformer magnetic circuit, this 
 M. M. F. will be in step with the induced secondary E. M. r.; 
 that is to say, it will be in step with the primary c. E. M. F. 
 and, neglecting primary drop, it will be in opposition to 
 the impressed E. M. F. It will therefore be opposed to 
 the M. M. F. in the primary circuit. The resultant will 
 be a M. M. F. at a phase intermediate between them. In 
 order to maintain the resultant M. M. F. at the magnitude 
 and phase of the M. M. F. of excitation, a greater current 
 strength will enter the primary coil. 
 
 Consequently, as load is added to the secondary cir- 
 cuit, the primary current is compelled to vary both in 
 magnitude and phase, so as to maintain the fixed M. M. F. 
 of excitation as a resultant. The result is a stronger pri- 
 mary current, a greater primary power factor, and a 
 greater primary activity. An automatic adjustment is 
 thus maintained in the primary c. E. M. F., whereby elec- 
 trical energy is transferred from the primary to the sec- 
 ondary circuit. 
 
 The foregoing operations might be readily observed 
 and computed in any transformer, if they were not con- 
 siderably complicated both by hysteresis and leakage. 
 
 Owing to hysteresis, the M. M. F. needed to establish 
 the primary c. E. M. F. is not of the same wave type as 
 the latter, and is different in the ascending and descend- 
 ing branches of each wave of flux, as is readily observed 
 from an inspection of Fig. 59. The simplest existing 
 means of predetermining the current wave, is by the 
 graphical application of Fig. 59 to the c. E. M. F. wave 
 required, so as to determine the primary M. M. F. and cur- 
 rent strength at different points in the cycle. Energy is 
 expended in the primary circuit and absorbed in the 
 
.an 
 
 core of the transformer hysteretically, as explained in 
 Sec. 151. 
 
 The effect of leakage is to unduly increase the drop at 
 secondary terminals under load. If there were no leak- 
 age, that is, if all the flux passed through each . primary 
 and secondary turn, the secondary coil would act as 
 through devoid of inductance and possessing only ohrnic 
 resistance, its inductive reaction being entirely expended 
 against the primary circuit ; but if some of its flux es- 
 capes the primary coil, that portion developes a c. E. M. F. 
 of self-induction in the secondary coil, and an apparent 
 inductance is added to the secondary circuit within the 
 transformer, increasing the drop at load. In practice, 
 theie is always some leakage in a transformer, and the 
 secondary drop due to leakage is frequently as great as 
 the drop due to the ohmic resistance of both coils. One 
 of the principal objects in the design of a transformer is 
 the reduction of magnetic leakage to a minimum ; for, 
 although the presence of leakage does not give rise to 
 waste of energy, yet it produces a drop in pressure which 
 unduly limits the output of the apparatus for incandes- 
 cent lighting. 
 
 When the load in the secondary circuit is non-induc- 
 tive, the wave form of secondary current will be very 
 nearly the same as the wave type of secondary E. M. F., 
 and therefore of impressed E. M. F. When the secondary 
 load is inductive, the secondary current and M. M. F. lag 
 behind the secondary E. M. F. . This necessitates a greater 
 primary M. M. F. and current to maintain the resultant 
 M. M. F. of excitation, and not only is the primary current 
 strength greater, but it is forced into more nearly com- 
 plete opposition with the secondary current. The former 
 
effect increases the ohmic drop and the latter effect in- 
 creases the leakage drop, since the two opposing M. M. F.'S 
 produce a greater magnetic difference of potential be- 
 tween the opposite surfaces of the magnetic circuit F F, 
 Fig. 119. 
 
 FIG. 119. 
 
 273. Let o E, Fig. 120 c, represent the effective c. E. 
 M. F. in the primary circuit of a transformer of 
 say 1000 volts, and o 0, the effective E. M. F. in the sec- 
 ondary circuit, in step with o E. When the secondary 
 
 FIG. 120. 
 
 circuit is open, let o M, 400 /90, be the effective M. M. F. 
 in gilberts or ampere-turns required to maintain the 
 c. E. M. F., o c ; then the primary current must be in phase 
 with o M. JS T ow suppose a non-inductive load connected 
 
2T9 
 
 to the secondary circuit. The E. M. F., o e, will send a 
 current through this circuit lagging in phase very little 
 behind o , and the M. M. F. of this current will be o w 2 , 
 say 400 \~~5^. I" order to maintain the resultant M. M. F. 
 o M, the primary M. M. F. must assume the position o w, 
 or approximately 000 /H0 and thus approach in 
 phase the impressed E. M. F., which will be equal but op- 
 posite tO O E. 
 
 If now, owing to magnetic leakage in the transformer, 
 inductance appears in the secondary coil, the second- 
 ary current and M. M. F. may lag 15, as shown at A, 
 
 FIG. 121. 
 
 and the primary M. M. F., (o M - - o />i a ), will become 
 approximately 625 /125. Again, if the same load in 
 watts be applied inductively to the transformer, as, for 
 example, an alternating-current motor, the power factor 
 of the secondary circuit will be reduced, and a greater 
 current strength will be required, which will lag con- 
 sid,erably and the M. M. F. may become, as at B, 770 \ 60. 
 The primary component will be increased to approxi- 
 mately 1100 /2<>, and the components will be nearly in 
 opposition. 
 
280 
 
 The effect of this opposition in M. M. F.'S upon the leak- 
 age through both coils is illustrated in Fig. 121. If om 2 
 and 6 m, are in quadrature, each M. M. F. is at its maxi- 
 mum when its neighbor is zero, and when as at A, rn is 
 at its maximum, //i 2 , is absent, and the flux tli rough the 
 reluctance R 3 , of the leakage path will be only that due 
 to the magnetic drop in the reluctance R 2 , of the iron oc- 
 cupied by the secondary coil. Similarly when m%, is at 
 its maximum the flux through R 3 , is that due to the drop 
 in KJ. When, however, the M. M. F.'S are forced into op- 
 position, the leakage flux from each through K 3 , is in- 
 creased. 
 
