- 
 
 r 
 
 REESE LIBRARY 
 
 <)! THIC 
 
 UNIVERSITY OF CALIFORNIA. 
 
 L 
 
 Accessions No. 
 
 Class M>. 
 
CHAPTERS 
 
 ON 
 
 ELECTEICITT 
 
 AN INTRODUCTORY TEXT-BOOK FOR 
 STUDENTS IN COLLEGE 
 
 BY 
 
 SAMUEL SHELDON, PH.D. (WURZBURG) 
 
 3TU1FS3SOR OF PHYSICS AND ELECTRICAL ENGINEERING, POLYTECHNIC INSTITUTE OP BROOK1YS 
 
 SECOND EDITION 
 WITH A COURSE IN ELECTRICAL MEASUREMENTS. 
 
 NEW YORK 
 CHAELES COLLINS, PUBLISHER 
 
 AND 
 
 THE BAKER & TAYLOR CO., 5 EAST SIXTEENTH STREET 
 
SHELDON'S CHAPTERS ON ELECTRICITY 
 
 COPYRIGHT, 1891 
 Br CHARLES COLLINS 
 
 SECOND EDITION 
 
 COPYRIGHT, 1895 
 BY CHARLES COLLINS 
 
PREFAO'E 
 
 fTlHESE Chapters on Electricity, prepared for and included in 
 -*- the Fourth Revised Edition of Olmsted's College Philos- 
 ophy, are here offered in a separate volume. They are intended 
 for use as a text-book by students in those colleges which devote 
 but thirty or forty hours to the subject. The principles presented 
 are those which ought to be known by every liberally educated 
 person. The economy of space necessitated by a clear and 
 thorough presentation within such limits, has required the omis- 
 sion of detailed descriptions of appa7*atus and of demonstrative 
 experiments. To master these chapters will require more effort 
 on the part of a student than to master an equal number of pages 
 in a more extended treatise. For the same efforts, however, he 
 will obtain a knowledge of a greater number of principles. Fur- 
 thermore, he will more readily perceive the correlation between 
 different parts of the subject. Even an ordinary comprehension 
 of the subject signifies a knowledge of many of these mutual 
 relations. 
 
 It has been the desire of the author to present each part of the 
 subject in its most modern dress. This desire, however, has been 
 tempered by a consideration of the intended functions of the book. 
 
 POLYTECHNIC INSTITUTE OF BROOKLYN, 
 June, 1891. 
 
 IN the present edition a few typographical errors have been 
 corrected, and a Course in Electrical Measurements has been 
 added. This course is written in the form of a laboratory manual 
 in which specific directions are given to the student. The experi- 
 ence of the author has shown that such a manual results in a saving 
 of time both to the instructor and the student. The enthusiasm 
 of the student is better maintained when his results are fairly ac- 
 curate and of frequent occurrence. A meagre laboratory equipment 
 is sufficient for carrying on the course, and the accuracy of the re- 
 sults obtained will depend almost entirely upon the student and the 
 instructor. 
 
 POLYTECHNIC INSTITUTE OF BROOKLYN, 
 July, 1895. 
 
CONTENTS. 
 
 (The figure* rv/vr to the page*,) 
 
 PART VII.-ELECTBIC1TY AND MAGNETISM. 
 CHAPTER I. 
 
 ELECTROSTATICS. POTENTIAL. CAPACITY. 
 
 Definition Common Indications of Electricity Repulsion, 351 ; Theories 
 of Electricity Electric Series, 352 ; Conductors and Insulators Cou- 
 lomb's Law, 353 ; Potential, 354 ; Equipotential Surfaces, 355 ; Dif- 
 ference of Potential Unit of Potential, 356 ; Zero Potential Potential 
 on a Sphere Capacity, 357 ; Equipotential of Connected Conductors 
 Position of Static Charge Distribution of a Charge on the Surface, 
 359 ; Surface Density Quadrant 'Electrometer, 360 ; Problems, 361. 
 
 CHAPTER II. 
 
 ELECTROSTATIC INDUCTION. 
 
 Gold-leaf Electroscope Phenomena, 362 ; Induction Precedes Attraction, 
 363 ; Quantity of the Induced Electricity Condensers, 364 ; Specific 
 Inductive Capacity, 365 ; Leyden Jar Seat of the Charge, 367 ; Resid- 
 ual Charge Modern Theory of Condensers, 368 ; Hertz's Experiments, 
 369 ; Electrical Machines Electrophorus Holtz Machine, 370 ; Effects 
 of Statical Discharge Lightning, 372. 
 
 CHAPTER III. 
 
 MAGNETISM. 
 
 Natural Magnets Artificial Magnets Poles of a Magnet Magnetic Needle, 
 373 ; Attractions and Repulsions North and South Poles'lnseparable 
 Magnetic Induction, 374 ; Retentivity or Coercive Force, 375 ; Law of 
 Magnetic Force Unit Magnet Pole, 376 ; Lifting Power Laminated 
 Magnets, 377 ; Magnetic Field Lines of Force, 378 ; Theory of the 
 Curvature of the Lines, 379 ; Fields from Several Magnets, 380 ; 
 Strength or Intensity of Magnetic Field Determination of the Strength 
 of a Field, 381 ; Hysteresis Number of Lines of Force from a Given 
 Pole, 382 ; Magnetic Susceptibility, 383 ; Magnetic Permeability Mag- 
 netic Circuit, 384 ; Paramagnetism and Diamagnetism, 385. 
 
 CHAPTER IV. V 
 
 TERRESTRIAL MAGNETISM. 
 
 The Earth a Magnet Declination of the Needle Ispgonic Curves, 386 ; 
 Secular and Annual Variation Diurnal Variation Magnetometer, 
 388 ; Dip of the Needle, 389 ; Isoclinic Curves, 390 ; Intensity of the 
 Earth's Magnetism, 391 ; Isodynamic Curves, 392 ; Variation in the 
 Strength of the Earth's Field Astatic Needles, 393 ; Magnetic Charts 
 The Declination Compass The Mariner's Compass, 394 ; Aurora 
 Borealis Why the Earth is a Magnet, 395. 
 
 CHAPTER V. 
 CURRENT ELECTRICITY. 
 
 Electricity in motion Galvanic Cells, 396 ; Electromotive Force, 397 ; 
 Polarization Types of Batteries, 398; Daniell's Cell Leclanche 
 Cell, 399 ; Combustion of Zinc Amalgamation of Zincs, 400 ; Prac- 
 
V1 CONTENTS. 
 
 tical Units of Current and Quantity Resistance, 401 ; Influence of 
 Temperature, 402; Ohm's Law Divided Circuits Shunts, 403; 
 Ratio of Currents in shunts Fall of Potential, 404; Resistance 
 Boxes or Rheostats Wheatstone's Bridge, 405 ; Cells in Series and 
 in Multiple Arc, 407 ; Problems, 408. 
 
 CHAPTER VI. 
 
 ELECTRO -MAGNETISM. 
 
 The Current's Lines of Magnetic Force, 409 ; Effect of a Current on a Mag- 
 net, 410 ; Solenoids, 411 ; Ampere's Theory of Magnetism, 412 ; Electro- 
 magnets Magneto- motive Force, 413 ; The Morse Telegraph System, 
 415; The Relay, 417; Duplex Telegraphy, 418; Atlantic Telegraph 
 Cable Electric Bells, 420 ; Galvanometers, 421. 
 
 CHAPTER VII. 
 
 ELECTRO-DYNAMICS. 
 
 Movements of Conductors Carrying Currents Parallel Currents, 423 ; Cur- 
 rents not Parallel, 424 ; Continuous Rotation Produced by Mutual Ac- 
 tion of Currents, 425 ; Electro-dynamometer, 426. 
 
 CHAPTER VIII. 
 ELECTRO-MAGNETIC INDUCTION. 
 
 Currents of Electricity Produced by Induction Methods of Producing the 
 Inducing Field, 427 ; Lenz's Law Self-induction, 429 ; Coefficients of 
 Mutual and Self-induction Induced Currents from the Earth, 430 ; 
 Arago's Rotations Induction Coils, 431 ; The Telephone, 432 ; The 
 Blake Transmitter, 433 ; Dynamos, 434 ; Electric Motors, 436. 
 
 CHAPTER IX. 
 
 ELECTRO-CHEMISTRY AND ELECTRO-OPTICS. 
 
 Electrolytes, 436; Electrolysis of Sulphuric Acid Metallic Salts, 437; 
 Faraday's Laws Voltameters, 438 ; Theory of Electrolysis Electro- 
 plating, 439 ; Electrotyping Counter - Electromotive Force, 440 ; 
 Storage Batteries, 441 ; Capillary Electrometer, 442 ; Light and Elec- 
 tricity Double Refraction from Electrostatic Strain, 443 ; Magneto- 
 optic Twisting of the Plane of Polarized Light Rotation of the Plane 
 by Reflection Photo-Electric Properties of Selenium, 444. 
 
 CHAPTER X. 
 
 THE RELATIONS BETWEEN ELECTRICITY AND HEAT. 
 
 Power of the Electrical Current, 445 ; Heat Developed in a Conductor 
 Rise in Temperature of the Conductor, 446 ; Hot Wire Ammeters and 
 Voltmeters, 447 ; Electric Welding The Electric Arc, 448 ; Incan- 
 descent Electric Lamps Thermo-Electricity, 449 ; Thermo-Electric 
 Pile Peltier Effect, 450 ; The Electrical Units, 451. 
 
 A COURSE IN ELECTRICAL MEASUREMENTS. 
 
 Intro duct 017, 453 ; Resistances, 455 ; Battery Resistances, 460 ; Com- 
 parison of Electromotive Forces, 464 ; Measurement of Currents, 
 466 ; Condensers, 468 ; Magnetism, 469 ; Calibrations, 472. 
 
f OF THE ^\ 
 
 (UNIVERSITY) 
 
 x. w s 
 
 PART VII. 
 
 ELECTEIOITT AND MAGNETISM, 
 
 CHAPTER I. 
 
 ELECTROSTATICS. POTENTIAL. CAPACITY. 
 
 557. Definition. The name Electricity, from the Greek word 
 for amber, is given to a peculiar agency, which causes mutual 
 attractions or repulsions between light bodies, and which, under 
 proper conditions, also produces heat, light, sound, and chemical 
 decomposition. 
 
 Lightning and thunder are familiar illustrations of the intense 
 action of this agency. , 
 
 558. Common Indications of Electricity. If amber, seal- 
 ing-wax, or any other resinous substance, be rubbed with dry 
 ^woollen cloth, fur, or silk, and then brought near the face, the 
 excited electricity disturbs the downy hairs upon the skin, and 
 thus causes a sensation like that produced by a cobweb. When 
 Tulcanite is strongly excited, it gives off a spark to the finger held 
 toward it, accompanied by a sharp snapping noise. A sheet of 
 writing-paper, first dried by the fire, and then laid on a table 
 and rubbed with India-rubber, becomes so much excited as to 
 adhere to the wall of the room or any other surface to which it is 
 applied. As the paper is pulled up slowly from the table by one 
 edge, a number of small sparks may be seen and heard on the 
 under side of the paper. In dry weather, the brushing of a gar- 
 ment causes the floating dust to fly back and cling to it. 
 
 Bodies are said to be electrically excited when they show signs 
 of electricity in consequence of some mechanical action performed 
 upon them, as in the experiments already described. 
 
 A body is electrified when it receives electricity, by communica- 
 tion, from another body already excited or electrified. 
 
 559. Repulsion. An electrically excited body does not 
 always produce attraction. It will be noticed that pith-balls, after 
 
352 ELECTRICITY AND MAGNETISM. 
 
 coining in contact with an electrified body, which has attracted 
 them, are repelled. They have received a portion of the elec- 
 tricity which attracted them and repulsion is the result. This 
 repulsion can be made much more apparent if an electrified vul- 
 canite rod be suspended in a wire loop at the end of a silk thread 
 and then a similarly electrified rod be approached to it. The 
 suspended rod can be made to revolve rapidly because of the 
 repulsion. 
 
 560. Theories of Electricity. As to the exact nature of 
 electricity science is still in the dark, though probably the dark- 
 ness which precedes dawn. 
 
 Symmer proposed a "two-fluid" theory. He supposed every 
 unelectrified body to contain equal quantities of two opposite 
 kinds of impooderable electric fluid. In equal quantities they 
 neutralized each other. But if, by friction or other means, the 
 amount of one fluid be made to exceed that of the other, then 
 the body becomes positively or negatively electrified. According 
 to this theory two positively or two negatively electrified bodies 
 repel each other ; a positively electrified body and a negatively 
 electrified body attract each other. 
 
 Franklin modified this into a " one-fluid " theory. Every body 
 contains its own normal amount of one electric fluid. This amount 
 is increased or decreased when rubbed by another body. The 
 surplus amount is obtained from or given up to this second body.. 
 The body with more than its normal amount is positively elec- 
 trified, and negatively electrified when it has less than this amount. 
 
 Lodge maintains that electricity is the luminiferous ether itself. 
 He arrives at this conclusion after considering a great number of 
 electrical phenomena which demand the ether for their proper 
 explanation. 
 
 Without adopting any theory, electrical laws and phenomena 
 may be understood by considering the fact that a body may be 
 subject to two opposite electrical conditions. It may be positively 
 or negatively electrified. The law regarding attraction and repul- 
 sion then is : 
 
 Similarly electrified bodies repel each other, and dissimilarly elec- 
 trified bodies attract each other. 
 
 561. Electric Series. If two bodies are rubbed together, 
 one of them is electrified positively and the other negatively. One 
 of these bodies, if rubbed by a third, may be oppositely electrified 
 to what it was in the first case. Silk, when rubbed with glass, is- 
 negatively electrified; but rubbed with sulphur, it receives a pos- 
 itive charge. In the following series each member becomes 
 
UNIVERSIT 
 
 COULOMB'S LA 
 
 353 
 
 positively charged when rubbed on one following it, negatively 
 when rubbed on one preceding it : fur, wool, resin, glass, cotton, 
 silk, wood, metals, sulphur, india-rubber, gutta-percha. 
 
 562. Conductors and Insulators. When a glass or vul- 
 canite tube is rubbed with cat's fur, it shows that it has become 
 electrified by attracting light articles. If a metal rod be substi- 
 tuted for the glass one, no attraction will be evidenced. This is 
 not because the metal was not electrified by the rubbing, but 
 because the electricity, as soon as generated, escaped, through the 
 rod itself and the hand holding it, to the ground. If the rod be 
 held by a glass or hard-rubber handle and then rubbed, it will 
 attract as the glass did. This shows that some substances, as 
 metals, allow electricity to pass freely through them, while others, 
 as glass, almost entirely prevent its passage. The first class of 
 substances are called conductors, the latter class non-conductors or 
 insulators. Some substances neither conduct nor insulate well, but 
 lie between the two classes. The following is a table of substances 
 arranged in the order of their electrical conductivity : 
 
 CONDUCTORS. 
 1. Metals. 
 2. Charcoal. 
 3. Graphite. 
 
 4. Acids. 
 5. Sea-water. 
 6. Vegetables. 
 7. Animals. 
 
 8. Wood. 
 9. Silk. 
 10. India-rubber. 
 11. Porcelain. 
 
 12. Glass. 
 13. Shellac. 
 14. Vulcanite. 
 INSULATORS. 
 
 A conductor mounted upon or suspended by an insulator is said 
 to be insulated. 
 
 A method for determining the conductivity of substances is to 
 suspend two pith-balls by moistened threads from a metal insulated 
 hook. Upon communicating a charge of electricity to the balls 
 they will stand out away from each other, owing to the repulsion 
 between the same kinds of electricity on each. If, now, one end of 
 the substance, whose conductivity is to be determined, be held in 
 the hand and the other be touched to the hook from which the 
 faalls are suspended, the rapidity with which the balls fall toward 
 each other determines the conductivity. If they fall instantly, the 
 substance is a good conductor. If they remain separated, the sub- 
 stance is a good insulator. After an insulator or an insulated con- 
 ductor has been charged with electricity, the electricity of necessity 
 remains at rest, and is, for this reason, called statical electricity. If, 
 now, it be connected, by means of a conducting wire, with the 
 moist earth, it will pass off instantly to the earth. During the 
 time of its passage it is called dynamical electricity. If by chemical 
 or other means the flow be maintained, then the dynamical elec- 
 tricity is called galvanic or voltaic. 
 
 563. Coulomb's Law. Coulomb showed that, correspond- 
 
354: ELECTRICITY AND MAGNETISM. 
 
 ing to Newton's law of gravitation, the force of attraction between 
 dissimilarly electrified bodies and the force of repulsion between sim- 
 ilarly electrified bodies is directly proportional to the product of the 
 quantities of electricity and inversely proportional to the square of the 
 distance between the bodies. 
 
 If we represent the force by / dynes, the distance by r centi- 
 metres, and the quantities of electricity by q and q' } then we can 
 indicate the law by the equation 
 
 If these magnitudes be connected by the sign of equality, a proper 
 unit of quantity must be had. Letting / = 1 dyne, r = 1 centi- 
 meter, and q = q', then g 2 = 1 and q = 1. Hence we may define- 
 the unit of electrical quantity as follows : 
 
 One unit of electricity is that quantity which, when placed at a dis- 
 tance of one centimetre from a similar and equal quantity, repels it 
 with a force of one dyne. 
 
 If the quantity of electricity be spread over a body of some 
 size, as a sphere, then the distance r must be measured from some 
 point as the centre of the sphere. This is evidently for the same 
 reason as in gravitation, where the distance is measured from the- 
 centre of gravity. 
 
 It must be borne in mind that the unit of quantity here given- 
 is based upon the force exerted by two statical quantities of elec- 
 tricity. Another unit, based upon the electro-magnetic force, will 
 be mentioned later. 
 
 564. Potential. Whenever a body is lifted vertically away 
 from the earth, the work performed in lifting it has been trans- 
 formed into potential energy. The body has, because of the 
 attraction between it and the earth, a potential energy capable of 
 doing exactly the same number of ergs or foot-pounds of work as 
 were used in raising it to its position (Art. 36). Similarly, if two 
 conductors, charged with the same kind of electricity, be ap- 
 proached towards each other, a certain number of ergs of work 
 will have been performed, owing to the repulsion between them. 
 (A more perfect analogy would be to suppose two dissimilarly 
 charged conductors to be separated.) The work which has been 
 performed is also changed into potential energy between the con- 
 ductors. The amount of energy made potential depends upon the 
 quantities of electricity on each of the conductors, and upon the 
 distance through which they have been moved toward each other. 
 For energy is measured by the work it can do, and work in ergs- 
 equals the product of the force in dynes by the distance in centi- 
 
EQUIPOTENTIAL SURFACES. 355 
 
 metres through which it has acted. Now the force of repulsion 
 between the two conductors equals the product of their quantities 
 divided by the square of their distance apart. 
 
 Suppose one of the conductors to have any charge and to 
 be fixed immovably. Then let three charges of respectively 1, 2, 
 and 3 units of quantity be successively approached, between the 
 same limits, towards the first conductor. In the first case a cer- 
 tain amount of energy will have been made potential ; in the 
 second case twice as much, and in the third three times as much. 
 Evidently a certain amount of the energy made potential is owing 
 to the immovable charge, and this amount is the same in each 
 case. The condition of the space around an electrified body is 
 termed the potential, owing to that charge. To obtain a quanti- 
 tative expression for it, 'the movable charge must be taken of unit 
 quantity. It must also be considered that the work necessary to 
 approach an unit through a given distance is not as great as to 
 approach it through twice that distance. Considering these two 
 points, we have the definition of electrostatic potential : 
 
 The potential at any point is the work that must be spent upon a 
 unit of positive electricity in bringing it up to that point from an 
 infinite distance. 
 
 If the immovable charge be negative, no work would be 
 required to move up a positive unit ; on the contrary, work would 
 be performed by the unit in travelling. Hence the potential, 
 owing to a negative charge, is negative potential. It is convenient 
 to consider it so. 
 
 565. Equipotential Surfaces. If the charge of electricity 
 be supposed to lie on a small sphere, then some point can be 
 found on every possible radius of the sphere produced where the 
 potential will be the same. That is, it would require the same 
 amount of work to bring a positive unit of electricity from an 
 infinite distance out on each radius to this point. In the case of a 
 sphere being charged, these points would be equally distanced 
 from the centre of the sphere. If now these points be connected 
 together, a spherical surface will result. Any such surface which 
 contains only points of the same potential is called an equipotential 
 surface. 
 
 In order that an equipotential surface may be spherical, the 
 charge must lie upon a sphere and must be free from other electri- 
 fied bodies. If the electrified body be irregular in shape, the 
 equipotential surfaces will be correspondingly so. 
 
 To transfer a quantity of electricity from one point in an equi- 
 potential surface to another in the same surface requires no work to 
 
356 ELECTRICITY AND MAGNETISM. 
 
 be performed. For while it may require work to move the charge 
 in one direction from the surface, it will require a negative expen- 
 diture of work to bring it back again, i.e., the attraction or repul- 
 sion between the electricities performs the work. 
 
 566. Difference of Potential. In the consideration of most 
 problems in electricity involving the idea of potential, the potential 
 of two points is required. However, it is not the absolute poten- 
 tial of each of the points, but the difference of potential between 
 them which is considered. If it requires a certain number of ergs 
 to bring a unit of positive electricity from an infinite distance up 
 to a given point, and more ergs to bring it up to a second point, 
 then this extra work is what would be required to move the unit 
 from the first to the second point. This number of ergs is then 
 the measure of the difference of potential between the two poiiits. 
 Hence we obtain the definition : 
 
 The unit difference of potential is that which must exist between 
 two points, that one erg may be required to move a positive unit 
 of electricity from one to the other. 
 
 567. Unit of Potential. The difference of potential between 
 two points, a and 6, Fig. 315, at distances r and r' from a quantity 
 
 FIG. 315. 
 
 of electricity q, is measured by the work necessary to move a 
 positive unit of electricity from 6 to a. 
 
 This 
 
 work (average) force x distance through which it is overcome. 
 The distance = r' r. 
 
 Force at a .= -^- ( , , * 
 
 } average force = * ' - 
 Force at b -75- 
 
 r 
 Hence the difference of potential 
 
 Va ~~ Vh = rT ( T ' q \~r ~ 
 
 This equation for the difference of potential between two points 
 enables us to obtain an equation for the absolute potential V a at 
 
 * That this is a true average can be proved by a simple application of the 
 calculus. 
 
CAPACITY. 357 
 
 any point a. We have only to suppose that the second point b is 
 removed to an infinite distance, where its potential F 5 = 0, and 
 r' = oo . Hence 
 
 Or, in general, 
 
 The potential, F, of any point at a distance, r, from a quantity of 
 electricity, q, is expressed by the equation, 
 
 F=i. 
 
 r 
 
 From this equation, supposing q and r each equal to unity, we ob- 
 tain the definition : 
 
 The unit potential is that due to a unit quantity of electricity at a 
 distance of one centimetre. 
 
 The potential at a point owing to several charges of electricity 
 is equal to the sum of the potentials at that point due to each 
 charge taken separately. Thus, if quantities of electricity q, q', and 
 q" a -e at distances r, r'., and r" from a point, the potential at that point 
 
 568. Zero Potential. At an infinite distance away from any 
 electrified body the potential would evidently be zero. If a pos- 
 itive charge were brought near, the potential would become positive, 
 and negative for a negative charge. In practice it is convenient to 
 take the earth as a standard zero, with which all other potentials 
 may be compared. This assumption is analogous to the use of the 
 sea-level as the zero in measuring the heights of mountains instead 
 of the centre of the earth. 
 
 569. Potential on a Sphere. By discussing the equa- 
 tions in Art. 567, and supposing r equal to zero, one might be led 
 io think that the potential would be infinite. But it must be 
 remembered that, just as in gravitation, there is a centre from 
 which all electric force apparently works. In the case of the earth 
 all attraction is toward the centre of gravity. With an electrified 
 sphere all action comes from the centre of the sphere. The elec- 
 tricity (Art. 572) lies upon the surface of it, but the resultant of 
 all attractions from all the particles of electricity passes through 
 the centre. Thus a point in the electricity itself on a charged 
 conductor has a finite potential, and, in the case of a sphere, it is 
 equal to the quantity of electricity divided by the radius of the sphere. 
 
 570. Capacity. Suppose that a point on the surface of a 
 charged spherical conductor, i.e., any point in the electiicify itself, 
 
358 ELECTRICITY AND MAGNETISM. 
 
 to have a certain potential. If, now, the radius of the sphere be 
 supposed to grow smaller, while the quantity of electricity remains 
 the same, then the potential will evidently increase as the radius 
 
 decreases, because the potential V Thus a large sphere, e.g., 
 
 the earth, can hold a large quantity of electricity without having a 
 high potential. This ratio between quantity and potential of elec- 
 tricity in a conductor is termed the electrostatic capacity of the 
 conductor. ^Representing this by C, we have the definition in the 
 form of an equation : 
 
 _0 
 
 ~ V 
 
 From this, by supposing Q and V each equal to unity, we have the 
 definition, 
 
 That conductor has a unit of electrostatic capacity, which requires- 
 a unit quantity of electricity to raise its potential from zero to one. 
 
 Applying the above equation to a sphere of radius r we have 
 
 v-Q- Q , 
 
 - c -- 7' 
 
 whence we see that the electrostatic capacities of spheres are 
 equal to their radii. Accordingly a sphere of 1 centimetre radius 
 has a unit capacity. 
 
 A conductor, no matter what its shape, will have a capacity, 
 and we may say that, 
 
 The capacity of any conductor is equal to the number of units 
 of quantity of electricity necessary to raise its potential from zero to 
 unity. 
 
 571. Equipotential of Connected Conductors. When a 
 conductor is charged with electricity each particle strives to get 
 out of the reach of its neighbors, because of the natural repulsion 
 between like kinds of electricity. The particle, however, cannot 
 escape, because the dry air is an insulator. If, now, it be con- 
 nected, by means of a conducting wire, with the earth, the par- 
 ticle, followed by others, will flow off to the earth. Now the earth, 
 having such a very large radius, would require an enormous 
 quantity of electricity to raise its potential even an infinitesimal 
 amount. The result is that the potential of the conductor and 
 earth are both reduced to zero. Suppose, however, that instead 
 of being connected with the earth it had been connected to another 
 insulated conductor. The particles escaping from the first con- 
 ductor would gradually raise the potential of the second until a 
 particle, at some place on the connecting wire, would be equally 
 repelled by the charges on each conductor, and would accordingly 
 
DISTRIBUTION. 359* 
 
 remain at rest. Now it will be found that, just as when two 
 vessels, one of which contains water, when connected by a tube at 
 the bottom, will allow the flow of water until the level in both is 
 the same, so with these conductors, the potentials of both will have 
 become the same because of the connecting wire. Furthermore, 
 just as is the case with the connected vessels of water, it makes no 
 difference whether the second conductor had originally a charge of 
 electricity or not. The potential of all electrostatically charged 
 conductors becomes the same when connected together. 
 
 If the potential of connected conductors becomes the same, 
 then it is quite evident the total quantity of electricity must be so 
 divided that each conductor shall have a quantity in direct propor- 
 tion to its capacity. This must necessarily follow from the defi- 
 nition of capacity at the end of Art. 570. Thus three connected 
 conductors of capacities 1, 2, and 3 would have respectively one-, 
 two-, and three-sixths of the total quantity of electricity upon them. 
 
 572. Position of Static Charge. A statical charge of elec- 
 tricity always resides on the outside surface of a conductor. It 
 also resides on the outside of the geometrical figure of the con- 
 ductor. Thus, if a charge be communicated to a wire bird-cage, 
 it will reside wholly on the outside half of the wires and none will 
 lie on the inside. This may be shown in many ways. 
 
 If a hollow, insulated, conducting cylinder (Fig. 316) be pro- 
 vided with two suspended pith balls in the interior and two on the 
 exterior, and a charge of electricity be communi- _ 
 
 cated to it, the outside balls will diverge, owing 
 to the repulsion of like electricities. The inside 
 balls will, on the other hand, remain at rest. It 
 makes no difference whether the charge be com- 
 municated to the inside or outside. As soon as it 
 has been communicated the inside balls drop to 
 their normal position. 
 
 In calculating the capacities of conductors, it 
 makes no difference whether a conductor is solid 
 or hollow. 
 
 573. Distribution of a Charge on the 
 Surface. Statical electricity resides at the sur- 
 face of a body, as we have seen, but is not uni- 
 formly diffused over it, except in the case of the sphere. In gen- 
 eral, the more prominent the part, and the more rapid its curvature, 
 the more intensely is the electricity accumulated there. 
 
 In a long, slender rod the density is greatest at the ends, nearly 
 the whole charge being collected at these points. On a sphere, 
 
 % 
 
 FT- T-< _ 
 
360 ELECTRICITY AND MAGNETISM. 
 
 not influenced by other electrified bodies, the density is uniform, 
 as illustrated in Fig. 317, the dotted line denoting by its constant 
 distance from the surface the uniform distribution of the charge. 
 Fig. 318 represents the varying density upon an ellipsoid. 
 
 FIG. 317. FIG. 318, 
 
 The two ellipsoids are similar, and the ellipsoidal shell included 
 between them represents the densities at various points. In this 
 case the densities at any two points of the ellipsoid are nearly 
 proportional to the diameters through those points. 
 
 The student must remember that the charge does not form a 
 layer upon the body in any sense whatever, and that the above 
 figures are given merely to aid the memory in retaining the law 
 of distribution. 
 
 574. Surface Density. The greater the quantity of elec- 
 tricity on a given conductor, the greater the tendency is for the 
 electricity to escape to surrounding objects. . 
 
 The surface density at any point of a surface, when the dis- 
 tribution is uniform, is the quantity of electricity per square 
 centimetre of surface. 
 
 If Q units of electricity reside on S square centimetres of sur- 
 face, then the surface density d is represented by the formula 
 
 '-* 
 
 The surface of a fine point is very small, hence, if there is any 
 quantity of electricity supplied to it, the density becomes very 
 great and the charge escapes into the air. 
 
 575. Quadrant Electrometer. This instrument is used for 
 determining very accurately differences of electrical potential. A 
 simple form, suited for qualitative work, is shown in Fig. 319. 
 Four like pieces of metal are suspended, by conducting rods, from 
 the insulating top of a glass case. They are symmetrically placed 
 (as shown in the small figure) and are fixed in position. Over 
 these quadrants, as they are termed, swings a flat aluminum 
 needle, suspended by a wire of small diameter. This prolonged 
 suspension hangs in a glass chimney, placed upon the top of the 
 
QUADRANT ELECTROMETER. 
 
 361 
 
 case. A small mirror, Jf, is attached to a rigid prolongation 
 of the suspension, prolonged beneath the needle. This mirror 
 
 FIG. 319. 
 
 serves to reflect the image of a scale. S, through a reading tele- 
 scope, L, by means of which deflections of the needle can be 
 observed. 
 
 To use the instrument, the needle is charged, through its 
 suspending wire, to a constant potential. This may be done by 
 connecting G with the knob of a charged Leyden jar. The 
 diagonally opposite quadrants are connected together, and the 
 two pairs connected with the points whose difference of potential 
 is to be determined. Now suppose that 2 and 4 (small diagram) 
 were of higher potential than 1 and 3. They would exert a greater 
 force upon the needle than 1 and 3, and according to the sign of 
 the charge on the needle, would cause rotation of the needle in one 
 direction or another. The needle, which was held in the zero 
 position by the torsion of its suspension, would come to rest at a 
 place where the force of torsion was equal and opposed to the 
 electrical force. For small deflections the forces are proportional 
 to the tangents of the angle, i.e., to the readings of the scale. 
 
 For very accurate work many complicated attachments are 
 added to this simple form. 
 
 Problems. 
 
 1. Two conductors, of capacity 10 and 15 respectively, are con- 
 nected by a fine wire and a charge of 1000 units is divided between 
 them : find the charge which each takes, and the potential to 
 which each is raised. 
 
362 ELECTRICITY AND MAGNETISM. 
 
 2. Three spheres of radii 1, 2, and 3 cm. are charged to poten- 
 tials 3, 2, and 1 respectively, and are then connected by a fine 
 wire : what is their common potential ? 
 
 3. Two spheres, of capacity 2 and 3, are charged respectively to 
 potentials 5 and 10 : what will be their common potential, if they 
 are placed in electrical connection ? 
 
 4. Two spheres, of 2 and 6 cm. radius, are charged respectively 
 with 80 and 30 units of electricity ; compare their potentials. If 
 they are connected by a fine wire, how much electricity will pass 
 along it ? 
 
 5. Twelve units of electricity raises the potential of a conductor 
 from to 3 : what is its capacity ? 
 
 CHAPTEE II. 
 
 ELECTROSTATIC INDUCTION. 
 
 576. Gold-leaf Electroscope. The gold-leaf electroscope 
 is a delicate instrument for detecting the presence of electric- 
 ity. It consists (Fig. 320) of a folded strip 
 
 FIG. 320. O f gold-leaf, suspended from the end of 
 
 a brass rod, which penetrates the stopper 
 of a glass insulating receiver. The outside 
 end of the rod is provided with a brass 
 ball. Whenever a charge of electricity is 
 communicated to the ball the gold-leaves 
 partake of it and diverge from each other, 
 because of the repulsion of like kinds of 
 electricity. The sides of the receiver are 
 provided with strips of tin-foil, which are 
 in electrical communication with the earth 
 through the base. The object of these is to 
 prevent the rupturing of the gold-leaves by 
 the sudden communication of too great a 
 charge. Upon receiving such a charge the}' diverge aiid com- 
 municate it to the tin-foil and it escapes thence to the earth. 
 