 274. The power factor of transformers varies not only 
 with their load, but also with the nature of their 
 load, for, when the secondary circuit is loaded inductively, 
 the current in the secondary circuit lags considerably be- 
 hind the impressed secondary E. M. F. Consequently the 
 c. M. M. F. is brought more nearly in opposition to the 
 primary M. M. F. The drop in each circuit is, therefore, 
 increased as will be evident from an inspection of Figs. 
 120 and 121. Large transformers, whose power factor 
 may be 0.995 at full non-inductive load, with a full load 
 drop at secondary terminals of 1 per cent., may have a 
 power factor of 0.90 with an inductive load, and have 
 their full load drop at the same time increased to 4 per 
 cent. On the other hand a condenser connected to 
 secondary terminals tends to diminish the secondary drop 
 and increase the power factor. 
 
 Laboratory of Houston & Kennelly, 
 Philadelphia. 
 
INDKX. 
 
 Activity, Definition of 7 
 
 Activity in Carbon Voltaic 
 
 Arc 217, 218 
 
 Admittance 249 
 
 Aero-Ferric Magnetic Cir- 
 cuit, Calculation of. . . 109, no 
 
 Alloys 26 
 
 All-Night Arc Lamps 224 
 
 Alternating-Current Arc 
 
 Circuits 228, 229 
 
 Alternating Current, Defi- 
 nition of 233 
 
 Alternating-Current Arc, 
 Distribution of Light 
 
 from 228, 229 
 
 Alternating Current, Mean 
 
 or Average Strength of. . 46 
 Alternating-Current Trans- 
 former 273 to 280 
 
 Alternating-Current Trans- 
 former,AutomaticAdjust- 
 
 mentsof 275, 276 
 
 Alternating-Current Trans- 
 former. Definition of 273 
 
 Alternating-Current Trans- 
 former, Hysteretic Loss 
 
 in 276, 277 
 
 Alternating-Current Trans- 
 former, Power-Factor of. 280 
 Alternating Currents 233 to 256 
 Alternating E. M. F., Defini- 
 tion of 233 
 
 Alternating or Pulsatory 
 Current , Determination 
 
 of Strength of 46 
 
 Alternation, Definition of.. 234 
 Alternator and Continuous 
 Current Generator, Es- 
 sential Difference b e - 
 
 tween 257 
 
 Alternator, Diphase 265 
 
 Alternator, Uniphase 265 
 
 Alternators 257 to 272 
 
 Alternators, Connection of 
 
 in parallel 263 
 
 Alternators, Definition of. . 238 
 Alternators, Multiphase.... 265 
 
 Ampere, Definition of 42 
 
 Ampere-Hour, Commercial 
 
 Unit of Electric Quantity 45 
 Arc Carbons , Consumption 
 
 of 223 
 
 Arc, Counter-Electromotive 
 
 Force of 217 
 
 Arc Lamps, All-night 224 
 
 Arc Lamp, Ordinary, Activ- 
 ity of 7 
 
 Arc Lamps, Alternating- 
 Current Circuit 228, 229 
 
 Arc Lamps, Double-Carbon 224 
 Arc Light Carbon, Positive 
 Crater in 218 
 
282 
 
 INDEX. 
 
 Arc Light Circuits, Con- 
 tinuous, Distribution of 
 
 Potential in 226 
 
 Arc Light Dynamos 225 
 
 Arc Light Globes 231 
 
 Arc Light Projectors . . 229, 
 
 230, 231 
 
 Arc-Lights, Mean Horizon- 
 tal Intensity of 221 
 
 Arc Lights, Mean Spherical 
 
 Candle-power of 221 
 
 Arc Lighting 216 to 232 
 
 Armature of Dynamo and 
 Motor, Circumstances Af- 
 fecting Direction of Rota- 
 tion of l87 , 18 8 
 
 Armature Reaction i 5o 
 
 Armatures, Toothed Core 
 
 of Dynamos I52 
 
 Attractive Electromagnets, 
 
 Definition of II3 
 
 Attractive Force of Electro- 
 magnets, Calculation of 
 
 114. 115, 116 
 
 Balances, Resistance, Vari- 
 ous Forms of 28, 29 
 
 Balance, Wheatstone's.. 28, 29 
 Battery, Voltaic, Efficiency 
 
 of 7i 
 
 Begohm, Definition of r8 
 
 Bichromate Voltaic Cell . 84, 85 
 
 Bicrohm, Definition of 18 
 
 Bridge Boxes, Various 
 
 Forms of 2 8, 39 
 
 Bridge, Wheatstone's. . . 28, 29 
 Brushes of Dynamo, Lead 
 
 of - M 149 
 
 Brushes, Shifting of on Com- 
 mutator f orVaryingSpeed 
 of Continuous Current 
 Motor 177> I7 8 
 
 C. E. M. F. of Polarization. . 81 
 c. G. s., Practical, Unit of 
 
 E. M. F n 
 
 c. G. s Units 4, 5 
 
 c. G. s. Unit of Force 5 
 
 c. G. s. Unit of Quantity. .. u 
 Cable, Insulation Resi- 
 stance of 35) 3 6 
 
 Candle-Foot 20 6 
 
 Candle-Power of Arc Lights, 
 
 Mean Spherical 221 
 
 Candle-Power of Incandes- 
 cent Lamp, Methods Pro- 
 posed for Regulating, 2 1 2, 213 
 
 Candle, Standard 205 
 
 Capability, Electrical , of 
 
 Voltaic Cell 69, 7 o 
 
 Carbon Voltaic Arc, Ac- 
 tivity in 2i 7 , 218 
 
 Carbons, Cored 228 
 
 Carbons, Electro-plated 223 
 
 Carcel Lamp 205 
 
 Carcel-Metre 2 o6 
 
 Carrying Capacity of Con- 
 ductors 45 
 
 Cell, Voltaic, Bichromate, 
 
 82, 83 
 
 Cell, Voltaic, Clark Standard 88 
 'ell, Voltaic, Edison-La- 
 
 lande 87, 88 
 
 ell, Voltaic, Electrical 
 
 Capability of 69, 7 o 
 
 Cell, Voltaic, Fuller .... 86, 8 7 
 
 lell, Voltaic, Gravity. . . 84, 85 
 
 Cell, Voltaic, Grenet 82, 83 
 
INDEX. 
 
 Cell, Voltaic, Leclanche... 85 
 Cell, Voltaic, Partz Gravi- 
 ty 85, 86 
 
 Cell, Voltaic, Poggendorff, 
 
 82, 83 
 
 Cell, Voltaic, Silver Chlor- 
 ide 87, 88 
 
 Cell, Voltaic, Smee 82 
 
 Centimetre-G r a m m e - Se- 
 cond Unit of Activity. ... 7 
 Central Lighting Stations, 
 Maximum Lighting Load 
 
 of 212 
 
 Central Lighting Stations, 
 Minimum Lighting Load 
 
 of 212 
 
 Charge, Electric, and Ether 
 Strains, Relation between 2 
 
 Charge, Negative 2 
 
 Charge, Positive 2 
 
 Circuit, Drop in 50 
 
 Circuit, Electric, Definition 
 
 of 57 
 
 Circuit, Ferric Magnetic. . 93 
 
 Circuit Impedance 244 
 
 Circuit, Multiple-Series 60 
 
 Circuit, Reactance 244 
 
 Circuit, Resonant 248 
 
 Circuits, Conducting, Clas- 
 sification of 57 
 
 Circuits, Magnetic 92 
 
 Circular Type of E. M. F. or 
 
 Current 235 
 
 Clark Standard Cell 15 
 
 Clark Standard Cell, Tem- 
 perature Coefficient of . . . 16 
 Clark Standard Voltaic Cell 88 
 Coefficient of Reduction 
 from Capability to Out- 
 put... 131, 132 
 
 Coils, Compensating 160 
 
 Combin ation Triphase 
 
 Winding 268 
 
 Compensating Coils, of Dy- 
 namo 160 
 
 Complex-Sinusoidal Wave. 258 
 Conductance, Definition of 25 
 Conductances, Formula for 
 
 Calculating 25 
 
 Conducting Circuits, Classi- 
 fication of 57 
 
 Conductivity. Definition of 25 
 Conductivity, Magnetic. ... 95 
 Conductor, Electric, Dissi- 
 pation of Heat by 196 
 
 Conductor, Electric, Tem- 
 perature Elevation of 198 
 
 Conductors, Carrying Capa- 
 city of 45 
 
 Conductors, Safe Current 
 
 Density in 45 
 
 Continuous-Current Dyna- 
 mo, Reversibility of 170 
 
 Cooling of Wire, Effect of 
 
 Covering on 198, 199 
 
 Co-periodic Simple-Harmo- 
 nic E. M. F.'S, Vector Sum 
 
 of 243 
 
 Cored Carbons 228 
 
 Coulomb, Definition of . . 1 1 , 42 
 
 Couple, Voltaic 66 
 
 Counter- E lectromotive 
 Force, Development of, 
 by Continuous Current . . 62 
 Counter- Electro motive 
 
 Force of Arc 217 
 
 Counter- Electromotive 
 
 Force of Arc, Origin of.. 218 
 Counter-Electromotive 
 Force of Induction . . 62 
 
28 4 
 
 INDEX. 
 
 Counter- E lectromotive 
 
 Force of Motor 170 
 
 Counter-E lectromotive 
 
 Force of Polarization . 62 
 Counter-E lectromotive 
 
 Force, Varieties of 62 
 
 Counter-E lectromotive 
 
 Force, Virtual 62 
 
 Crater in Positive Arc Light 
 
 Carbon 218 
 
 Current, Alternating, De- 
 finition of 233 
 
 Current, Circular Type of 
 
 Periodic-Alternating 235 
 
 Current Density 45 
 
 Current, Displacement, 
 
 Probable Nature of 10 
 
 Current, Electric ... 41 to 48 
 Current, Electric, Does Not 
 Pass Through Conductor 
 
 41, 42 
 
 Current, Periodic-Alternat- 
 ing, Definition of 233 
 
 Current, Sinusoidal 236 
 
 Curve, Sinusoidal 237 
 
 Curve, Simple-Harmonic . . 237 
 
 Curve, Simple-Periodic 237 
 
 Curves of Reluctivity in 
 Iron and Steel in Relation 
 
 to Flux Density 107 
 
 Cut-Out, Film 213, 214 
 
 Cycle, Definition of 234 
 
 D. E. M. F 170 
 
 Daniell Voltaic Cell 84, 85 
 
 Density of Current 45 
 
 Density of Flux, Definition 
 
 of 90 
 
 Depolarizer 8 1 
 
 Derived Circuit, Applica- 
 tion of Ohm's Law to $2 
 
 Detectors, Phase 264 
 
 Diagram, Hysteretic 142 
 
 Dielectric Displacement , 
 
 Current in 2 
 
 Dielectrics, Maintenance of 
 
 Electric Displacements in 2 
 Difference of Potential ... 13 
 Differential Calculus, Sim- 
 ple Explanation of 43 
 
 Direct Electromotive Force 
 
 of Generator 1 70 
 
 Diphase, Alternator 265 
 
 Diphase, Connection of In- 
 terconnected Circuits. . . . 266 
 Diphase Connections, Sep- 
 arate Circuits 266 
 
 Diphase E. M. F.'S 266 
 
 Displacement Current, 
 
 Probable Nature of 10 
 
 Displacement Flux, Nature 
 
 of 2 
 
 Displacement Strain. ...9, 10 
 Displacement, Electric, Na- 
 ture of 2 
 
 Double-Carbon Arc Lamps 224 
 Double-Fluid Cells, Defini- 
 tion of 82 
 
 Drop in Circuit 50 
 
 Dynamo and Motor, Co- 
 Generation of Electro- 
 dynamic and Electro 
 
 motive Forces in 169 
 
 Dynamo, Counter Electro- 
 dynamic Force of 1 70 
 
 Dynamo-Electric Machine, 
 
 Armature of 150, 151 
 
 Dynamo-Electric Machine, 
 Classification of Losses in 137 
 
INDEX. 
 
 285 
 
 Dynamo-Electric Machine, 
 Electrical Losses in. . 138, 139 
 
 Dynamo-Electric Machine, 
 Lead of Brushes of . . . . 149 
 
 Dynamo-Electric Machine, 
 Limitations to Output of, 
 Classification of 145 
 
 Dynamo-Electric Machine, 
 Mechanical Lossesin, 137, 138 
 
 Dynamo-Electric Machine, 
 Principles of Design of. . 
 