 577. Phenomena of Induction. Whenever an electrified 
 t>ody is approached toward the brass ball of an electroscope, it 
 will be noticed that, while it is even a great distance away from 
 it, the gold-leaves begin to separate and show the presence of 
 electricity upon them. This electricity is the result of the presence 
 

 EXPLANATION OF ATTRACTION. 363 
 
 of an electrified body in the neighborhood and is called induced 
 electricity. The process under which it was generated is termed 
 electrostatic induction. 
 
 Whenever a charged conductor is brought near to an uncharged 
 conductor, and is separated from it only by an insulator, which in 
 this case is called a dielectric, the uncharged conductor undergoes 
 an electrical change. The side which is toward the first con- 
 ductor is charged with an opposite kind of electricity, while the 
 remote side has a charge of same kind as the original charge. 
 
 Thus (Fig. 320), if a negatively electrified piece of hard rubber 
 be brought near to the gold-leaf electroscope and is separated from 
 it by air for a dielectric, there will be positive electricity induced 
 on the nearer side of the electroscope, which is the ball, and neg- 
 ative on the remote, which includes the gold-leaves. The leaves 
 accordingly diverge. The electricity on A is called the inducing 
 charge, that in the electroscope the induced charge. 
 
 Whenever an insulated conductor, which contains the two kinds 
 of induced electricity and is still under the influence of the induc- 
 ing charge, is connected with the earth, the electricity of the same 
 kind as the inducing charge will escape to the earth. This is 
 because of the repulsion between like kinds of electricity. It is 
 equally true whether the near or remote side of the conductor is 
 connected to the earth. 
 
 The remaining opposite kind, however, cannot escape because 
 of the attraction exerted by the original inducing charge. If now 
 the earth connection be removed, it will be found that only a small 
 portion of the original inducing charge can escape when connected 
 to the earth. It is held in place by an opposite kind of electricity, 
 which it has itself produced. These two opposite electricities, 
 separated by a dielectric, are said to be bound, while electricity 
 free to follow an earth connection is called free electricity. 
 
 For illustration, suppose that the apparatus is in the condition 
 represented in Fig. 320. If the finger be touched at (7, the elec- 
 tricity n n will escape to the earth and the leaves will collapse. The 
 positive charge at C remains bound by ^4's charge. If now A be 
 removed, this charge will diffuse over the electroscope and the 
 leaves will diverge because of the portions which they receive. 
 
 As might be expected, successive inductions may be obtained 
 from one original charge. The induced charge in one case acts as 
 the inducing charge in a new induction. 
 
 578. Induction Precedes Attraction. Whenever a body 
 is attracted because of the charge of electricity on another body, it 
 is always subjected to induction before it is attracted. 
 
ELECTRICITY AND MAGNETISM. 
 
 Thus, if B (Fig. 321) is attracted by a positive charge on A, 
 the attraction is always preceded by an induction, whereby B is 
 charged negatively at c and positively at d ; 
 c is nearer than d, hence the attraction be- 
 tween a and c is greater than the repulsion 
 between a and d. Accordingly attraction 
 predominates. 
 
 579. Quantity of the Induced Elec- 
 tricity. The total quantity of electricity, of 
 the opposite kind to its own, which a charged 
 body induces on neighboring bodies is ex- 
 actly equal to its own charge. This was experimentally proved by 
 Faraday by means of an "ice-pail." A metallic pail, A (Fig. 322), 
 was mounted upon an insulating support. The outside of the pail 
 was connected with a delicate electroscope. Into 
 this pail was lowered a positively charged ball, FIG. 322. 
 
 B, which was suspended from an insulating silk 
 thread. Upon introducing the ball the leaves of 
 the electroscope commenced to diverge, because 
 the charge on B induced negative electricity on 
 the interior of the pail and held it bound. The 
 positive electricity of the pail, being free and re- 
 pelled, passed partly into the electroscope. As 
 the ball was lowered further the leaves diverged 
 more and more until, after a certain depth had 
 been reached, a further descent produced no 
 extra divergence. Even when the ball was 
 brought into contact with the bottom of the pail 
 the leaves remained undisturbed and extended. 
 Upon removing the ball, after contact, the charge 
 was found to have disappeared from it. The 
 fact that the gold-leaves were undisturbed by the contact of the 
 ball with the pail proves that there was the same quantity of 
 negative electricity on the inside of the pail as positive electricity 
 on the ball. Coming together the two neutralized each other and 
 left the positive outside charge undisturbed. 
 
 580. Condensers. If a pane of glass be taken, and a piece 
 of tin-foil be pasted upon the middle of each face of the pane, and 
 one piece be charged positively, the inner surface of the other 
 piece will receive a negative charge by induction. If the second 
 piece be connected with the earth positive electricity will escape. 
 The positive electricity of the first tin-foil will attract and hold the 
 negative of the second bound. If the connections to the source 
 
SPECIFIC INDUCTIVE CAPACITY. 365 
 
 the earth be now removed, it will be found that hardly any 
 electricity can be obtained by merely touching either of the foils. 
 It may be said that each charge is inducing the other. It will be 
 found that these two pieces of tin-foil may be, when thus arranged r 
 much more strongly charged than either of them could possibly 
 be, if it were placed alone upon a piece of glass and then elec- 
 trified. In other words, the capacity of a conductor is greatly 
 increased when it is placed near to a conductor electrified with 
 the opposite kind of charge. Considering then (Art. 570) that the 
 
 potential V = -^> it will be seen that such a piece of apparatus 
 
 L> 
 
 can receive a large quantity of electricity, Q, without raising its 
 potential, V, as much as if it were separated from all conducting 
 or electrified bodies. Such an arrangement is called a con- 
 denser. 
 
 Condensers are much used in practical electricity for measur- 
 ing quantities of electricity. A pane of glass, however, would not 
 have a sufficiently large capacity for technical purposes. Accord- 
 ingly commercial condensers are made by piling together alternate 
 sheets of tin-foil and paraffined paper. The alternate layers of 
 tin-foil are connected together. In this manner a large surface 
 of tin-foil can be used and yet not occupy an inordinate amount of 
 space. The capacity of a condenser varies inversely as the thick- 
 ness of the dielectric between the conducting sheets, and directly as 
 the product of the area of the sheets and a constant depending 
 upon the nature of the dielectric. This constant is called the 
 specific inductive capacity. 
 
 581. Specific Inductive Capacity, It has been stated (Art. 
 563) that a body charged with Q units of electricity will attract an 
 unlike unit of electricity on a body which is r centimetres away 
 with a force 
 
 F Q 
 ~~^' 
 
 This is strictly true only when the two bodies are in a vacuum. 
 It is very nearly true when they are separated from each other by 
 dry air or any other gas. That the expression for the force may 
 be universally true, whatever be the dielectric which intervenes 
 between the bodies, it must be modified into the form 
 
 F -^. 
 ~ Kr* 
 
 Here K is a constant, which is peculiar to each substance, and it 
 is called the specific inductive capacity or the dielectric constant of 
 the substance. 
 
366 ELECTRICITY AND MAGNETISM. 
 
 The following is a table of specific inductive capacities referred 
 to air at C. and 760 mm. pressure as unity : 
 
 Air and most gases 1.0 
 
 Bisulphide of Carbon 2.2 
 
 Ebonite and Rubber 2.3 
 
 Paraffin 2.3 
 
 Shellac 2.9 
 
 Sulphur 3.7 
 
 Glass ... 3. 2 to 6.0 
 
 Water 6.0 
 
 Metals oc 
 
 The name "inductive capacity" was introduced by Faraday in the 
 publication of a series of experiments upon condensers. He con- 
 structed a number of exactly similar condensers, differing from 
 each other only in the dielectric between the conducting surfaces. 
 The dielectrics which he used were air, sulphur, shellac, and glass. 
 He measured the capacities of these equally dimensioned con- 
 densers and found that all the others had greater capacities than 
 the one containing air. Remembering that induction is the prin- 
 ciple upon which the condenser works, it can readily be seen why 
 Faraday adopted the term. 
 
 Modern writers, however, in employing the term "dielectric 
 constant " indicate their appreciation of the important light thrown, 
 by the mere existence of different values of K, upon the true 
 nature of electricity. The fact that the nature of the substance 
 between two charges of electricity influences the magnitude of 
 their repulsions, disproves the idea that electrical attractions and 
 repulsions are action at a distance. There must be something be- 
 tween the bodies which plays a part. Again, the repulsion of two 
 charges of electricity, even when suspended in a vacuum, indicates 
 that this something must be the ether. The ether, then, in differ- 
 ent dielectrics, must in some manner be modified from what it is 
 in a vacuum. This is known to be the case from the different 
 optical properties of bodies. 
 
 A method for showing directly the effect of K in Coulomb's law 
 has been constructed by Mayer. Suspend horizontally a silvered 
 circular disc of mica, 16 cms. in diameter, by a long, slender, spiral 
 spring. Let the spring be in contact with the silvered surface. 
 Under this disc place another of metal, which is movable in a 
 vertical direction, and is connected to the earth. Charge the 
 silvered mica with electricity, using the spring as a means of 
 connection. If the distance between the two discs is but two or 
 three centimetres, the mica will be attracted so as to extend the 
 spring. If, now, a sheet of paraffin or plate of glass be interposed 
 between the two discs, the attractive force will be observed to 
 
LEYDEN JAR. 367 
 
 decrease. This is because K in the denominator of the fraction 
 expressing the force of attraction is greater for glass and paraffin 
 than for air. 
 
 It will be noticed, in the table given, that K for metals and 
 conductors is x. According to this, a charged body cannot 
 attract a pith-ball through a metal plate. The metal is therefore 
 called an electric screen. The screen must be sufficiently large to 
 prevent any attractive force from working around its edges, and it 
 should be connected with the earth to avoid any induced electricity 
 from exerting an influence. It is in consideration of these facts 
 that electrometers are surrounded by conducting cages, which are 
 connected with the earth. Any neighboring accidental charges of 
 -electricity cannot then influence the electrometer needle. 
 
 582. Ley den Jar. A most convenient form of condenser, 
 for demonstrative experiments, is the Leyden jar. It usually con- 
 sists (Fig. 323) of a glass jar coated up to a certain height on the 
 inside and outside with tin-foil. A brass knob fixed 
 
 on the end of a stout brass wire passes downward FlG - 
 through an insulating lid and is connected by a chain 
 with the interior coating of tin-foil. To charge the jar, 
 it is held, by the outer coating, in the hand, and the 
 brass knob is approached to any source of electricity. 
 If the source furnishes positive then the internal coat- 
 ing becomes charged positively, and this induces and 
 binds an equal amount of negative electricity on the 
 outer coating, while an equal amount of positive will be 
 rendered free and will escape through the hand to the 
 ground. The jar being now removed, is said to be 
 charged there exists a state of positive potential on the inside and 
 negative potential on the outside. Both electricities are bound, 
 and neither can produce effects independently. If, however, they 
 be allowed to come in connection with each other (by joining the 
 outside coating and the ball at the top with a wire) the electricities 
 rush to neutralize each other, and will even spark across an air 
 gap. The jar is then said to be discharged. The length of the 
 air gap through which the spark will pass depends upon the differ- 
 ence of potential between the inner and outer coatings. Some- 
 times the difference of potential becomes so great, owing to 
 carelessness in charging, that the electricities, in striving to get 
 together, will pierce and fracture the glass itself. 
 
 583. Seat of the Charge. If a jar is made with a wide, open 
 top, and the coatings movable, then, after charging the jar, the 
 coatings may be removed and tested without showing any trace of 
 
368 ELECTRICITY AND MAGNETISM. 
 
 electricity upon them. If they be then replaced, the jar will be 
 found to be charged as before removal. Benjamin Franklin in- 
 ferred from this that the electricity resides upon the dielectric and 
 the coatings serve only to readily diffuse the charge over the surface. 
 
 584. Residual Charge. If a jar be charged, left for a time, 
 discharged, and left for a while longer, it will be found that, upon 
 connecting the two coatings, a spark may be obtained. The elec- 
 tricity remaining in the jar after the first discharge is called the 
 residual charge. The amount of residual charge varies with the 
 time that the jar has been left charged. It also depends upon 
 the kind of dielectric used. No residual charge has been found 
 in connection with an air-condenser. 
 
 585. Modern Theory of Condensers. The modern ether 
 theory of electricity gives a very satisfactory explanation of con- 
 densers. According to this theory electricity is the ether itself. 
 When a conductor is statically charged, it is not the ether of the 
 conductor which constitutes the charge, but the ether of the dielec- 
 tric which surrounds the conductor. More exactly, charging a 
 conductor is straining the ether particles of the surrounding dielec- 
 tric out of a definite position, which they are presumed to have a 
 tendency to remain in. Thus, if a positive charge is communicated 
 to the inner coating of a Leyden jar, the ether particles of the glass 
 will all be strained away from the inside. All the particles will be 
 strained away from the inner coating and toward the outer coat- 
 ing. We may thus say that the inner is positively electrified and 
 the outer negatively. We have but one ether electrification, but 
 two ways of looking at it just as a dent in a tin plate may be con- 
 vex on one side and concave on the other. 
 
 In all dielectrics the ether particles are supposed to be held in 
 position by elastic ties of some sort. A mechanical analogy is to- 
 represent the particle (Fig. 324) by a bead fastened to the centre 
 of an elastic wire, clamped at both sides. When 
 FIG. 324. subjected to an electrifying influence, the bead is 
 
 pulled to one side. Upon releasing the bead, or 
 / % discharging the electricity, two things are to be 
 
 / \ noticed. First, the bead will not only go back to 
 
 "4" its original position, but will go beyond it and 
 / oscillate a number of times before coming to rest. 
 
 According to this, then, the spark, at discharging 
 a Leyden jar, should be oscillatory and made up 
 of a succession of small sparks. Such is the case, 
 as has been shown by reflection upon a screen from a rapidly 
 rotating mirror. Were the spark a continuous one, its reflected 
 
HERTZ'S EXPERIMENTS. 369 
 
 image would appear as a prolonged line. It appears, however, as 
 a, dotted line. Secondly, it must be considered that, if the strain 
 on the wire be maintained for any length of time, it will not, upon 
 release, immediately return to its normal position, but will assume 
 a new one, which is displaced in the direction of the strain from 
 the original position. This is a common phenomenon and is 
 known as elastic fatigue. The electrical parallel is the residual 
 charge. After the first discharge the ether particles have not 
 returned to their normal position. It requires one or more resid- 
 ual discharges before they return to that position. 
 
 Of course in a dielectric we cannot suppose that each of the 
 infinite number of particles of ether is supported upon anything 
 similar to an elastic wire, for the dielectric would act well in one 
 direction and not at all in the direction of the length of the wire. 
 'This is not in accordance with facts. Accordingly it is supposed 
 that the dielectric acts as a mass of jelly, in which its ether par- 
 ticles are suspended, or possibly the ether is a jelly-like mass in 
 itself, lacking, however, the physical property impenetrability. 
 The jelly then exerts a restraining force to strains exerted in any 
 direction upon the particles. 
 
 Conductors, on the other hand, are supposed to exercise little 
 or no restraint upon the free movement of the ether within them. 
 
 Viewed in this light, when a positive charge is communicated 
 to a conductor, an attempt is made to force more ether into tho 
 conductor than it ordinarily has. But the ether is absolutely 
 incompressible. Hence room is made for the extra amount, by 
 pressing the ether of the dielectric away from the conductor. The 
 xtra ether must have been taken from somewhere, and the place 
 which it formerly occupied must be filled. This is done by the 
 distention of the remote portions of the dielectric. It presses out 
 of some conductor an equal amount of ether. We can thus see the 
 truth of Faraday's statement that it is impossible to charge one 
 body alone. Whenever a body is charged positively, some other 
 body or bodies must receive an equaj negative charge. 
 
 When a Leyden jar is discharged, by connecting the two coat- 
 ings through a conductor, the ether in the positive coating flows 
 toward the negative and the strain on the dielectric is relieved. 
 This flow will, of course, be vibratory, owing to the inertia of the 
 dielectric jelly. 
 
 586. Hertz's Experiments. Professor Hertz has shown ex- 
 perimentally that the electrical ether is wonderfully like, if not iden- 
 tical with, the ether presupposed in light. By rapidly charging 
 and discharging a conductor he causes the ether upon it to surge 
 
370 ELECTRICITY AND MAGNETISM. 
 
 to and fro. This agitates the surrounding dielectric ether, and! 
 the disturbances travel in waves. The velocity of propagation 
 he determines to be the same as the velocity of light. He has 
 made these waves interfere, has reflected them from metal mirrors, 
 refracted them through lenses and prisms of pitch, and has pro- 
 duced diffraction effects. He has shown that many optical experi- 
 ments can be electrically performed by substituting dielectrics for 
 transparent and conductors for opaque bodies. 
 