 133, 134, 135 
 
 Dynamo, the 128, 152 
 
 Dynamos and Motor, Dif- 
 ference of Output of . 181, 182 
 
 Dyne, Definition of 5 
 
 Dyne Centimetre, Defini- 
 tion of . . 6 
 
 E. M. F 9 to 16 
 
 E. M. F., Alternating, De- 
 finition of 233 
 
 E. M. F., Circular Type of 
 Periodic-Alternating 235 
 
 E. M. F., Direction of In- 
 duced, Rule for Deter- 
 mining 123,214 
 
 E. M. F., Effective, Value of 239 
 
 E. M. F., Monocyclic Dia- 
 gram of 271 
 
 E. M. F., or Current, Alter 
 nating Flat-top Type of.. 235 
 
 E. M. F. of Self-Induction . . 127 
 
 E. M. F. of Voltaic Cell, Cal- 
 culation of 76, 77 
 
 E. M. F., Periodic Alternat- 
 ing, Definition of 233 
 
 E. M. F., Self-Induced 127 
 
 E. M. F., Sinusoidal 236 
 
 E. M. F., Sources of, in Vol- 
 taic Cell 67, 68 
 
 E. M. F.'S, Diphase 266 
 
 Earth's Crust, Resistance 
 of 31, 32 
 
 Earth's Crust, Resistivity 
 of Materials Forming. . . 30 
 
 Edison-Lalande Voltaic 
 Cell 86, 87 
 
 Efficiency, Commercial, of 
 Dynamo Electric Ma- 
 chine 137 
 
 Efficiency of Electrical Dis- 
 tribution, Definition of . . 51 
 
 Efficiency of Lamp 207 
 
 Efficiency of Lamp, Effect 
 of Temperature on 207 
 
 Efficiency of Lamp, So- 
 called 207 
 
 Efficiency of^Lamp, True. . 207 
 
 Efficiency of Voltaic Bat- 
 tery 71 
 
 Electric Capability of Gene- 
 rator 131 
 
 Electric Circuits 57, 64 
 
 Electric Discharge, Classi- 
 fication of Effects of 3 
 
 Electric Displacement, 
 Maintenance of, in Non- 
 Conductors or Dielectrics 2 
 
 Electric Displacement, 
 Nature of 2 
 
 Electric Motor, Continuous 
 Current Type of . . . 168 to 192 
 
 Electric Railroad Motor. . . 180 
 
 Electric Sources 13 
 
 Electric Sources, Classifica- 
 tion of 14 
 
 Electrical Effects . . . . i to 8 
 
286 
 
 INDEX. 
 
 Electrical Energy of Voltaic 
 Cell, Cost of 69 
 
 Electrification, Nature of . . 10 
 
 Electro-Chemical Equiva- 
 valents, Tables of 74 
 
 Electro-Dynamic Force 
 of Dynamo 170 
 
 Electro-Dynamics . . .161 to 168 
 
 Electro-Dynamics, Defini- 
 tion of 161 
 
 Electrolyte, Action of E.M.F. 
 on 73 
 
 Electromagnet, Attractive 
 Form of 119, 120 
 
 Electromagnet, Portative 
 Form of 118, 119 
 
 Electromagnets 113 to 120 
 
 Electromagnets, Attractive, 
 Definition of 113 
 
 Electromagnets, Computa- 
 tion of Attractive Force 
 of 114, 115, 116 
 
 Electromagnets, Determin- 
 ation of Polarity of 113 
 
 Electromagnets, Dual Char- 
 acter of Flux in 113 
 
 Electromagnets, Iron-clad. 119 
 
 Electromagnets, Induced or 
 Structural Magnetic Flux 
 of 113 
 
 Electromagnets, Portative, 
 Definition of .... 113 
 
 Electromagnets, Prime or 
 Magnetizing Flux of 113 
 
 Electromotive Force of 
 Electric Sources 14, 15 
 
 Electro-plated Arc Carbons 223 
 
 Element of Voltaic Cell 66 
 
 Energy, Conservation of . . 4 
 
 Energy, Definition of 3 
 
 Energy, Doctrine of Con- 
 servation of 4 
 
 Energy, Kinetic, Definition 
 
 of 3 
 
 Energy, Potential, Defini- 
 tion of 3 
 
 Energy, Potential, a Pos- 
 .sible Variety of Kinetic 
 
 Energy 4 
 
 Energy, Total Amount of, 
 
 in Sun 7 
 
 Entrefer, Definition of, 150, 151 
 Equivalent, Electro-Chem- 
 ical 74, 75 
 
 Equivalent Resistance 253 
 
 Erg, Definition of 6 
 
 Erg, Value of , 6 
 
 Ether, Stresses and Strains 
 
 in i, 2 
 
 Excessive Heating of Dy- 
 namo-Electric Machine, 
 Limitations to Output of, 
 Caused by 144, 145, 146 
 
 Factor, Impedance 254, 255 
 
 Feeders. 215 
 
 Ferric Circuit, Calculation 
 
 of 108, 109 
 
 Ferric-Magnetic Circuit 93 
 
 Filament, Causes of De- 
 crease of Cross-Sectional 
 
 Area of 210 
 
 Filament, Coking of 209 
 
 Filament, Decrease of Area 
 
 of Cross Section of 208 
 
 Filament, Disintegration of 208 
 Filament of Incandescent 
 Lamp 210 
 
INDEX. 
 
 287 
 
 Filament of Incandescent 
 Lamp, Variation of, Dur- 
 ing Use, 209 
 
 Film Cut-out 213, 214 
 
 First Harmonic, Frequency 
 
 of 258, 259, 260, 261 
 
 Five-wire System 61 
 
 Fleming's Hand Rule for 
 Direction of Induced 
 
 E. M. F 123, 124 
 
 Fleming's Hand Rule for 
 
 Motors 163 
 
 Flux Density, Definition of 90 
 
 Flux Density, Unit of 90 
 
 Flux, Displacement,Nature 
 
 of 2 
 
 Flux Intensity, Definition 
 
 of ? 
 
 Flux, Magnetic 89 
 
 Flux, Magnetic, Convention 
 
 as to Direction of 89 
 
 Flux, Physiologically Effec- 
 tive 206 
 
 Force, Counter Electromo- 
 tive of Motor 170 
 
 Force, Definition of 3 
 
 Force, Electric i 
 
 Force, Electromotive and 
 Electrodynamic, Co-gen- 
 eration of in Dynamo and 
 
 Motor 169 
 
 Force, Magnetic, Definition 
 
 of 99, ioo 
 
 Force or Stress, Electromo- 
 tive, Cause of 2 
 
 Force, Varieties of 3 
 
 Formulas for Resistivity.22, 23 
 
 Fourier's Theorem 258 
 
 Frequencies, Luminous and 
 Non-Luminous. .,...,., 201 
 
 Frequencies, Definition of. 234 
 Frequency of First Har- 
 monic 258, 259, 260, 261 
 
 Frequency of Second Har- 
 monic 258, 259, 260, 261 
 
 Fuller Voltaic Cell 86, 87 
 
 Fuses, Electric, Capacity of, 
 for Heat 200 
 
 Galvanometer, High Grade 
 
 Thomson's Mirror. .. .47, 48 
 Galvanometer, Shunt. . .36, 37 
 Galvanometer, Thomson's 
 
 Mirror 36 
 
 Gases, Effect of Pressure on 
 
 Resistivity of 26 
 
 Gauss, Definition of 90 
 
 Generator, Direct E. M. F. of 170 
 Generator, Electric Capa- 
 bility of 131 
 
 Generator, Output of 130 
 
 Generator, Series Wound. . 154 
 Generator, Shunt- Wound .. 154 
 
 Gilbert, Definition of 92 
 
 Globes, Arc-light 231 
 
 Gravity Voltaic Cell. . . 84, 85 
 Grenet Voltaic Cell,. . . 82, 83 
 
 Harmonics 258 
 
 Heat, Development of in 
 
 Safety Fuse. 200 
 
 Heat, Dissipation of, by 
 
 Electric Conductor 196 
 
 Heat, Loss by Radiation . . 197 
 
 Heat, Radiation of 197 
 
 Heat, Unit of. 192 
 
 Heating, Electric. . . .193 to soo 
 
288 
 
 INDEX. 
 
 Heating, Excessive, of Dy- 
 namo-Electric Machine, 
 Limitations to Output of, 
 
 Caused by 144, 145, 146 
 
 Hefner-Alteneck Lamp . . . 205 
 High Resistance Appara- 
 tus, Effect of Leakage on 
 
 Accuracy of 37 
 
 Hysteresis, Definition of. . . 139 
 Hysteresis, Magnetic . . 139, 
 
 140, 141, 142, 143 
 Hysteresis, Magnetic. Loss 
 
 of Energy of 141 
 
 Hysteretic Diagram 142 
 
 Hysteretic Loss in Alter- 
 nating-Current Trans- 
 former 276, 277 
 
 Illumination, Physiological, 
 Coefficient of 203 
 
 Illumination, Physiologic- 
 ally Effective 203 
 
 Illuminating Power, Phys- 
 iologically Effective. . 202, 203 
 
 Impedance Factor 254, 255 
 
 Impedance of Circuit 244 
 
 Incandescent Lamp, Activ- 
 ity of 7 
 
 Incandescent Lamp, Me- 
 thods Proposed for Re- 
 gulating Candle-power 
 of 212, 213 
 
 Incandescent Lighting.. 201 
 
 to 224 
 
 Induced Electromotive 
 Force 121 to 128 
 
 Induced or Structural Mag- 
 netic Flux of an Electro- 
 magnet ii 
 
 Inductance, Influence of on 
 Sparking of Brushes of 
 Dynamo 147, 148 
 
 Induction, Counter-Electro- 
 motive Force of 62 
 
 Inductor Alternators 257 
 
 Insulation Resistance of 
 Line or Conductor 33 
 
 Insulator, Circumstances 
 Affecting Resistance of. . 33 
 
 Insulator, Oil 33, 34 
 
 Intake of Machine, Defini- 
 tion of 8 
 
 Intensity, Maximum of Arc 
 Light ., 221 
 
 Intensity, Mean Horizontal, 
 of Arc Lights 221 
 
 Intensity of Flux, Defini- 
 tion of ... 90 
 
 International c. G. s. Unit 
 of Quantity n 
 
 International Ohm , Defini- 
 tion of 17 
 
 International Practical Unit 
 of E. M. F ii 
 
 Ions, Definition of. 73 
 
 Iron-clad Electromagnets. . 119 
 
 Joint Admittance 249, 250 
 
 Joint Resistance 51 
 
 Joule 194 
 
 Joule, Definition of 7 
 
 Kinetic Energy, Definition 
 of 3 
 
 Kirchoff's Laws 52, 53 
 
 Laborer, Average Activity 
 
 of 7 
 
 Lamp, Carcel 205 
 
INDEX. 
 
 289 
 
 Lamp, Effect of Tempera- 
 ture on Life of 207 
 
 Lamp, Efficiency of 207 
 
 Lamp Globe, Blackening 
 
 of 208, 2ii 
 
 Lamp, Hefner-Alteneck . . . 205 
 
 Lamp, Violle 205 
 
 Laws, Kirchoff's 52, 53 
 
 Lead of Dynamo Brushes.. 149 
 Leading Pole of Motor- 
 Armature 186 
 
 Leakage Paths. Magnetic. . 96 
 Leakage, Magnetic, Effect 
 of on Efficiency of Trans- 
 former 277 
 
 Leclanche, Voltaic Cell. ... 85 
 
 Lesser Calorie 192 
 
 Light, Standard of 205 
 
 Lighting, Load of Central 
 
 Stations 212 
 
 Limiting Current Strength 
 
 in Wires 198, 199 
 
 Line or Conductor, Insula- 
 tion Resistance of . . . .33, 34 
 
 Localized Vector 1 1 
 
 Loop, Conducting, Rotation 
 
 of, in Magnetic Flux 126 
 
 Losses, Eddy Current, in 
 Continuous-Current Mo- 
 tors 174 
 
 Losses, Magnetic, in Dyna- 
 mo-Electric Machine, 139, 140 
 Losses, Mechanical, in Dy- 
 namo-Electric Machine, 
 
 137, 138, 139 
 
 Luminous and Non-Lumin- 
 ous Frequencies 201 
 
 Luminous Radiation, Effect 
 of Temperature on 204 
 
 M. M. F 89, 96 
 
 M. M F.. Unit of . . . 92 
 
 Machine, Definition of In- 
 take of 8 
 
 Machine, Definition of Out- 
 put of 8 
 
 Machine, Dynamo-Electric, 
 
 Commercial-Efficiency of 137 
 Machine, Dynamo Electric, 
 Principles UnderlyingDe- 
 
 signof 133, 134, 135 
 
 Machine, Efficiency of 8 
 
 Magnetic and Material 
 Fluxes, Difference be- 
 tween 91 
 
 Magnetic Circuits 92 
 
 Magnetic Conductivity 95 
 
 Magnetic Force, Definition 
 
 of 99, 100 
 
 Magnetic Flux. . . . 89, 104, 112 
 Magnetic Leakage, Effect 
 on Efficiency of Trans- 
 former 277 
 
 Magnetic Losses of Dyna- 
 mo-Electric Machine 139, 140 
 Magnetic Permeability .... 95 
 Magnetic Reluctance 96 to 104 
 Magnetic Reluctance, and 
 Magnetizing Force, Rela- 
 tion between 101, 102 
 
 Magnetic Saturation 92 
 
 Magnetism Residual 93 
 
 Magneto-Dynamics, Defini- 
 tion of 161 
 
 Magnetomotive Force 91 
 
 Magnetomotive Force, 
 
 Structural 93 
 
 Mangin Reflector. . . . . .230, 231 
 
 Maximum Intensity of Arc 
 Light 221 
 
2go 
 
 INDEX. 
 