 587. Electrical Machines. The method of rubbing sealing- 
 wax with fur is too slow for the production of large quantities of 
 electricity. Franklin improved upon this method, employing a 
 machine, which rotated a large glass cylinder, the cylinder being 
 rubbed by a silk rubber. But, at present, machines which gen- 
 erate electricity by friction are little used, recourse being made 
 instead to the principle of induction. Two machines of this sort, 
 most commonly found, are the electrophorus and the Holtz ma- 
 chine. 
 
 588. Electrophorus. The electrophorus consists of a cir- 
 cular cake of resin, sulphur, or vulcanized rubber in a metallic 
 base, A (Fig. 325), and a metallic disc, B, having an insulating 
 
 FIG 325 handle. Stroking with flannel or fur elec- 
 
 trifies the resin negatively. This induces 
 and binds positive electricity on the lower 
 face of the disc, when placed upon it. Free 
 negative is repelled to the upper face. If 
 the finger be touched to the disc, while it 
 yet remains upon the resin, the free neg- 
 ative will escape to the earth. Upon then 
 lifting the disc it will be found charged 
 with positive electricity. This operation may be repeated in- 
 definitely. 
 
 589. Holtz Machine. This machine, illustrated in Fig. 326, 
 consists of a revolving glass disc, A, and a stationary glass disc, B, 
 both well coated with shellac to further insulation. In front of A, 
 and close to it, as shown in the figure, are two combs connected 
 with the discharging knobs at G. On the back of the disc B, 
 opposite to the combs, are two paper sectors, a paper tongue 
 or point from each projecting, through an opening (window) in 
 the stationary disc, toward the revolving plate. If a plate of 
 vulcanite be excited, and then be laid against one of the paper 
 sectors, while the disc A is rapidly rotated toward the point of the- 
 sectors, the discharging knobs being in contact, electrical induction. 
 
HOLTZ MACHINE. 
 
 371 
 
 FIG. 326. 
 
 will ensue, and after a few moments the knobs may be gradually 
 separated until sparks perhaps 12 or 20 inches long pass, accord- 
 ing to the size of the ma- 
 chine. To produce sparks 
 of great density two Leyden 
 jars, D, D, with their inner 
 coatings connected to the 
 discharging knobs and their 
 outer coatings connected with 
 each other, are added. 
 
 To explain, in a very gen- 
 eral way, the action of the 
 machine, let A (Fig. 327) 
 represent the revolving plate 
 and B the stationary disc be- 
 hind it, carrying the paper 
 sectors a and 6. Imagine 
 the combs in front of A, and 
 call them a and b also, re- 
 membering that the sectors 
 are on the plate B, behind A. 
 If now a positive charge be 
 communicated to the sector 
 a, it will act inductively upon 
 the comb a, through the re- 
 volving plate, as a dielectric. Negative electricity will be induced 
 in the comb, and, if it were of proper shape, would be bound. 
 But, being pointed, the negative charge 
 escapes to the surface of A and is carried 
 around with it. The positive electricity 
 of the comb is repelled by the process of 
 induction to the discharging knob con- 
 nected with it. Both knobs being in 
 contact it passes to the comb b. From 
 here it escapes to the front of the revolv- 
 ing disc, and at the same time induces 
 negative electricity on the upper portion 
 of the sector b. Because of the induction 
 positive electricity escapes from the point 
 of the sector b to the back of the revolv- 
 ing disc. If now the disc be revolved half-way around, the pos- 
 itive charge on the back of A will be taken up by the point of 
 sector a, thus strengthening its original charge. Sector b, having 
 now become charged negatively increases the flow of positive from 
 
 
372 ELECTRICITY AND MAGNETISM. 
 
 comb 6, and sector a, having its charge increased, still further 
 increases this flow. All the arrangements conspire to charge both 
 the rear and front of the upper half of A with positive, and of the 
 lower half with negative, electricity. The action requires that 
 positive electricity shall flow continuously through the knobs 
 from a to b. When sufficient potential difference between the 
 combs has been obtained, the discharging knobs may be separated 
 and a spark will rupture the air. 
 
 The Ley den jars serve to increase the capacity of the knobs, and 
 thus, for a spark at a given potential difference, to increase the 
 quantity of electricity passed. 
 
 A modification of the Holtz machine has been made by Wims- 
 hurst. The two plates, furnished with numerous sectors of tin- 
 foil, are rotated in opposite directions. A full description is out 
 of place here. 
 
 590. Effects of Statical Discharge. Most electrical effects 
 are best obtained by the use of current electricity. Those which 
 require the high potential of statical electricity are the following : 
 
 MECHANICAL. If a heavily charged Leyden jar be made to dis- 
 charge itself through a piece of glass or card-board, it will, by the 
 passage, pierce a hole through the piece. In case card-board is 
 used, it will be found that there is a burr on both sides of the 
 card. This is because of the vibratory character of the discharge. 
 
 PHYSIOLOGICAL. If a discharge is made through a human being, 
 the muscles which lie along its path will be strongly contracted. 
 Those who have received very powerful shocks from electrical 
 discharges say that the feeling is as though all the muscles had 
 been so severely contracted as to result in spraining them. The 
 action of the electricity is through the medium of the nerves. 
 
 HEATING. A very sudden development of heat accompanies the 
 spark at discharge. This can be easily shown by allowing a spark 
 to pass to the tip of a gas-burner. If the gas be turned on, it will 
 become ignited. If gas be not available, the spark may be passed 
 to a spoon containing a few drops of common ether. 
 
 591. Lightning. Water, in the process of evaporation, is 
 supposed to become electrified. From the surface of large bodies 
 of water multitudes of small electrified particles of moisture rise 
 into the air, under the influence of the hot sun. These particles 
 have a definite capacity (their radius) and a definite quantity of 
 electricitj'. In the process of cloud formation these particles 
 come into drops. Each drop receives the electricity of its com- 
 ponent particles and has its capacity increased. The quantity on 
 the drop equals the sum of the quantities on the particles. The 
 
MAGNETS. 373 
 
 capacity of the drop is less than the sum of the capacities of the 
 particles. Hence the potential on the drop is greater than it was 
 upon the particles. In this manner clouds are formed, having 
 large quantities of electricity at a high potential. The opposite 
 kind of electricity is induced in the earth, and the air, acting as a 
 dielectric, is placed under severe strain. Eventually the strain 
 becomes too great and the air gives way. The equalization of 
 potential, at that instant, gives what is termed a stroke of light- 
 ning. The intense heat developed by the discharge expands the 
 air, and the rushing of cold air into the partial vacuum, thus 
 formed, produces the sound thunder. 
 
 Sheet lightning, where a large surface is momentarily illu- 
 minated, is but the reflection from a cloud of an invisible true 
 discharge. 
 
 CHAPTER III. 
 
 MAGNETISM. 
 
 592. Natural Magnets. The ancients discovered that a 
 certain black stone, abundantly found in Magnesia, had the prop- 
 erty of attracting to it small pieces of iron. Accordingly, from 
 their source, they called these stones magnets. Afterwards they 
 found that, when hung by threads, a certain part of each stone 
 always pointed north. From this property the stone received the 
 name Lodestone (leading stone). 
 
 593. Artificial Magnets. If a piece of steel be rubbed with 
 a lodestone, it will be found to have acquired the property of 
 attraction. Steel artificial magnets are what are employed in 
 -experiments in the laboratory. 
 
 594. Poles of a Magnet. If a steel-bar magnet be rolled in 
 ironfilings(Fig.328), 
 
 it will be observed 
 
 that the attractions 
 
 seem to have two 
 
 common sources, two 
 
 points near the ends 
 
 of the bar. These two points are called the poles of the magnet. 
 
 The straight line connecting the poles is called the magnetic axis. 
 
 595. Magnetic Needle. For investigating the attractions 
 
374 
 
 ELECTRICITY AND MAGNETISM. 
 
 FIG. 329. 
 
 FIG. 330. 
 
 of magnets use is made of the magnetic needle. This consists 
 (Fig. 329) of a light steel needle, which has been magnetized, and, by 
 
 some suitable arrangement, is mounted 
 upon a pivot. It is capable of moving 
 in a horizontal plane with little friction. 
 Left to itself it will assume a north and 
 south direction. That end of it which 
 points north is called the north pole, and 
 the other end the south pole. The com- 
 passes sold by opticians are magnetic needles, whose north poles 
 are generally more pointed than their south poles. 
 
 596. Attractions and Repulsions. If a piece of iron be 
 approached, in any manner, to either end of a magnetic nee- 
 dle, the needle will be attracted to- 
 ward the iron. The same result 
 
 will follow if either end of a magnet 
 be approached to an iron non-mag- 
 netic needle. However, if either end 
 of a magnet be approached to a mag- 
 netic needle (Fig. 330) attraction 
 will follow when the adjacent poles 
 are unlike, and repulsion takes place 
 when the adjacent poles are of the 
 same kind. Hence, as with quan- 
 tities of electricity : 
 
 Poles of the same name repel, and those of contrary name attract 
 each other. 
 
 597. North and South Poles Inseparable. If any one 
 portion of a piece of steel be touched by a north pole of a lode- 
 stone, it will be found to have developed a south pole. At the 
 same time, however, a north pole has been developed in some 
 other part of the steel. Again, if a bar magnet be broken at a 
 point half-way between its poles, each of the fragments will possess 
 two poles. Successive breaking leaves each fragment with its two 
 different poles. The end of a fragment which had a pole before 
 the rupture retains the same polarity afterwards. It may thus be 
 concluded that every magnet must have two poles. 
 
 598. Magnetic Induction. When a bar of iron is brought 
 near to the pole of a magnet, though attraction is the phenomenon 
 first observed, yet it is readily proved that this attraction results 
 from a change, which is previously produced in the iron. Similar 
 to the case of electrostatic attraction, the iron becomes a magnet 
 
COERCIVE FORCE. 375 
 
 by induction exerted by the original magnet. By moving a mag- 
 netic needle around the iron it will be found that the end of the 
 iron which is placed near one pole of the magnet becomes a pole 
 of the opposite name, and the remote end a pole of the same name. 
 Hence the adjacent, unlike poles of the iron and magnet, attract 
 each other. 
 
 The induced magnet is more powerful the nearer it is to the 
 inducing magnet ; it is, therefore, greatest when the two bars are 
 in contact. 
 
 Soft iron retains its magnetic properties only while under the 
 influence of the magnet. Upon removing, it will be found to have 
 returned to its neutral state. Had steel, or impure iron, or cast- 
 iron been used, it would have been found to have retained more or 
 less of the magnetic properties caused by the induction. 
 
 The inductive action may be well seen by placing iron and 
 magnet upon a sheet of paper and then sifting iron-filings upon 
 them. The filings will attach themselves to the iron in the same 
 manner as to the magnet. If the magnet be now withdrawn, the 
 filings around the iron will collapse, showing the. loss of magnetic 
 polarity. 
 
 The induced temporary magnet will, in its turn, induce tem- 
 porary magnetism in a second piece of iron, and this again in a 
 third piece. The strength, however, decreases as the pieces get 
 further away from the original magnet. 
 
 If the north ends of two equal magnets be touched to the 
 opposite ends of a bar of steel, south poles will be induced in both 
 ends of the bar. But we have seen that every south pole must 
 have a north pole with it. Accordingly examination will reveal 
 that the bar has two coincident north poles at its middle. Such 
 intermediate poles are termed consequent poles. 
 
 599. Retentivity or Coercive Force. The extension of 
 the experiment of breaking a magnet (Art. 597) leads to the 
 inference that every particle of steel is a magnet in itself. Before 
 magnetization these molecular magnets point in all directions, and 
 hence exert no external magnetic influence. Under the influence 
 of induction, however, these are made to assume the same direc- 
 tion. Fig. 331 gives an idea of the probable arrangement of a 
 magnetized piece of steel. 
 
 The shaded ends represent FlG - 331. 
 
 the south poles of the mole- 
 cular magnets. When they 
 are all arranged as in the 
 
 figure the external effect is as though there were a south pole at S> 
 and a north pole at N. 
 
376 ELECTRICITY AND MAGNETISM. 
 
 Now experiments show that tempered steel is much more diffi- 
 cult to magnetize than a piece of soft iron, and, after being once 
 magnetized, retains its magnetism much better. It is, then, rea- 
 sonable to suppose that the existence of foreign particles (carbon) 
 in the steel hinders and clogs the turning of the molecular mag- 
 nets from their chaotic state into regular arrangement. Once 
 arranged, the same cause prevents a disarrangement. In pure 
 iron the hindrance is not present. This resistance against a 
 magnetizing or demagnetizing force is called retentivity or coercive 
 force. As might be expected, the retentivity is modified by any- 
 thing which will cause the molecules to vibrate, as hitting sharp 
 blows with a hammer or heating to a high temperature. A magnet 
 may be demagnetized by dropping it several times upon the floor. 
 
 The extreme amount of magnetism that could be imparted to a 
 bar would be that which arranged all the molecular magnets in 
 the same direction. The magnet is then said to be saturated. 
 After removing the magnetizing force, however, some of the mole- 
 cular magnets would of their own accord turn from line and others 
 would follow their example in time. Hence a magnet must be 
 kept for some time before its strength can be considered as 
 constant. Yet a constant strength may be obtained by " cooking " 
 the magnet. It is saturated and then placed for several hours in a 
 bath of steam, removed and again saturated and cooked. Magnets 
 treated in this manner are said to remain very constant. 
 
 600. Law of Magnetic Force. Magnetic attractions and 
 repulsions take place according to a law similar to Coulomb's 
 law for electrical forces. Two like isolated magnetic poles of 
 strengths m and ra', d centimetres from each other, will repel each 
 other with a force in dynes, 
 
 d* 
 
 If the poles were different, as m and m r , then the value of F 
 would be negative. A negative value indicates attraction, and a 
 positive, repulsion. 
 
 The magnetic force will act through all substances except 
 through magnetic substances, i.e., those which are attracted by 
 a magnet. No attraction can take place through a large iron 
 sheet. Such a piece of iron is called a magnetic screen. A small 
 magnet suspended in a hollow iron sphere cannot be deflected by 
 an outside magnet. 
 
 601. Unit Magnet Pole. If, in the formula for the force, 
 given in the previous article, F and d be supposed each equal to 
 unity, then, as in electrostatics (Art. 563), 
 
LAMINATED MAGNETS. 
 
 37T 
 
 The unit magnetic pole is one that mil repel an equal like pole f 
 when at a unit's distance, with a unit force. 
 
 Of course an isolated pole cannot be obtained, for, in a magnet, it 
 is always accompanied by an opposite equal pole, and the algebraic 
 sum of the strengths of the poles of a magnet always equals zero. 
 
 The poles of a bar magnet are the points from which all the- 
 forces may be considered to emanate. If the strength of one of 
 these poles be multiplied by the distance between the two poles, a 
 quantity results which is termed the magnetic moment of the bar. 
 In ordinary bar magnets the pole distance is about f of the total 
 length of the bar. 
 
 The magnetic moment of a bar divided by its weight in grams 
 gives the specific magnetism of the substance of which the bar is com- 
 posed. This is greatest in very hard-tempered steel. 
 The magnetic moment divided by the volume of a 
 magnet, i.e., the magnet strength per unit volume, 
 is termed the intensity of magnetization and is gen- 
 erally represented by the letter I. 
 
 602. Lifting Power. The strength of a mag- 
 net must not be confounded with its lifting power. 
 The latter depends upon the shape of the magnet 
 and also upon the shape of the body lifted. A mag- 
 net bent into the shape of a horseshoe (Fig. 332) 
 will lift about four times what it would with one 
 end, if straight. The lifting power of a magnet 
 grows very curiously, if the load be gradually in- 
 creased from time to time. 
 
 603. Laminated Magnets. Long, thin steel 
 magnets are more powerful in proportion to their 
 weight than thicker ones. Hence compound mag- 
 nets are constructed, consisting of thin laminae of 
 
 steel separately magnetized and afterwards bound together in 
 bundles. These laminated magnets (Fig. 333) are more powerful 
 
 than simple bars of steel. 
 The explanation of this 
 fact seems to be that 
 ordinary steel magnets 
 are never saturated, and 
 
 what magnetism they have results from molecular arrangements 
 near the surface. The compound magnets have a greater surface 
 and are hence stronger. Since the mutual action of the like poles 
 in juxtaposition tends to weaken them, the strength of a compound 
 magnet will never equal the sum of the strengths of its parts. 
 
 FIG. 333. 
 
378 
 
 ELECTRICITY AND MAGNETISM. 
 
 That the magnetism of ordinary bars is confined to the surface 
 has been shown by placing the magnet in acid and dissolving 
 its surface. After removal, the bar showed very little magnetic 
 polarity. 
 
 604. Magnetic Field. Lines of Force. The space around 
 a magnet where its action is felt is termed the field of the magnet. 
 When several magnets are near to each other each one furnishes 
 its own field, and superposed upon each other they form a result- 
 ant field. 
 
 The field is supposed to be permeated by magnetic lines of 
 force. These lines represent the direction along which the mag- 
 netic attractions and 
 
 FIG. 334. repulsions act. An 
 
 isolated magnetic 
 pole would move 
 along one of these 
 lines under the at- 
 traction exerted by 
 the field magnet. The general direction of the lines of force of a 
 bar magnet are represented in Fig. 334. 
 
 The properties of these lines can be best discussed by con- 
 sidering only those which lie in a given plane passing through the 
 magnet. Such a section is called a magnetic spectrum. The spec- 
 trum may be graphically represented by placing a sheet of white 
 paper over a magnet and then sifting fine iron-filings upon the 
 paper. A slight tapping on the paper will cause the filings to 
 arrange themselves along the lines of force, as represented in 
 
 FIG. 335. 
 
 Fig. 335. With a sufficiently large figure it would be seen that 
 every line starting from one pole finds its way, by a curved path, 
 to the other pole. 
 
MAGNETIC FIELD. 379 
 
 An isolated north magnetic pole, placed upon one of these 
 lines, would travel along it away from the north pole of the field 
 magnet and toward the south pole. An isolated south pole would 
 move in an opposite direction. For many reasons it is desirable 
 to direct the lines. Hence, as represented in Fig. 334, the direc- 
 tion which an isolated north pole would move is taken as the 
 positive direction. 
 
 Of course it is impossible to get an isolated pole, but the unde- 
 sired companion can be so far removed as not to interfere with 
 demonstrative experiments. If a shallow glass dish, containing a 
 little water, be placed over the magnet and spectrum shown in Fig. 
 335, and then a magnetized sewing-needle be floated in a vertical 
 position, by means of a small cork, the lower pole of the needle 
 will be so much nearer the magnet than the upper pole that it will 
 act as an isolated pole. When placed over any line it will move 
 along that line, however circuitous, until it reaches the pole of the 
 field magnet, which attracts it. This experiment is much more 
 satisfactory when the field magnet is an electro-magnet. The 
 needle may then be placed at any desired point and commences 
 to move only after the magnet is excited. Professor Spice sifts, the 
 filings upon a glass plate and projects the whole experiment from 
 a vertical lantern. 
 
 If a short magnetic needle be moved around a field whose lines 
 of force are graphically shown by iron-filings, the needle will turn 
 until its magnetic axis coincides with the direction of the lines of 
 force. In fact the filings themselves are little magnets, made so 
 by induction, and tapping the paper upon which they rest serves 
 the stead of a pivot. That the needle should so place itself is 
 quite natural, for its north end tends to travel in one direction 
 and its south end in an opposite direction. The result is a couple, 
 which turns the needle until the pulls are from the same line of 
 force, passing through the pivot. 
 
 605. Theory of the Curvature of the Lines. In any 
 
 plane passing through a magnet, N, S (Fig. 336), let P be an 
 isolated unit north pole. Assume its distance from the north 
 pole PN, to be twice as great as from the south pole PS. The 
 unit will be repelled by the north pole with a certain force, which 
 is represented in amount and direction by the line, PB. Then, 
 according to the law of magnetic force (Art. 600), the attraction 
 exerted by the south pole, which is only half as far away, will be 
 four times as great, and is represented in magnitude and direc- 
 tion by the line A P. The resultant of these two forces must 
 be the diagonal, EP, of the completed parallelogram, and the 
 
3SO 
 
 ELECTRICITY AND MAGNETISM. 
 
 unit pole would move along the line EP. If elementary paral- 
 lelograms be constructed in this manner throughout the field, 
 
 FIG. 336. 
 
 their diagonals, when connected, will represent the lines of 
 force. 
 
 The curvature, then, is the result of combined attraction and 
 repulsion. The lines of magnetic force from an isolated pole 
 would be straight, as are the lines along which gravitation acts, 
 and the law given in Art. 600 is true for isolated poles only. 
 
 606. Fields from Several Magnets. When several mag- 
 nets are in the same vicinity, the resultant field, compounded 
 from the separate fields of each magnet, is sometimes curiously 
 
 arranged. Thus the field 
 
 IG> 337 * from two magnets, whose 
 
 north and south poles are 
 opposed to each other, is 
 represented in Fig. 337. 
 A short magnetic needle 
 would be in stable equi- 
 librium if placed in any 
 part of this field. Fig. 338 shows quite a different field where 
 the opposed poles are like named. A needle moved about this 
 field would suddenly turn 
 half round on its axis at 
 the moment of crossing the 
 line cd. When the pivot 
 is exactly upon cd, the 
 needle's south pole is at- 
 tracted equally in opposite 
 directions by the two ex- 
 posed north poles. In the same manner its north pole is repelled.. 
 
 FIG. 338. 
 
STRENGTH OF THE FIELD. 381 
 
 The result is that the needle places itself so that its axis is per- 
 pendicular to the axis of the field magnets. 
 
 Much may be learned by experimenting with iron filings on 
 variously compounded fields. 
 
 607. Strength or Intensity of Magnetic Field. It may 
 
 be reasonably supposed that each line of force exerts, along its 
 length, a given amount of force. Hence a piece of iron, which 
 was traversed by several lines, would be more powerfully attracted 
 than if traversed by a fewer number. Thus a magnet pole of 
 definite size, placed near to the pole of the field magnet, would be 
 attracted with more force than at a distance, for the lines are 
 closer together near the poles of the field magnet. The number 
 of lines of force, then, which penetrate a given area, determines 
 the relative force exerted by the field at that place. This is termed 
 the strength or intensity of the field. 
 
 In order to compare the strengths of different fields, it is neces- 
 sary to have a unit of strength. Hence 
 
 A magnetic field of unit strength is one which exerts a unit force 
 (dyne) upon a free unit magnet pole. 
 
 608, Determination of the Strength of a Field. If a 
 
 magnet, suspended by a fibre, be placed in magnetic fields of 
 different strengths, it will oscillate for a long time, and the times 
 of oscillation will be shorter the stronger the field. This is paral- 
 lel to the case of pendulum vibrations. The pendulum vibrates 
 because of the force exerted by gravity and because of its inertia. 
 Gravity pulls its centre of gravity as near as possible to the earth, 
 and inertia carries it beyond this position. If the force of gravity 
 were increased, the pendulum would vibrate quicker. In the case 
 of a magnet, the force of the field takes the place of gravity. 
 Now, just as the force of gravity can be measured by the time of 
 oscillation of a given pendulum (Art. 163), so the strength of a 
 magnetic field can be measured by the time of oscillation of 
 a given magnet. 
 
 If t = the time taken by the magnet in passing from one 
 turning-point to the other in an oscillation, K = the moment of 
 inertia of the magnet (Art. 160), M = the magnetic moment of the 
 magnet, then the strength of the field 
 
 &=**. 
 
 f M 
 
 When the same magnet is used K and M are constant, hence 
 
 , 
 where n = the number of single vibrations in a second. Then if 
 
382 ELECTRICITY AND MAGNETISM. 
 
 a given magnet vibrates n and ri times per second in two fields of 
 strengths H and H', 
 
 If the values of M and K are known or determined, then the first 
 equation gives the absolute strength of the field, provided all the 
 quantities are expressed in proper units. 
 
 609. Hysteresis. If a piece of iron be placed in a magnetic 
 field, it will have two opposite poles induced in it w r hose strengths 
 depend upon the strength of the field. If the strength of the 
 field be vajied from zero to a maximum, and then to zero again, 
 there will be two times when 'the field will have a definite strength 
 once when the field is growing stronger and again when it is 
 decreasing in strength. The strengths of the induced poles in the 
 iron are different in these two equal fields. They will be less in 
 the increasing field than in the decreasing. The strength of the 
 iron's poles depends upon the iron's previous history. The iron 
 has a tendency to remain in its previous condition and behind the 
 field's requirements. This peculiarity of the iron is termed by 
 Ewing static hysteresis. 
 
 If iron be placed in a magnetic field of constant strength, it 
 will require a certain time before its induced poles assume con- 
 stant strengths. To this property "of the iron Ewing gives the 
 name viscous hysteresis. 
 
 610. Number of Lines of Force from a Given Pole. It 
 is convenient to consider the number of lines of force passing 
 through a given area in a field as the measure of the strength of 
 the field. Each line may be supposed to exert a dyne of force on 
 a unit pole pierced by it. The given area is a square centimetre 
 and is placed so as to l?e perpendicular to the lines of force. A 
 unit field would then have one line passing through a square centi- 
 metre. 
 
 Suppose now that, around a unit magnet pole, we conceive a 
 spherical shell of one centimetre radius. From the definition of a 
 unit pole (Art. 601) we know that the enclosed pole exerts, on 
 another unit pole, a dyne of force at every point on this shell. 
 The strength of the field, then, at all these points, is unity. Hence 
 every centimetre of it is pierced by one line of force. But the 
 whole .surface of the sphere of unit radius contains 4 TT centi- 
 metres. The unit pole, therefore, sends off 4 TT lines of force. An 
 enclosing surface of any size would be pierced by the same number 
 of lines. 
 
MAGNETIC SUSCEPTIBILITY. 
 
 3S3 
 
 If the strength of the pole were 2 units, it would send off 8 TT 
 lines ; or, in general, 
 
 A magnet pole, of strength m, sends out 4 TT m lines of force. 
 This conception of the magnetic lines has recently developed into 
 many important theoretical conclusions, which have equally im- 
 portant practical applications. 
 
 With a real magnet, having two poles, it is important to re- 
 member that the lines of induction,* starting out from one pole, 
 finally arrive at the other pole and thence pass through the magnet 
 itself. Hence the number passing through a section of the mag- 
 net lying midway between the poles is 4 TT m. 
 
 611. Magnetic Susceptibility. If two magnets, with their 
 opposite poles opposed to each other, be arranged along a common 
 axis, and if the lines of induction be made visible by iron-filings, the 
 resulting spectrum will be as in Fig. 339. If, now, a piece of iron 
 
 FIG. 339. 
 
 FIG. 340. 
 
 is placed between the poles, the field alters and will give, e.g., the 
 spectrum shown in Fig. 340. The lines are much more numerous 
 where the iron is than they were before it was placed there. Had 
 a piece of brass been used instead of iron, the field would have 
 remained unclistorted. A piece of cobalt would have produced 
 some distortion, but not as much as the iron. 
 
 The cause of the additional lines is that the iron has, under the 
 influence of the field, become an induced magnet and has added 
 its lines to those already in the field. 
 
 If the field magnets were made stronger, they would send out 
 more lines, and the iron would become more strongly magnetized 
 and would also send out more lines. Thus, supposing that the 
 iron does not become saturated, the strength of its pole depends 
 upon the strength of the field and upon the volume of the iron. 
 Suppose that the strength of the induced pole of a rectangular 
 prism of iron is m; that the pole length equals the physical 
 
 * A line of induction differs from a line of force in that it does not change 
 :its direction on its return through the body of the magnet. 
 
384 ELECTRICITY AND MAGNETISM. 
 
 length of the iron, I; that the cross-section of the iron is s. Ther* 
 the intensity of magnetization (Art. 601) 
 
 . _ m I m 
 s I ~ ' s 
 
 If the cross-section s be one centimetre, then I = m, or the inten- 
 sity of magnetization is equal to the strength of the induced pole. 
 It has been found that if the strength of the field equals H, 
 
 I =&H, 
 
 where k is a constant called the magnetic susceptibility. It depends 
 upon the kind of iron or other substance placed in the field. For 
 iron, nickel, and cobalt the value is positive ; for vacuum, air, and 
 most gases is practically zero, and for bismuth, antimony, and 
 phosphorus it is negative, though extremely small. 
 
 612. Magnetic Permeability. In almost all of the practical 
 problems on magnetic induction it is desirable to know the total 
 number of lines which pass through the iron suffering induction. 
 In the iron prism of the preceding article the total number 
 traversing it is made up of two parts : 4 TT I = 4 IT k H lines from 
 the induced pole and H lines from the original field. Represent- 
 ing this sum by B, we have 
 
 B = H + 47T&H 
 
 = (1 + 4 7T k) H. 
 
 It is customary to place 1 + 4 TT k = /*, whence 
 
 B = ^H. 
 
 Since /* involves k, it depends upon the character of the substance 
 under induction. For air and gases it is unity; for iron, etc.,, 
 greater than unity (sometimes reaching 16,000), and for bismuth,, 
 etc., less than unity. 
 
 As B represents the number of lines that pass through a square 
 centimetre of iron, and H the number through air, then the iron 
 may be said to conduct magnetic lines //, times better than air. 
 From consideration in this light //. has received the name magnetic 
 permeability. 
 
 The magnetic permeability of a substance is its relative con- 
 ductivity for magnetic lines of force as compared with vacuum (or 
 air) as a standard. 
 
 The equations connecting B, H, I, /*, and k, which have beem 
 given are true whatever be the cross-section of the iron under 
 induction. The assumption of a square centimetre cross-section 
 is for simplification only. 
 
 613. The Magnetic Circuit. In the construction of most 
 electro-magnetic apparatus it is of utmost importance that as much 
 as possible of the field of the magnetizing agent shall be occupied by a 
 
DIAMAGNETISM. 385 
 
 substance of great permeability such as iron. For instead of having 
 merely the lines which can be sent through air by the agent we 
 can just as well have the additional ones from the iron. Of course 
 an air gap must be left somewhere in the circuit of the lines in 
 order to introduce the body to be acted upon. But this gap 
 should be as small as possible if a maximum effect be desired. 
 
 If the opposite poles of two straight electro-magnets be caused 
 to attract a piece of iron, the iron fills in one gap, but the lines 
 from the other ends pass through the air. The force of the 
 original attraction would be much increased if the extreme ends 
 were connected by an iron bar. This last bar sends its additional 
 lines through the magnets and increases the force. 
 
 614. Paramagnetism and Diamagnetism. Substances 
 'which have a permeability greater than 1 (that of vacuum) as iron, 
 steel, nickel, cobalt, etc., are attracted by a magnet and tend to 
 move toward it. If not allowed to move toward, but allowed to 
 rotate, they will tend to set themselves axially with the lines of 
 induction. These are called paramagnetic substances. 
 
 Substances of permeability less than unity show the opposite 
 tendencies. They are repelled by magnets and set themselves 
 perpendicular to the lines of force. They are bismuth, antimony, 
 phosphorus, etc. Without making use of the term permeability 
 we may say : 
 
 Those substances which are attracted by a magnetic pole, or which 
 in a magnetic field tend to move from places of less to places of 
 -greater intensity, are called Paramagnetic. 
 
 Those substances which are repelled by either pole indifferently, 
 or which move from ^places of greater intensity to places of less 
 intensity in the field, are called Diamagnetic. 
 
 In order to explain the phenomena of paramagnetism and dia- 
 magnetism we have to consider that the movable parts of a mag- 
 netic circuit strive to adjust themselves so that the maximum lines 
 of induction shall pass through the circuit. Paramagnetic sub- 
 stances are thus drawn into the circuit and place themselves 
 longitudinally with the lines, while diamagnetic substances act 
 in an opposite manner, the air furnishing more lines than if they 
 should displace it. 
 
 The repulsion of diamagnetic substances is hard to illustrate 
 before a large audience. A huge electro-magnet may be made to 
 slightly repel a piece of bismuth suspended on a long, delicate 
 fibre. Better results can be obtained by approaching a large 
 piece of bismuth to one of the needles in an astatic magnetom- 
 eter (Art. G25). 
 
386 
 
 CHAPTER IY. 
 
 TERRESTRIAL MAGNETISM. 
 
 615. The Earth a Magnet. If a needle is carried round! 
 the earth from north to south, it takes approximately all the 
 positions in relation to the earth's axis which it assumes in rela- 
 tion to a magnetic bar, when carried round it from end to end. 
 At the equator it is nearly parallel to the axis, and it inclines 
 at larger and larger angles as the distance from the equator 
 increases ; and in the region of the poles it is nearly in the direc- 
 tion of the axis. The earth itself, therefore, may be considered a 
 magnet, since it affects a needle as a magnet does, and also induces 
 the magnetic state on iron. But it is necessary, on account of the 
 attraction of opposite poles, to consider the northern part of 
 the earth as being like the south pole of a needle, and the south- 
 ern part like the north pole. 
 