 Mean Horizontal Intensity 
 
 of Arc Lights 221 
 
 Mean Spherical Can die- 
 Power of Arc Lights 221 
 
 Megadyne , Approximate 
 
 Value of 6 
 
 Megadyne, Definition of . . . 6 
 
 Megohm, Definition of 18 
 
 Megohm, Standard 30 
 
 Metal-Coated Arc Light 
 
 Carbons 223 
 
 Metallic Reluctivity 103 
 
 Mho, Definition of 25 
 
 Microhm, Definition of ... 18 
 Molecules, Dis-associated. . 73 
 Molten-Platinum Standard 205 
 Monocyclic E. M. F., Dia- 
 gram of 271 
 
 Monocyclic System 271 
 
 Monocyclic System Trans- 
 former 272 
 
 Motion, Simple-Harmonic.. 236 
 Motor- Armature, Leading 
 
 Pole of 186 
 
 Motor- Armature, Reaction 
 
 of 186, 187 
 
 Motor-Armature, Toothed 
 
 Core 185 
 
 Motor- Armature, Trailing 
 
 Pole of 1 86 
 
 Motor-Armatures, Smooth 
 
 Core. 185 
 
 Motor, Continuous-Current, 
 Speed Varied by Shifting 
 Brushes on Commutator 
 
 128, 177 
 
 Motor, Continuous-Current, 
 under Constant Torque, 
 Methods of Carrying 
 Speed of... 177, 178, 179 
 
 Motor, Counter-Electromo- 
 tive Force of 170 
 
 Motor, Electromotive Force 
 
 of 62 
 
 Motor, How to Reverse Di- 
 rection of. . .187, 188, 189, 190 
 Motor, Relation of Torque 
 and Speed to Activity of 171 
 
 Motor, Series 179 
 
 Motor, Shunt 180 
 
 Motor, Starting Resistance 
 
 of 181 
 
 Motor, Street-car 191 
 
 Motor, Torque of 167 
 
 Motor, Work Absorbed by, 170 
 Motors, Classification of 
 for Torque and Speed 
 
 of 171 
 
 Motors,Continuous-Current, 
 
 Eddy Current Losses in.. 174 
 Motors, Electric, Weight 
 
 of 190, 191 
 
 Multiphase Alternators 265 
 
 Multiphaser 265 
 
 Multiple Arc Lighting, 
 
 Cost 227, 228 
 
 Multiple Circuit 59 
 
 Multiple-Series Circuit .... 60 
 Multiplying Power of 
 Shunt 36, 37 
 
 Negative Arc Light Carbon, 
 Nipple on 219 
 
 Negative Charge 2 
 
 Negative Plate of Voltaic 
 Cell 66 
 
 Negative Pole of Voltaic 
 Cell 66 
 
 Negative Resistivity Tem- 
 perature Coefficient 23 
 
INDEX. 
 
 291 
 
 Negative Terminal of Vol- 
 taic Cell 66 
 
 Network of Conductors, 
 Application of Ohm's 
 Law to . 53 
 
 Nipple on Negative Arc 
 Light Carbon 219 
 
 Non-Luminous Radiation.. 201 
 
 Obscure Radiation 201 
 
 Oersted, Definition of. .97 
 Ohm, International, Defi- 
 nition of 17 
 
 Ohm, Multiples and Sub- 
 Multiples of 17. 18 
 
 Ohm, Standard ....... 29, 30 
 
 Ohrn's Law ... ...49 to 56 
 
 Ohm's Law, Application of, 
 
 to Branch Circuit 52 
 
 Ohm's Law, Application of, 
 to Network of Conduc- 
 tors 53 
 
 Oil Insulator 33, 34 
 
 Output of Dynamo Electric 
 Machine, Classification of 
 
 Limitations to 145 
 
 Output of Dynamos and 
 Motors, Difference be- 
 tween 181, 182 
 
 Output of Generator 130 
 
 Output of Machine 8 
 
 Parallel Connection of Al- 
 ternators 263 
 
 Partz Gravity Voltaic Cell 
 
 85, 86 
 Paths, Magnetic Leakage. . 96 
 
 Period, Definition of 234 
 
 Periodic Alternating Cur- 
 rent, Definition of 233 
 
 Periodic- Alternating E.M.F., 
 Definition of 233 
 
 Periodic Alternating E.M.F., 
 or Current. Peaked Type 
 of 235 
 
 Periodic- Alternating E. M. F. , 
 or Current, Sinusoidal 
 Type of. 235 
 
 Permanent Magnetomotive 
 Force 91 
 
 Permeability, Magnetic ... 95 
 
 Phase 238 
 
 Phase Detectors 264 
 
 Physiological Coefficient of 
 Illumination 203 
 
 Physiologically Effective 
 Flux 206 
 
 Physiologically Effective 
 Illuminating Power. 202, 203 
 
 Physiologically Eilective 
 Illumination 203 
 
 Plate, Negative, of Voltaic 
 Cell 66 
 
 Plate, Positive, of Voltaic 
 Cell 66 
 
 Poggendorff Voltaic Cell 82 , 83 
 
 Polarity, Nature of 2 
 
 Polarization, c. E. M. F. of.. 8r 
 
 Polarization, Counter-Elec- 
 tromotive Force of 62 
 
 Pole, Leading of Motor- 
 Armature 1 86 
 
 Pole, Negative, of Voltaic 
 Cell 66 
 
 Pole, Positive, of Voltaic 
 Cell 66 
 
 Pole, Trailing of Motor- 
 Armature 186 
 
 Portative Electromagnets, 
 Definition of 113 
 
2 9 2 
 
 INDEX. 
 