 616. Declination of the Needle. When the needle is 
 balanced horizontally, and free to revolve, ;t does not generally 
 point exactly north and south ; and the angle by which it deviates 
 from the meridian is called the declination. A vertical circle coin- 
 cident with the direction of the needle at any place is called the 
 magnetic meridian. As the angle between the magnetic and 
 the geographical meridians is generally different for different 
 places, and also varies at different times in the same place, the 
 word variation expresses these changes in declination, though it 
 is much used as synonymous with decimation itself. 
 
 The force which causes the needle to set in the magnetic 
 meridian is merely directive. 
 
 If the needle be weighed before it is magnetized and again 
 after it has been made a magnet, no change of weight can be 
 detected, proving that the earth's attraction for one pole is exactly 
 equal to its repulsion of the other. This may also be shown by 
 attaching a magnet to a cork and thus floating it upon water. It 
 will set in the magnetic meridian but will show no tendency to 
 move across the water toward the north, nor in any other direc- 
 tion. This effect is due to the earth's uniform magnetic field. 
 The magnetic pole of the earth being practically at an infinite 
 distance, the forces of attraction and repulsion, being equal, con- 
 stitute a couple. 
 
 617. Isogonic Curves. This name is given to a system of 
 lines imagined to be drawn through all the points of equal decli- 
 
ISOGONIC CURVES. 
 
 387 
 
 nation on the earth's surface. We naturally take as the standard 
 line of the system that which connects the points of no declina- 
 tion, or the isogonic of (Fig. 341). Commencing at the north 
 
 FIG. 341. 
 
 pole of dip, about Lat. 70, Lon. 96, it runs in a general direc- 
 tion E. of S., through Hudson's Bay, across Lake Erie, and the 
 State of Pennsylvania, and enters the Atlantic Ocean on the coast 
 of North Carolina. Thence it passes east of the West India 
 Islands, and across the N. E. part of South America, pursuing its 
 course to the south polar regions. It reappears in the eastern 
 hemisphere, crosses Western Australia, and bears rapidly westward 
 across the Indian Ocean, and then pursues a northerly course 
 across the Caspian Sea to the Arctic Ocean. There is also a 
 detached line of no declination, lying in eastern Asia and the 
 Pacific Ocean, returning into itself, and inclosing an oval area of 
 40 N. and S. by 30 E. and W. Between the two main lines of 
 no declination in the Atlantic hemisphere, the declination is west- 
 ward, marked by continued lines in Fig. 341 ; in the Pacific 
 hemisphere, outside of the oval line just described, it is eastward, 
 marked by dotted lines. Hence, on the American continent, in 
 all places east of the isogonic of 0, the north pole of the needle 
 declines westward, and in all places west of it, the north pole 
 declines eastward; on the other continent this is reversed, as 
 shown by the figure. 
 
 Among other irregularities in the isogonic system, there are 
 two instances in which a curve makes a wide sweep, and then 
 intersects its own path, while those within the loop thus formed 
 return into themselves. One of these is the isogonic of 8 40' E., 
 which intersects in the Pacific Ocean west of Central America; 
 the other is that of 22 13' W., intersecting in Africa. 
 
388 ELECTRICITY AND MAGNETISM. 
 
 In the northeastern part of the United States the declination 
 has long been a few degrees to the west, with very slow and 
 somewhat irregular variations. 
 
 618. Secular and Annual Variation. The decimation 
 of the needle at a given place is not constant, but is subject to a 
 slow change, which carries it to a certain limit on one side of the 
 meridian, when it becomes stationary for a time, and then returns, 
 and proceeds to a certain liinit on the other side of it, occupying 
 two or three centuries in each vibration. At London, in 1580, the 
 declination was 11 E. ; in 1657, it was ; after which time the 
 needle continued its western movement till 1818, when the decli- 
 nation was 24^- W. ; since then the needle has been moving 
 slowly eastward, and in 1879, at Kew, the declination was 19 
 7' west. 
 
 The entire secular vibration will probably last more than three 
 centuries. The average variation from 1580 to 1818 was 9' 10" 
 annually. But, like other vibrations, the motion is slowest to- 
 ward the extremes. . 
 
 There has also been detected a small annual variation, in which 
 the needle turns its north pole a few minutes to the east of its 
 mean position between April and July, and to the west the rest 
 of the year. This annual oscillation does not exceed 15 or 18 
 minutes. 
 
 619. Diurnal Variation. The needle is also subject to a 
 small daily oscillation. In the morning the north end of the 
 needle has a variation to the east of its mean position greater than 
 at any other part of the day. During winter this extreme point 
 is attained at about 8 o'clock, but as early as 7 o'clock in the sum- 
 mer. After reaching this limit it gradually moves to the west, 
 and attains its extreme position about 3 o'clock in winter, and 
 1 o'clock in summer. From this time the needle again returns 
 eastward, reaching its first position about 10 P.M., and is almost 
 stationary during the night. The whole amount of the diurnal 
 variation rarely exceeds 12 minutes, and is commonly much less 
 than that. These diurnal changes of declination are connected 
 with changes of temperature, being much greater in summer than 
 in winter. Thus, in England the mean diurnal variation from 
 May to October is 10 or 12 minutes, and from November to 
 April only 5 or 6 minutes. 
 
 620. Magnetometer. In determining and observing the 
 variation of the declination use is made of a magnetometer. 
 
OF THE lr 
 
 MGfNIVE 
 
 MAGNETOMETERS. 
 
 3S9 
 
 FIG. 342. 
 
 Fig. 342 represents such an instrument. It consists of a mag- 
 netized ring surmounted by a circular mirror, both being sus- 
 pended by a silk fibre. The poles of the 
 ring are at the sides and the plane of 
 the ring, when at rest, coincides with the 
 plane of the magnetic meridian. Any vari- 
 ation of the meridian is followed by a move- 
 ment of the ring. The mirror, being con- 
 nected with the ring, moves also. This 
 small movement may be magnified and 
 observed by means of a telescope and scale. 
 The image of the scale is reflected from 
 the mirror into the telescope. 
 
 Surrounding the ring magnet is a 
 hollowed-out piece of pure copper. This 
 brings the magnet quickly to rest by means 
 of the electrical currents induced in it 
 (Art. 671) by the moving magnet. 
 
 Magnetometers are also used in deter- 
 mining the magnetic moment of bar magnets. 
 
 621. Dip of the Needle. A needle 
 
 first balanced on a horizontal axis, and then magnetized and 
 placed in the magnetic meridian, assumes a fixed relation to the 
 
 horizon, one pole or the 
 other being usually de- 
 pressed below it. 
 
 The axis of the needle 
 must be placed very ac- 
 curately at right angles to 
 the plane of the magnetic 
 meridian, or false indications 
 will be given ; if the axis of 
 suspension were placed in 
 the plane of the meridian 
 the angle of depression 
 would be 90 at all places 
 on the earth's surface. 
 
 The angle of depression is 
 called the dip of the needle. 
 Fig. 343 represents the dip- 
 ping-needle, with its adjust- 
 ing screws and spirit-level ; 
 and the depression may be 
 read on the graduated scale. After the horizontal circle m is 
 
 FIG. 343. 
 
390 ELECTRICITY AND MAGNETISM. 
 
 levelled by the foot-screws, the frame A is turned horizontally till 
 the vertical circle M is in the magnetic meridian. For north 
 latitudes, the north end of the needle is depressed, as a in the 
 figure. 
 
 622. Isoclinic Curves. A line passing through all points 
 where the dip of the needle is nothing, i.e., where the dipping- 
 needle is horizontal, is called the magnetic equator of the earth. 
 It can be traced in Fig. 344 as an irregular curve around the 
 
 FIG. 344. 
 
 earth in the region of the equator, nowhere .departing from it 
 more than about 15. At every place north of the magnetic 
 equator the north-seeking pole of the needle descends, and south 
 of it the south-seeking pole descends ; and, in general, the greater 
 the distance, the greater is the dip. Imagine now a system of 
 lines, each passing through all the points of equal dip ; these will 
 be nearly parallel to the magnetic equator, which may be regarded 
 as the standard among them. These magnetic parallels are called 
 the isoclinic curves ; they somewhat resemble parallels of latitude, 
 but are inclined to them, conforming to the oblique position of 
 the magnetic equator. In the figure, the broken lines show the 
 dip of the south pole of the needle ; the others, that of the north 
 pole. The points of greatest dip, or dip of 90, are called the 
 poles of dip. There is one in the northern hemisphere, and one in 
 the southern. The north pole of dip was found, by Captain James 
 C Ross, in 1831, to be at or very near the point, 70 14' N. ; 96 
 40' W., marked x in the figure. The south pole is not yet so well 
 determined. 
 
 At the poles of dip the horizontal needle loses all its directive 
 power, because the earth's magnetism tends to place it in a verti- 
 cal line, and, therefore, no component of the force can operate in 
 
HORIZONTAL INTENSITY. 391 
 
 a horizontal plane. The isogonic lines in general converge to the 
 two dip-poles ; but, for the reason just given, they cannot be 
 traced quite to them. 
 
 The dip of the needle, like the declination, undergoes a varia- 
 tion, though by no means to so great an extent. 
 
 In 1576, the date of its discovery, the dip at London was 
 71 50'; it increased to a maximum of 74 42' in 1723, since 
 which time it has gradually decreased. In 1879 the dip at Kew 
 was 67 42'. 
 
 In the course of 250 years, it has diminished about five degrees 
 in London. In 1820 it was about 70, and diminishes from two 
 to three minutes annually. 
 
 Since the dip at a given place is changing, it cannot be sup- 
 posed that the poles are fixed points ; they, and with them the entire 
 system of isoclinic curves, must be slowly shifting their locality. 
 
 623. Intensity of the Earth's Magnetism. The axis of 
 the dip-needle, when placed in the magnetic meridian, coincides 
 in direction with the lines of force of the earth's magnetic field. 
 The magnetic force, then, acts in this inclined direction. In most 
 magnetic determinations, however, the needle employed swings in 
 a horizontal plane, and the force exerted upon it by the earth is 
 only that portion of its total force which acts 
 in a horizontal direction. This horizontal com- FlG - 345> 
 ponent of the strength of the field is called the ~fa 
 horizontal intensity of the earth's magnetism. Let 
 / (Fig. 345) represent the strength of the earth's 
 
 field along the lines of force, i.e., along the I 
 
 axis of the dip-needle, d = angle of dip, then 
 
 h the horizontal intensity. From the diagram it is seen that 
 
 h = I cos d. 
 
 The determination of the horizontal intensity is effected after 
 the manner described in Art. 608. Its values for places in North 
 America are given in the following table : 
 
 HORIZONTAL INTENSITY. (C. G. S. UNITS.) 
 
 Boston 0.172 
 
 Cleveland 0.184 
 
 Chicago 0.184 
 
 Halifax 0. 1 59 
 
 Montreal 0.147 
 
 New York 0.184 
 
 New Orleans 0.281 
 
 Niagara 0.167 
 
 Philadelphia '. 0. 194 
 
 San Francisco 0.255 
 
 Washington 0.200 
 
392 ELECTRICITY AND MAGNETISM. 
 
 624. Isodynamic Curves. An inspection of the table just 
 given shows that the horizontal intensity increases as we near the 
 equator. The strength of the earth's field in the direction of its 
 lines 'of force, however, decreases on nearing the equator, as might 
 be expected, the equator being farthest from the poles. After 
 ascertaining, by actual observation, the intensity of the magnetic 
 force in different parts of the earth, lines are supposed to be drawn 
 through all those points in which the force is the same ; these 
 lines are called isodynamic curves, represented in Fig. 346. These 
 
 FIG. 346. 
 
 also slightly resemble parallels of latitude, but are more irregular 
 than the isoclinic lines. There is no one standard equator of 
 minimum intensity, but there are two very irregular lines sur- 
 rounding the earth in the equatorial region, in some places almost 
 meeting each other, and in others spreading apart more than two 
 thousand miles, on which the magnetic intensity is the same. 
 These two are taken as the standard of comparison, because they 
 are the lowest which extend entirely round the globe. The inten- 
 sity on them is therefore called unity, marked 1 in the figure. In 
 the wide parts of the belt which they include lying one in the 
 southern Atlantic, and the other in the northern Pacific oceans 
 there are lines of lower intensity which return into themselves, 
 without encompassing the earth. In approaching the polar regions, 
 both north and south, the curves, retaining somewhat the form of 
 the unit lines, are indented like an hour-glass, as those marked 1.7 
 in the figure, and at length the indentations meet, forming an 
 irregular figure 8 ; and at still higher latitudes, are separated into 
 two systems, closing up around two poles of maximum intensity. 
 Thus there are on the earth four poles of maximum intensity, two 
 in the northern hemisphere and two in the southern. The Ameri- 
 
ASTATIC NEEDLES. 393 
 
 can north pole of intensity is situated on the north shore of Lake 
 Superior. The one on the eastern continent is in northern Siberia. 
 The ratio of the least to the greatest intensity on the earth is 
 about as 0.7 to 1.9 ; that is, as 1 to 2-|. In the figure, intensities 
 less than 1 are marked by dotted lines. 
 
 625. Variation in the Strength of the Earth's Field. 
 Astatic Needles. The intensity of the earth's magnetism i& 
 constantly changing. These changes consist in small fluctuations 
 about an average constant strength. Many electrical determina- 
 tions require for their accuracy either that the horizontal intensity 
 should remain constant 01 that its fluctuations should be taken 
 into account. As the latter is the only alternative, a means must 
 be had of determining, at any moment, whether the intensity has 
 changed, and, if so, how much. 
 
 One method is to employ a magnetometer (Fig. 342), which is 
 rendered nearly astatic by a supplementary bar magnet. (A needle 
 is astatic when the earth has no directive effect upon it.) This 
 auxiliary magnet is placed north and south, directly under, or 
 over, the needle of the magnetometer. When placed at a proper 
 distance above the needle, depending upon its strength, it will act 
 upon the needle with the same force as the earth, onl}' in an op- 
 posite direction. It will thus neutralize the influence of the earth 
 and the needle can turn into any position. If the magnet be 
 brought a little nearer, the needle will suddenly turn around and 
 its north-seeking pole will point south. Now, by a little delicate 
 manipulation, the needle may be made to point nearly east and 
 west. In this position it is very sensitive. Any small increase in 
 the earth's intensity will cause its north-seeking end to turn to the 
 north, and any decrease to the south. Thus, by looking through 
 the telescope at the mirror, any change in 
 the intensity can be detected at any mo- FIG. 347. 
 
 ment, and the amount of change can be 
 arrived at by calculation. 
 
 Astatic needles are of great value in 
 electrical measurements. Liberated from 
 the earth's directive action they may still 
 be affected by electrical currents. Another 
 method of obtaining this end is shown in 
 Fig. 347. 
 
 A compound needle, consisting of two 
 simple needles fixed upon a wire, with 
 
 their unlike poles opposed, may be suspended in any of the usual 
 modes. If the needles are exactly equal in all respects the system 
 
394 ELECTRICITY AND MAGNETISM. 
 
 will be perfectly astatic. The condition of perfect equality in all 
 the conditions is never realized. 
 
 626. Magnetic Charts. These are maps of a country, or of 
 the world, on which are laid down the systems of curves which 
 have been described. But for the use of the navigator, only the 
 isogonic lines, or lines of equal declination, are essential. There 
 are large portions of the globe which have as yet been too imper- 
 fectly examined for the several systems of curves to be accurately 
 mapped. It must be remembered, too, that the earth is slowly 
 but constantly undergoing magnetic changes, by which, at any 
 given place, the declination, dip, and intensity are all essentially 
 altered after the lapse of years. A chart, therefore, which would 
 be accurate for the middle of the nineteenth century, will be, to 
 some extent, incorrect at its close. 
 
 627. The Declination Compass. This instrument con- 
 sists of a magnetic needle suspended in the centre of a cylindrical 
 brass box covered with glass ; on the bottom of the box within is 
 fastened a circular card, divided into degrees and minutes, from 
 to 90 on the several quadrants. On the top of the box are two 
 uprights, either for holding sight-lines or for supporting a small 
 telescope, by which directions are fixed. The quadrants on the 
 card in the box are graduated from that diameter which is verti- 
 cally beneath the line of sight. 
 
 When the axis of vision is directed along a given line, the 
 needle shows how many degrees that line is inclined to the mag- 
 netic meridian. In order that the angle between the line and the 
 geographical meridian may be found, the declination of the needle 
 for the place must be known. 
 
 628. The Mariner's Compass. In the mariner's compass 
 ,{Fig. 348) the card is made as light as possible, and attached to 
 
 the needle, so that the north and 
 south points marked on the card 
 always coincide with the magnetic 
 meridian. The index, by which 
 the direction of the ship is read, 
 consists of a pair of vertical lines, 
 diametrically opposite to each 
 other, on the interior of the box, 
 These lines, one of which is seen 
 at a, are in the plane of the ship's 
 keel. Hence, the degree of the card which is against either of 
 the lines shows at once both the angle with the magnetic meridian 
 .and the quadrant in which that angle lies. 
 
( 
 
 AURORA BOREALIS. 395 
 
 In order that the top of the box may always be in a horizontal 
 position, and the needle as free as possible from agitation by the 
 rolling of the ship, the box, B, is suspended in gimbals. The 
 pivots, A, A, on opposite sides of the box, are centred in the brass 
 ring, C, D, while this ring rests on an axis, which has its bear- 
 in^s in the supports, E, E. These two axes are at right angles to 
 each o'lier, and intersect at the point where the needle rests on its 
 pivot. Therefore, whatever position the supports, E. E, may have, 
 the box, having its principal weight in the lower part, maintains 
 its upright position, and the centre of the needle is not moved by 
 the revolutions on the two axes. 
 
 On account of the dip, which increases with the distance from 
 the equator, and is reversed by going from one hemisphere to the 
 other, the needle needs to be loaded by a small adjustable weight, 
 if it is to be used in extensive voyages to the north or south. 
 
 629. Aurora Borealis. This phenomenon is usually accom- 
 panied by a disturbance of the needle, thus affording visible indi- 
 cations of a magnetic storm; but the contrary is by no means 
 generally true, that a magnetic storm is accompanied by auroral 
 light. The connection of the aurora borealis with magnetism is 
 manifested not only by the disturbance of the needle, but also by 
 the fact that the streamers are parallel to the dipping-needle, as 
 is proved by their apparent convergence to that point of the sky 
 to which the dipping-needle is directed. This convergence is the 
 effect of perspective, the lines being in fact straight and parallel. 
 
 630. Why is the Earth a Magnet? Modern discoveries 
 in electro-magnetism and thermo-electricity furnish a clew to the 
 hypothesis which generally prevails at this day. Attention has 
 been drawn to the remarkable agreement between the isothermal 
 and the isomagnetic lines of the globe. The former descend in 
 crossing the Atlantic Ocean toward America, and there are two 
 poles of maximum cold in the northern hemisphere. The isoclinic 
 and the isodynamic curves also descend to lower latitudes in cross- 
 ing the Atlantic westward ; so that, at a given latitude, the degree 
 of cold, the magnetic dip, and the magnetic intensity, are each con- 
 siderably greater on the American than on the European coast. 
 This is only an instance of the general correspondence between 
 these different systems of curves. It has likewise been noticed 
 (Art. 619) that the needle has a movement diurnally, varying west- 
 ward during the middle of the day, and eastward at evening, and 
 that this oscillation is generally much greater in the hot season 
 than the cold. It is obvious, therefore, that the development of 
 magnetism in the earth is intimately connected with the tempera- 
 
39G ELECTRICITY AND MAGNETISM. 
 
 ture of its surface. Hence it has been supposed that the heat, 
 received from the sun excites electric currents in the materials of 
 the earth's surface, and these give rise to the magnetic phenomena. 
 Most interesting is the hypothesis recently projected by Pro- 
 fessor Bigelow, viz., the earth is revolving and moving in a 
 magnetic field, which is created by the sun. According to this 
 the earth is a magnet by induction and the variations in its mag- 
 netism are caused by differences in the strength of the field 
 through which it is moving. 
 
 CHAPTEK V. 
 
 CURRENT ELECTRICITY. 
 
 631. Electricity in Motion. It has been seen (Art. 571) 
 that when conductors which have a difference of electrical poten- 
 tial are connected together by a conducting substance, a flow, or 
 current, of electricity from the higher to lower potential takes 
 place. This current, however, lasts for an instant only, and any 
 phenomena due directly to the flow would have to be observed 
 during that instant. If by any means the difference of potential 
 of the bodies could be maintained in spite of their being con- 
 nected, a continuous current would be made to traverse the con- 
 necting conductor. Such a means was accidentally discovered in 
 1786, by Galvani, Professor of Anatomy at Bologna. After exper- 
 imenting, one day, upon the effects of statical electricity on a 
 frog's leg, he hung the moist leg, by means of a copper hook, upon 
 an iron window-guard. He then noticed that, whenever the free 
 end of the leg touched the guard, it gave a spasmodic twitch, as 
 though a statical charge had been passed through it. He accord- 
 ingly surmised that he had found a new method of obtaining 
 electricity. 
 
 632. Galvanic Cells. Galvani's discovery has developed 
 into the Galvanic Cell or Element an arrangement of apparatus 
 designed to give a continuous flow of electricity. 
 
 If, when two different substances are submerged in an oxidizing 
 fluid,* one of them has a greater affinity for oxygen than the other, 
 then a difference of potential will be set up between them. The 
 one having the greater affinity will have a lower potential. If de- 
 sirable, the substances may be considered as having become elec- 
 trified the least oxidizable positively, and the other negatively. 
 
 * For simplicity, affinity for oxygen is alone mentioned here. The princi- 
 ple is true for any chemical affinity. 
 
ELECTROMOTIVE FORCE. 397 
 
 If, now, the substances be connected by a wire, a current will 
 flow through it from the higher to the lower potential. As long as 
 the chemical action keeps up, the difference of potential and the 
 current resulting from it will be maintained. 
 
 If, for example, the two substances were copper and zinc 
 plates, and the fluid was dilute sulphuric 
 acid (Fig. 349), the zinc, having greater 
 affinity for the oxygen of the acid, would 
 have a lower potential than the cop- 
 per. Upon connecting them by a wire, a 
 current would flow from the copper to the 
 zinc. This would be a simple galvanic ele- 
 ment. 
 
 The arrangement need not be as shown 
 in the figure, for a zinc rod, wrapped in 
 blotting-paper, upon which is wound bare 
 copper wire, would, upon moistening the paper with dilute acid, 
 give a current. 
 
 The flow from copper to zinc, in the connecting wire, is always 
 accompanied by an equal flow from zinc to copper through the 
 submerging fluid. (This latter flow is found necessary for the 
 maintenance of the potential difference.) - Thus, if we start at any 
 point and follow the current, we will eventually come back to the 
 point whence we started, i.e., a current of electricity always flows in 
 a closed circuit. 
 
 633. Electromotive Force. The difference of potential set 
 up in a galvanic element is due to an Electromotive Force, which 
 is generally represented by the letters E. M. F. Its amount de- 
 pends upon the nature of the two substances employed their 
 relative affinities for the active part of the fluid. In dilute sul- 
 phuric acid they arrange themselves in the following order : 
 
 Hydrogen, 
 ;.i Zinc, 
 
 Iron, 
 
 Lead, 
 
 Nickel, 
 
 Bismuth, 
 
 Copper, 
 
 Carbon, 
 
 Silver, 
 
 Platinum, 
 
 Oxygen. 
 
 Of the metals given, zinc has the greatest affinity for oxygen, 
 and platinum the least. These two metals then would give the 
 
39S ELECTRICITY AND MAGNETISM. 
 
 greatest E. M. F. Platinum and silver would give hardly any. If 
 two elements be constructed, using lead-zinc for one and lead-cop- 
 per for the other, the current would flow out of the lead in the 
 first case, and into the lead in the second. 
 
 The absolute electrostatic unit of potential difference is too 
 large for practical purposes, hence a practical unit of E. M. F., 
 called the -volt (= ^J electrostatic unit) is employed. The E. M. 
 F. of copper-zinc in dilute sulphuric acid, at the instant of making 
 first contact, is 0.921 volt. 
 
 The E. M. F. of a cell is independent of the size of the electrodes. 
 
 A copper-zinc cell of 1 sq. cm. electrodes has the same E. M. 
 F. as one with 1,000 sq. cms. 
 
 The total E. M. F. in a circuit is equal to the algebraic sum of 
 the separate E. M. F. 'a. 
 
 Thus, if two copper-zinc cells be connected in a circuit in the 
 order (Cu Zn) (Zn Cu) one will tend to send a current in one 
 direction, and the other in the opposite direction. The result will 
 be no current at all. 
 
 If, in trying this experiment, one of the cells be very large and 
 the other very small, the fact that no current flows would illustrate 
 the fact that the E. M. F. is independent of the size of electrodes. 
 
 634. Polarization. If a copper-zinc sulphuric-acid cell be 
 connected with an electric bell (or any other current indicator) it 
 will at- first ring loudly, but will soon weaken, and finally cease to 
 give a sound. Upon investigating the cause of this weakening it 
 will be found that the E. M. F. has fallen from 1 volt to possibly 
 0.2 volt. This is because the current, which the element has sent 
 through its own liquid, has decomposed that liquid, and hydrogen 
 (Art. 678) has been deposited upon the copper and oxygen upon 
 the zinc. The oxygen immediately enters into chemical union 
 with the zinc, but the hydrogen remains in its gaseous form. The 
 hydrogen, from its affinity for oxygen, sets up a counter E..M. F., 
 tending to send a current in an opposite direction. The resulting 
 current is smaller than at first, and the cell is said to have become 
 polarized. 
 
 635. Types of Batteries. (A collection of galvanic cells is 
 termed a battery.) Practical cells, designed for giving a constant 
 flow of electricity, employ different methods for avoiding the 
 counter E. M. F. of polarization. The market affords a great 
 variety, but we need consider but three : 
 
 BUNSEN'S CELL. As has been shown, the counter E. M. F. is 
 due to hydrogen upon the electrode having the higher potential. 
 
BATTERIES. 
 
 399 
 
 FIG. 350. 
 
 In Bunsen's cell this hydrogen is made to combine with oxygen 
 furnished by nitric acid. The cell (Fig. 350) employs two 
 different acids, which are kept separate 
 by a porous, unglazed cup. This allows 
 the electricity to flow, but prevents a 
 free mixture of the acids. Outside the 
 cup is zinc in dilute sulphuric acid ; in- 
 side is carbon in nitric acid. The hy- 
 drogen, which above was deposited upon 
 the copper, now comes off at the carbon. 
 Instead of being allowed to exert a coun- 
 ter E. M. F., it is immediately oxidized 
 l>y the nitric acid. On the other hand, 
 this acid is prevented by the porous cup 
 from violently attacking the zinc. 
 
 This cell has an E. M. F. of 1.8 volt, 
 and is capable of maintaining it for a 
 long time. It is a disagreeable cell to 
 work with because of the nitric-acid 
 fumes. These fumes can be avoided by 
 substituting a solution of bichromate of 
 potash for the nitric acid. It is also an active oxidizer ; but, in 
 time, large crystals form inside the walls of the porous cup and 
 cause them to break in pieces. 
 
 DANIELL'S CELL. This cell is more used than any other, in the 
 laboratory. It also employs two liquids and 
 a porous cup. The arrangement is (Fig. 
 351) zinc in dilute sulphuric acid inside the 
 cup, and copper in copper sulphate outside. 
 The cell's own current, instead of depositing 
 hydrogen upon the copper, deposits copper 
 from its sulphate. Now copper upon copper 
 cannot alter the E. M. F. of the cell, and 
 hence the Daniell has the most constant E. M. 
 F. of ordinary cells. The E. M. F. depends 
 somewhat upon the dilution of the sul- 
 phuric acid, but is very nearly 1 volt for any 
 arrangement. 
 
 A modified form of Daniell's cell, called the gravity cell, is used 
 in telegraphy. The porous cup is dispensed with, and the two 
 liquids are kept separate by the action of gravity. The dilute sul- 
 phuric acid is floated on top of the copper sulphate. 
 
 LECLANCHE CELL. There are more of this form of cell in use 
 than of all others put together. They are not designed to main- 
 
 FIG. 351. 
 
 OF THE 
 
 TINTVE'RRTTV 
 
400 
 
 ELECTRICITY AND MAGNETISM. 
 
 FIG. 352. 
 
 tain a constant E. M. F. for any great length of time. They are- 
 intended for purposes where a current is needed for only a few 
 
 moments at most, as for electric 
 bells or on telephone circuits. After 
 use they regain their original E. M. 
 F. The arrangement (Fig. 352) is 
 zinc and carbon in a solution of sal 
 ammoniac (NH 4 C1). An attempt is 
 made to get rid of the hydrogen of 
 polarization by surrounding or mix- 
 ing the carbon with an oxide of 
 manganese. This eventually oxi- 
 dizes the hydrogen, but not as 
 rapidly as the nitric acid in Bun- 
 sen's cell. Some forms of Le- 
 clanche cell employ a porous cup 
 containing the carbon amid the 
 manganese oxide. The E. M. F. of 
 a fresh Leclanche is 1.5 volt. 
 
 636. Combustion of Zinc. 
 Nearly all batteries employ zincs for 
 the lower potential electrode. A 
 current flow is always accompanied 
 
 by an oxidation of zinc, and the energy which accompanies the 
 current comes from this oxidation. This is parallel to the case of 
 a steam-engine, where the energy comes from the oxidation of the 
 fuel under the boiler. 
 
 637. Amalgamation of Zincs. Ordinary commercial zinc is 
 impure. If this impurity were, say copper, and a particle should 
 be embedded near the surface of a zinc electrode, then, upon im- 
 mersing in acid, the zinc and copper would form a small cell by 
 themselves. This would be giving a current, whether the complete 
 cell were in use or not, and would be continually wasting zinc. 
 This wasting of zinc, because of impurities in it, is called local 
 action of the cell. 
 
 It has been found that local action can be prevented by amal- 
 gamating the zinc. This is done by dipping the zinc in acid and 
 then in mercury. The mercury unites with the zinc and floats: 
 the impurities to its surface. These are then detached by the gas 
 bubbles, which are caused by their union with the acid. The zinc 
 of the amalgam is oxidized by the action of the battery, but the 
 mercury remains unaffected. It is, therefore, constantly going 
 
RESISTANCE. 401 
 
 Into combination with new zinc, as the action of the battery con- 
 tinues. 
 
 638. Practical Units of Current and Quantity. As, in 
 considering the flow of water in a pipe, we give the current a 
 definite value of say so many gallons per hour, so we can give a 
 definite value to the electrical current. 
 
 The quantity of water passing through any cross-section of a 
 water-pipe of varying diameter is the same for the same time and 
 current. Likewise 
 
 The quantity of electricity passing in the unit time through any 
 -cross-section of a simple undivided circuit is the same for the same 
 -current. 
 
 To obtain a unit for current we have only to use the unit for quan- 
 tity and the one for time. Now, the absolute electrostatic unit of 
 quantity is not of convenient size for practical purposes. Hence, a 
 new unit, termed the Coulomb, is employed. It equals 3,000,000,000 
 absolute electrostatic units. We have, then, 
 
 The practical unit of current, the ampere, is that current which 
 delivers one coulomb per second to any cross-section of the circuit. 
 
 639. Resistance. All substance offers a resistance to the flow 
 of electricity. Just as motion against resisting friction produces 
 heat, so a current overcoming electrical resistance produces heat. 
 
 The resistance offered by a given conductor depends upon two 
 things, viz., the character of the substance and its shape. If we 
 represent the length of a conductor by I metres, its cross-section 
 toy q sq. mm., then its electrical resistance 
 
 T 
 
 s being a constant depending upon the character of the substance 
 and termed its specific resistance.* If we assumed s, I, and q each 
 equal to unity, we would have a unit resistance. A unit, much 
 used in Germany, the Siemen's quicksilver unit, is defined by as- 
 suming that s for quicksilver at C. is unity. Hence, Siemen's unit 
 of resistance is the resistance offered by a column of quicksilver 1 me- 
 tre long and 1 sq. mm. cross-section, at C. 
 
 The international practical unit, the legal ohm, is a little larger 
 than the Siemen's unit. 
 
 1 ohm 1.06 Siemens unit. 
 
 If R represents the resistance of a conductor, J /* evidently repre- 
 sents its conductivity the greater the resistance the smaller the 
 
 * The absolute specific resistances depending upon I and q being measured in 
 centimetres, and Bin absolute units, are expressed by unwieldy numbers, and 
 a comprehension of the subject does not require their consideration. 
 
402 ELECTRICITY AND MAGNETISM. 
 
 conducting power. Accordingly, 7s can be called the specific con- 
 ductivity of a substance. 
 
 SPECIFIC CONDUCTIVITIES, k = J /^ 
 
 Mercury 1.06 
 
 Silver 63. 
 
 Copper 58. 
 
 Iron 7.4 to 9.5 
 
 Platinum 6.9 
 
 German silver 2.5 to 6.4 
 
 Zn SO 4 (sat. soU) 0000043 
 
 Pure Water 000000000025 
 
 Glass 
 
 These figures evidently represent the length in metres of a 
 wire of 1 sq. mm. cross-section, that the resistance may be 1 ohm. 
 
 Their application can be best understood by an example. Deter- 
 mine the resistance of a copper wire 11.6 m. long and 0.1 sq. mm. 
 in cross-section. 
 