 Positive Carbon, Rate of 
 
 Consumption, of 228 
 
 Positive Charge 2 
 
 Positive Plate of Voltaic 
 
 Cell... 66 
 
 Positive Pole of Voltaic Cell 66 
 Positive Terminal of Voltaic 
 
 Cell 66 
 
 Potential Difference 13 
 
 Potential, Distribution of, 
 in Continuous-Arc Light 
 
 Circuits 226 
 
 Potential Energy, Difini- 
 
 tion of 3 
 
 Power Factor of Alternat- 
 ing Current Transform- 
 ers 280 
 
 Practical Unit of E. M. F. . . u 
 Practical Unit of Electric 
 
 Resistance 17 
 
 Practical Unit of Heat. . . . 194 
 Projectors for Arc Lights. . 
 
 229, 230, 231 
 
 Quantity, Electric, Com 
 
 mercial Unit of 45 
 
 Quegohm, Definition of 18 
 
 Radiation, Non luminous.. 201 
 
 Radiation, Obscure 201 
 
 Radiation of Heat 197 
 
 Radiation, Physiologically 
 Effective Luminous, Var- 
 iation of, with Current 
 
 Strength 211 
 
 Radiation, Standard, of 
 Physiologically Effective 
 
 Luminous 205 
 
 Railroad Electric Motor. . . 180 
 
 Ratio of Transformation . . 
 
 273. 274 
 
 Reactance of Circuit 244 
 
 Reflector, Mangin. ... 230, 231 
 Regulation of the Dynamo 
 
 153. i 60 
 
 Reichsanstalt Unit 205 
 
 Reluctance, Magnetic,^ to 104 
 Reluctance, Magnetic, Defi- 
 nition of 97 
 
 Reluctance, Unit of 97 
 
 Reluctivity 97 
 
 Reluctivity, Curves of, in 
 Iron and Steel, in Rela- 
 tion to Flux Density 107 
 
 Reluctivity, Curves of, in 
 Iron and Steel, in Rela- 
 tion to Magnetizing Force 102 
 
 Reluctivity, Metallic 103 
 
 Residual Magnetism 93 
 
 Resistance, Balances. ..28, 29 
 
 Resistance, Electric 17, 40 
 
 Resistance, Electric, Nature 
 
 of Unknown 36 
 
 Resistance, Equivalent 253 
 
 Resistance, Insulation of 
 
 Cable 35, 3& 
 
 Resistance, Joint 51 
 
 Resistance of Insulator, 
 Circumstances Affecting, 33 
 
 Resistance, Specific 18 
 
 Resistance, Specific, Mag- 
 netic 97 
 
 Resistance, Starting of Mo- 
 tor 181 
 
 Resistance, Surface Contact 39 
 Resistances, Formula for 
 
 Calculating 25 
 
 Resistances, Methods of 
 Measurement of ... .26 to 31 
 
INDEX. 
 
 293 
 
 Resistivities, Diagram of, 
 
 atDifferentTemperatures 21 
 Resistivities, Table of . .19, 20 
 Resistivities, Thermal, 
 
 Table of. 196 
 
 Resistivity 18 
 
 Resistivity, Formulae 22 
 
 Resistivity, Temperature 
 
 Coefficients 19 
 
 Reversibility of Continuous- 
 Current Dynamo. .. .170, 171 
 
 Resistivity, Thermal 194 
 
 Resonant Circuit 248 
 
 S. H. M 236 
 
 Safety Fuse, Development 
 
 of Heat in 200 
 
 Saturation, Magnetic 92 
 
 Search Lights 229 
 
 Second-Harmonic, F r e - 
 quency of. . . 258, 259, 260, 261 
 
 Self. Induced E. M. F 127 
 
 Semi- Period of Alternating 
 E. M. F. or Current Wave, 
 
 Definition of 234 
 
 Series Arc Light Circuits . . 
 
 225, 226, 227 
 
 Series Circuit 58 
 
 Series-Connected In- 
 candescent Electric 
 
 Lamps 213, 214 
 
 Series Motor 179 
 
 Series Motor, Commutation 
 
 of Field Coils of 179 
 
 Series Motor, Method of 
 
 Varying Speed of 179 
 
 Series-Wound Machine 
 
 187, 188 
 
 Shunt, Alternating-Current 
 Circuit, MultiplyingPower 
 
 of 252 
 
 Shunt Circuit, Application 
 
 of Ohm's Law to 52 
 
 Shunt, Continuous Current 
 Circuit, Multiplying 
 
 Power of 251 
 
 Shunt Galvanometer 36, 37 
 
 Shunt Motor 180 
 
 Shunt Motor, Care Re- 
 quired in Starting 181 
 
 Shunt, Multiplying Power 
 
 of 36, 37, 251 
 
 Shunt- Wound Machines, 
 Direction of Rotation as 
 Motors and Generators. . 
 
 187, 188 
 Silver Chloride Voltaic Cell 
 
 87, 88 
 
 Simple-Harmonic Curve. . . 237 
 Simple-Harmonic Motion . 236 
 
 Simple-Periodic Curve 237 
 
 Single-Fluid Cells, Defini- 
 tion of 81 
 
 Sinusoidal Current 236 
 
 Sinusoidal Current Circuit, 
 
 Activity of 253 
 
 Sinusoidal Curve 237 
 
 Sinusoidal E. M. F 236 
 
 Smee Voltaic Cell 82 
 
 Smooth Core Motor Arma- 
 tures 185 
 
 Sources, Electric 13 
 
 Sources, Electric, Classifi- 
 cation of 14 
 
 Sources, Electric, Electro- 
 motive Force of 14, 15 
 
 Sparking at Dynamo Brush- 
 es, Cause of 147, 148 
 
294 
 
 INDEX. 
 
 Specific Magnetic Resis- 
 tance 97 
 
 Specific Resistance, Defini- 
 tion of 18 
 
 Speed and Torque, Classi- 
 fication of, in Motors. ... 171 
 Speed of Motor, Varied by 
 Inserting Resistance in 
 Armature Circuit. . . .177, 178 
 Speed of Motor, Varied by 
 Varying Magneto-motive 
 Force of Field Magnets. . 
 
 178, 179 
 
 Standard Candle 205 
 
 Standard Cell, Clark. ..15, 16 
 
 Standard Megohm 30 
 
 Standard of Physiologically 
 Effective Luminous Radi 
 
 ation 205 
 
 Standard Resistance 29, 30 
 Star Triphase Winding, 
 
 Diagram of 267 
 
 Star- Winding of Triphase 
 
 Generator 267 
 
 Step-Down Transformer. . 273 
 
 Step-Up Transformer 273 
 
 Strain, Displacement ...9, 10 
 
 Street-Car Motors 191 
 
 Stress, Electromotive, Cause 
 of 2 
 
 Stresses and Strains in 
 Ether i, 2 
 
 Structural Magnetomotive 
 Force 93 
 
 Sun, Total Amount of 
 Energy in 7 
 
 Surface, Contact Resis- 
 tance 39 
 
 Table of Electro-Chemical 
 Equivalents 74 
 
 Table of Resistivities 19, 20 
 
 Table of Thermal Resis- 
 tivities 196 
 
 Temperature Coefficients 
 for Clark Standard Cell. . 16 
 
 Temperature Coefficients 
 for Resistivity 19, 20 
 
 Temperature, Effect of, on 
 Efficiency of Lamp 207 
 
 Temperature, Effect of, on 
 Life of Lamp 207 
 
 Temperature, Effect of, on 
 Luminous Radiation. . . . 204 
 
 Temperature, Effect of, on 
 Resistivity of Conductors 26 
 
 Temperature, Safe Limit- 
 ing, of Wire 198, 199 
 
 Terminal, Negative , o f 
 Voltaic Cell 66 
 
 Terminal, Positive, of 
 Voltaic Cell 66 
 
 Thales i 
 
 Therm 192 
 
 Therm-Calorie... 193 
 
 Thermal Conductivity 194 
 
 Thermal Resistivities, 
 Table of 196 
 
 Thermal Resistivity. . . 194, 195 
 
 Thomson's High Grade 
 Mirror Galvanometer. 47, 48 
 
 Thomson's Marine Galvano- 
 meter 46 
 
 Thomson's Mirror Galvano- 
 meter 46 
 
 Three-Wire System, Cal- 
 culation of Current 
 Strength in 55, 56 
 
INDEX 
 
 295 
 
 Three Wire System, De- 
 scription of 54, 55 
 
 Three- Wire System, Neutral 
 Wire in 55 
 
 Toothed Core Motor- Arma- 
 ture 185 
 
 Torque and Speed, Classifi- 
 cation of, in Motors.. 171 
 
 Torque and Speed, Rela- 
 tion of, to Activity of 
 Motor . . . 171 
 
 Torque of Motor 167 
 
 Trailing Pole of Motor- 
 Armature. 186 
 
 Transformation, Ratio of 
 
 273. 274 
 
 Transformer, Step-Down. . 273 
 
 Transformer, Step-Up 273 
 
 Transient Magnetomotive 
 Force 91 
 
 Tregohm, Definition of .. 18 
 
 Triangular Triphase Wind- 
 ing Diagram of 267 
 
 Triangular Winding of Tri- 
 phase Generator 267 
 
 Tricrohm, Definition of.... 18 
 
 Triphase Circuit, Analysis 
 of 270 
 
 Triphase E. M. F'S 267 
 
 Triphase E. M. F.'S, Diagram 
 of 268 
 
 Triphase Generator, Star- 
 Winding of 267 
 
 Triphase Generator, Wind- 
 ing of 267 
 
 Triphase Generators, Tri- 
 angular-Winding of 267 
 
 Unit Arc-Light Crater In- 
 tensity 223 
 
 Unit of Activity, c. G. s 7 
 
 Unit of Flux, Density of . . 90 
 
 Unit of Force, c. G. s 5 
 
 Unit of Heat 192 
 
 Unit of Illumination, Name 
 
 Proposed for 206 
 
 Unit of M. M. F 92 
 
 Unit of Quantity, c. G. s. . . n 
 
 Unit of Reluctance 97 
 
 Unit of Resistance, Prac- 
 tical, Definition of 17 
 
 Unit of Work 6 
 
 Units, c. G. s 4, 5 
 
 Units, Fundamental, Sci- 
 entific 4, 5 
 
 Vector, Localized 1 1 
 
 Vector Quantities 1 1 
 
 Violle Lamp 205 
 
 Virtual Counter-Electro- 
 Motive Force 62 
 
 Voltaic Cell 65 to 88 
 
 Voltaic Cell, Calculation of 
 
 E. M. F. in 76, 77 
 
 Voltaic Cell, Cost of Elec- 
 tric Energy, produced by 69 
 Voltaic Cell, Elements of . . 66 
 Voltaic Cell, Simple Form 
 
 of 67 
 
 Voltaic Cell, Source of 
 
 E. M. F. of 67, 68 
 
 Voltaic Cells, Classification 
 
 of 81 
 
 Voltaic Couple 66 
 
 Water-Gramme -Degree- 
 
 Centigrade 193 
 
 Water, Pure, Resistivity of 21 
 
 Wave, Complex-Sinusoidal 258 
 
 Wheatstone's Balance . 28, 29 
 
2 9 6 
 
 INDEX. 
 
 Wheatstone's Bridge, Vari- 
 ous Forms of 28, 29 
 
 Winding, Combination Tri- 
 phase . . 268 
 
 Wire, Formula for Calcula- 
 ting Size of, Required to 
 Fill Given Bobbin. 37, 38, 39 
 
 Wires , Limiting Current 
 Strength in 198, 199 
 
 -Work, Absorbed by Mo- 
 tor 170 
 
 Work, Definition of 3 
 
 Work Unit of... 6 
 
 ERRATA. 
 
 Page 23, If 23, 5 lines from bottom of page. For resistivity of a mile 
 
 read resistance of a mile. ^ 
 " 24, Syllabus, 9th line. For begohm read bicrohm. - 
 
 34, 1[ 34. For R = 
 
 r app . coth-i \/ ^ <, 
 
 -ttapp. 
 
 read R = \/R &pv . r app . /tanbr ' 
 
 34, last line. For coth 
 
 V; 
 
 2656 
 
 read 1 / tanh 
 
 -iA/2656 
 
 V R(Y).A 
 
 6024 " K 6024 
 
 " 175, If 182. For reluctance read retardation. ~* 
 " 203, " 211. For yellow read green. -S 
 " 230, Fig. 77, caption. For Magnetic read Mangin. 
 44 258, If 261. For n\ read n + 1. - 
 " 264, Syllabus. For n 1 read n + 1. J 
 
 OT THB 
 
 UJIVEBSITT 
 
ill