 7 1 1 A 
 
 R = - = == -7 2 ohms. 
 kq 58 x 0.1 
 
 Silver and copper are the best conductors we have. Because of 
 the expense of the former, copper is universally employed on 
 electrical circuits. In fact, some modern copper is said to con- 
 duct better than silver. Absolutely pure water is probably a non- 
 conductor. The purest water yet obtained, if placed in a tube 
 of unit diameter and 1 mm. long would offer the same resistance 
 as a copper wire of same diameter, but as long as the orbit of the 
 moon. 
 
 The influence of specific conductivity upon resistance can be 
 prettily shown by the following experiment : Pass the current 
 from a dynamo through an electric lamp, and, by means of two 
 electrodes, through a vessel of rain-water. As long as the water is 
 pure the lamp will not be illuminated. Place a few drops of sul- 
 phuric acid in the water, and the lamp will instantly commence to 
 glow. 
 
 640. Influence of Temperature. The resistance of con- 
 ductors changes with the temperature. In all metals an increase 
 of temperature increases the resistance. At ordinary temperatures 
 the increase for most pure metals is 0.004 of the whole, per de- 
 gree centigrade. The amount for German silver is about 0.0003. 
 
 Carbon and liquids decrease in resistance when the temperature 
 is raised. The change per degree for liquids is between two and 
 three per cent. 
 
 The dependence of resistance upon temperature furnishes a 
 means of measuring the latter. A conductor of large temperature 
 
oiiri'3 LAW. 403 
 
 coefficient is subjected to the heat whose temperature is to be de- 
 termined, and while still in place its resistance is measured. The 
 increase of resistance furnishes data for calculation of the tempera- 
 ture. By this means Professor Langley has measured the heat 
 radiated from the moon. 
 
 641. Ohm's Law. The three electrical magnitudes cur- 
 rent, E. M. F., and resistance are connected together by an impor- 
 tant relation called Ohm's law. Letting E represent, in volts, the 
 algebraic sum of all the E. M. F.'s of a circuit, R the sum of all 
 the resistances, in ohms (of battery, conducting wires, and all 
 instruments in circuit), then this law states, the current strength 
 in amperes, 
 
 The strength of the current varies directly as the E. M. F., and 
 inversely as the resistance. 
 
 642. Divided Circuits. Shunts. If a current from a 
 battery of E. M. F. E and internal resistance r be sent 
 through a wire which divides at a certain point (Fig. 353) into 
 two branches, which however re- 
 unite further on, and if the resist- 
 ances of the undivided conductor 
 
 and its branches are E, r lt r a re- 
 spectively, then the substitution of 
 r -+ R 4- r 1 + r, in Ohm's law 
 would not give the correct current 
 strength. The reason for this is 
 that the whole current does not 
 pass through each of the branches 
 r l and r 2 . They each take a por- 
 tion of the current, depending upon their resistances. A single 
 conductor might be found, which, if substituted for the two, 
 would leave the current in R unchanged. The resistance of this 
 single conductor might be called the equivalent resistance of the 
 branches. To determine this equivalent resistance it is most con- 
 venient to consider the conductivities of the branches. Evidently 
 the conductivity of the single replacing conductor must equal the 
 sum of the conductivities of the ' separate paths. But the con- 
 ductivities are the reciprocals of the resistances. Hence we have 
 
404: ELECTRICITY AND MAGNETISM. 
 
 The current C flowing through the undivided portion of the 
 circuit, e.g,, through 72, would be, by Ohm's law, 
 E _ E_ 
 
 R + r + K E + r + ~^^- 
 
 r, + r, 
 
 In the same manner the equivalent resistance of any number of dif- 
 ferent paths may be determined. 
 
 When a conductor is placed so as to take a portion of the 
 current which is passing through another conductor it is called 
 a shunt and the current is said to be shunted. 
 
 Many delicate instruments for measuring electrical quantities 
 would be ruined if the whole current passed through them. In 
 such cases a portion of the current is shunted off from the instru- 
 ment. From the known resistances of the instrument and the 
 shunt the quantities to be determined can be calculated. 
 
 643. Ratio of Currents in Shunts. In order to determine 
 the portion of the current flowing in any branch of a divided 
 circuit, we must consider that the whole current is carried by 
 the branches as a whole. Letting C = current in undivided por- 
 tion (Fig. 353) and c l and c 2 = currents in r l and r a , we have 
 
 C = c, + c,. 
 
 Again, bearing in mind that the difference of potential (E. M. F.) 
 between the ends of each branch is the same e, we have, by 
 Ohm's law, 
 
 e . e 
 
 c, =-.. = -. "to. 
 
 . '. c. : a. : etc. = : : etc. 
 r, r 2 
 
 The currents carried by different branches between two points of a 
 circuit are inversely as the resistances of the branches. 
 
 644. Fall of Potential. If we have a battery connected 
 through a uniform straight wire of given resistance, we may con- 
 sider the potential at the zinc end to be = zero, and that at the 
 other end positive, and = E. M. F. of the battery. Now, inasmuch 
 as the resistances of equal lengths of the wire are the same, the 
 potential at the middle of the wire equals one-half the E, M. F, 
 At one-quarter the distance from each end of the wire the poten- 
 tials are one-quarter and three-quarters of the E. M. F. The 
 potential varies all along the wire, from zero at the zinc end to E. 
 M. F. at the other end. If we commence at the other end we may 
 say that 
 
 The potential falls directly as the resistance. 
 
 Of course, if the conductor were not homogeneous, e.g., made 
 
WHEATSTONE'S BRIDGE. 
 
 405 
 
 FIG. 355. 
 
 of copper and then German silver, the fall would not be the same 
 for the same lengths. It would be more rapid in the German 
 silver portion of the circuit 
 than in the copper portion. FIG. 354. 
 
 645. Resistance Boxes 
 or Rheostats. These are 
 boxes (Fig. 354) containing dif- 
 ferent spools of wire, whose 
 resistances have been deter- 
 mined, and which can be used 
 for standards of comparison. 
 -German silver wire is gener- 
 ally used, because its resist- 
 ance changes least with the 
 temperature. The proper length 
 of wire is taken, and, after be- 
 ing doubled at its middle (Fig. 355), is wound upon a spool, the 
 two parts being wound side by side. This is indicated in the 
 
 figure. The reason for this doubling is 
 to avoid the self-induction disturbances 
 of the wire (Art. 668). The spool, when 
 wound, is placed inside the box and the 
 terminals are fastened to two separate 
 brass blocks on the top of the box. To 
 each of these blocks is fastened one end 
 of the two neighboring coils. In the 
 ^4. figure, a and b of one resistance are 
 
 fastened to blocks E and H. The ends 
 
 'C and d of the neighboring coil are fastened, one to H and the 
 other to M. The blocks can be connected together at will by 
 brass plugs fitting into holes between them. 
 
 Suppose, now, that the two terminals of a battery be connected 
 with E and M respectively. If the plugs 1 and 2 be removed, the 
 current will be obliged to traverse both of the resistance coils. If 
 plug 1 be inserted, the current will divide between the plug and 
 the coil. But the resistance of the plug is infinitesimal, and hence, 
 practically, the whole current passes through it and none through 
 the coil. 
 
 When a box of coils is inserted in a circuit, the resistance can 
 be varied at will, by simply inserting- or pulling out plugs. 
 
 646. Wheatstone's Bridge. An important application of 
 the preceding principles is Wheatstone's bridge. It is an arrange- 
 
406 
 
 ELECTRICITY AND MAGNETISM. 
 
 merit of apparatus by means of which resistances can be very accu- 
 rately determined. 
 
 If a current of electricity arriving at V (Fig. 356) divides and 
 
 by two paths, A B and CD, to V, where the paths 
 unite, then the difference of potential (V-V) is acting on both 
 paths. The potential along each path must fall from V to V. If 
 at any point of the path A B, the potential is g, then some point (g'} 
 of the other path, CD, can be found having * the same potential. 
 If these two points, g and g' be connected through a galvanometer 
 or any other current detector, no current will flow, because there is 
 no potential difference between g and g'. 
 
 Inasmuch as the fall or loss of potential along each path is pro- 
 portional to the resistance, the loss in passing A must be the same 
 as in passing C, and the resistance of A must bear the same ratio 
 to A -f B as C does to C + D. In order that the potentials may be 
 the same at g and g', it must be true that the resistances follow 
 
 the proportion 
 
 A-.B = C:D. 
 
 In Wheatstone's bridge, when no current passes through the 
 galvanometer, the products of the opposite resistances are equal. 
 
 The method of determining resistances by the bridge is to place 
 the unknown resistance in one arm of the bridge, as D. Known 
 resistances are placed in A and B, and a resistance-box in C. By 
 manipulating the plugs in C a balance can be made so that no cur- 
 rent flows through the galvanometer. A, B, and C are known, and 
 the required resistance 
 
 It is sometimes convenient to make G constant, and vary bo^h 
 A and B until a balance is obtained, A and B consisting of parts 
 of the same straight wire of uniform diameter. The balance is 
 
ARRANGEMENT OF CELLS. 40T 
 
 obtained by sliding the contact (g) with the galvanometer along 
 this wire. The resistances of A and B are then proportional to 
 their lengths. 
 
 647. Cells in Series and in Multiple Arc. A battery of 
 two cells can be connected to a circuit 
 in two different manners. The copper FIG. 357. 
 
 of one may be connected to the zinc of 1 1 1 1 
 
 the other (Fig. 357), and the circuit < \\\\ 
 
 connected to the remaining zinc and ! I ca 
 
 copper. The cells would then be in 
 
 series. Again, the coppers of each and the zincs of each might 
 be connected together and the circuit connected to these short 
 
 connecting wires (Fig. 358). The two 
 
 cells are then said to be in multiple arc. 
 
 Jl Let us consider the results of these 
 
 /||\ different arrangements. Represent the 
 
 < ( j E. M. F. of each cell by E, and the in- 
 
 \|L/ ternal resistance by r. 
 
 Evidently, when in series, the E. M. 
 F. of the circuit is equal to the sum of 
 
 the two E's, and the internal resistance of the battery is 2 r. If 
 the resistance of the total external circuit be R, then the current, 
 when the cells are in series, 
 
 c--= R 2 + E 2 r - 
 
 When the cells are in multiple arc, the E. M. F. is no greater 
 than for a single cell. The two cells are like a single cell of twice 
 the size, and size does not affect the E. M. F. (Art. 633). The re- 
 sistance, however, is only half that of a single cell, because the 
 cross-section of the liquid, which the current has to pass, is twice 
 as great. For two cells in multiple arc, then, the current 
 
 We can extend this reasoning to any number of cells, and say, 
 n cells, in series, multiply the E. M. F. and the internal resistance 
 
 by n, and m cells, in multiple arc, divide the internal resistance by 
 
 m, but leave the E. M. F. unaltered, it being that of a single cell. 
 
 In general, if we have m n cells, consisting of n groups in series. 
 
 each group containing m cells in multiple arc, the resulting cur- 
 
 rent will be 
 
 0= 
 
 R + n 
 m 
 
408 ELECTRICITY AND MAGNETISM. 
 
 With a given number of cells and a given external resistance 
 some arrangement of the cells can be found which will give a maxi- 
 mum current. It can be proved that this arrangement will ren- 
 der the internal resistance as nearly equal to the external as possible. 
 
 When the external resistance is very great compared with the 
 battery, it is advisable to get as much E. M. F. as possible. This 
 is accomplished by placing the cells in series. 
 
 Problems. 
 
 1. An incandescent lamp takes a current of 0.7 ampere, and the 
 E. M. F. between its terminals is found to be 98 volts : what is its 
 resistance ? 
 
 2. A current of 8.5 amperes flows through a conductor, the 
 ends of which are found to have a difference of potential of 24 
 volts : what is its resistance? Ans. 2.823 ohms. 
 
 3. A battery, arranged in series, consists of 5 Daniell cells, each 
 having an E. M. F. of 1.08 volt and an internal resistance of 4 
 ohms : what current will the battery produce with an external re- 
 sistance of 7 ohms. Ans. 0.2 ampere. 
 
 4. Two cells of E. M. F., 1.8 volt and 1.08 volt respectively, 
 are placed in circuit in opposition (i.e., with their poles in such 
 positions that the cells tend to send currents in opposite direc- 
 tions). The current is found to be 0.4 ampere : what current 
 will be produced, if the cells are placed properly in series? 
 
 Ans. 1.6 ampere. 
 
 5. A Bunsen cell has an internal resistance of 0.3 ohm and 
 its E. M. F. on open circuit is 1.8 volt. The circuit is completed 
 by an external resistance of 1.2 ohm : find the current produced 
 and the difference of potential which now exists between the ter- 
 minals of the cell. A \ C = 1.2 ampere. 
 
 ns ' \P.D. = 1.44 volt. 
 
 6. Two wires of the same length and material are found to have 
 resistances of 4 and 9 ohms respectively : if the diameter of the 
 first is 1 mm., what is the diameter of the second? 
 
 7. The resistance of a bobbin of wire is measured and found 
 to be 68 ohms : a portion of the wire 2 metres in length is now cut 
 off, and its resistance is found to be 0.75 ohm. What was the 
 total length of wire on the bobbin? Ans. 181.3 metres. 
 
 8. What length of platinum wire 1 mm. in diameter is required 
 in order to make a 10 ohm resistance coil? 
 
 9. A wire ra metres in length and I/nth of a millimetre in di- 
 ameter is found to have a resistance r: what is the specific re- 
 sistance of the material of which it is made ? 
 
THE CURRENT'S LINES OF FORCE. 400 
 
 10. A uniform wire is bent into the form of a square : find the 
 resistance between two opposite corners in terms of the resistance 
 of one of the sides. 
 
 11. Twelve incandescent lamps are arranged in.parallel between 
 two electric light leads. The difference of potential between the 
 leads is 99 volts, and each lamp takes a current of 0.75 ampere : 
 what is the equivalent resistance between the leads ? 
 
 Ans. 11 ohms. 
 
 12. A battery of 20 ohms resistance is joined up in circuit with 
 a galvanometer of 10 ohms resistance. The galvanometer is then 
 shunted by a wire of the same resistance as its own : compare the 
 currents produced by the battery in the two cases. 
 
 Ans. C : G' = 5 : 6. 
 
 13. In the preceding example determine the ratio between the 
 currents which flow through the galvanometer before and after it 
 is shunted. 
 
 14. How would you arrange a battery of 12 cells, each of 0.6 
 ohm internal resistance, so as to send the strongest current 
 through an electro-magnet of resistance of 0. 7 ohm. 
 
 15. In a Wheatstone's bridge (Fig. 356) A = 10 ohms, B = 
 1,000 ohms, and C = 50 ohms : what is the resistance of D, if the 
 galvanometer shows no current? Ans. 5,000 ohms. 
 
 CHAPTEK VI. 
 
 ELECTRO -MAGNETISM. 
 
 648. The Current's Lines of Magnetic Force. If a 
 wire, carrying a current of electricity, be passed through a sheet of 
 paper, as indicated in Fig. 359, and if iron filings be sprinkled upon 
 the paper, they will arrange themselves so as to form circles around 
 the wire. If then a short magnetic needle be moved about the 
 wire, it will tend to place itself tangentially to the circle passing 
 through its centre. If the direction of the current be reversed, 
 the needle will turn through 180. The circles of the filings show 
 the paths of magnetic lines of force, which owe their existence to 
 the electrical current, just as the filings in Fig. 335 showed the 
 paths of the lines of force of a magnet. In order to give a direc- 
 tion to these circular lines we must consider in what direction an 
 isolated north magnetic pole would move. In the diagram this 
 
410 
 
 ELECTRICITY AND MAGNETISM. 
 
 would evidently be contrary to the motion of the hands of a clock. 
 In general, to remember the directions which these lines will have, 
 
 FIG. 359. 
 
 BATTERY 
 
 Maxwell makes use of the thrust and turn of an ordinary screw 
 (Fig. 360). Suppose the current to flow along the axis of the 
 
 screw, from the head 
 
 FIG. 360. to the point when it is 
 
 being screwed into any- 
 thing, and vice versa 
 when it is being re- 
 moved i.e., the direc- 
 tion of the current is the same as the direction of propagation of 
 the screw then the direction of the circular lines of force is the 
 same as the motion of the circumference of the head of the screw 
 when it is screwed in or out. 
 
 649. Effect of a Current on a Magnet. The experiment 
 in the preceding article shows that there is a connection between 
 electricity and magnetism. In 1819, Oerstedt showed that a 
 magnet tends to set itself at right angles to a wire carrying 
 an electric current. He found, further, that the way in which 
 the north end of the needle turns, whether to the right or left of 
 its normal position, depends upon the position of the wire that 
 carries the current whether it is above or below the needle 
 and upon the direction in which the current flows through the 
 ivire. The position which a magnet will tend to take, when under 
 
SOLENOIDS. 
 
 411 
 
 FIG. 361. 
 
 the influence of a current, can be easily determined by knowing 
 the direction of the lines of force of both current and magnet, 
 and by considering that the magnet will move in such a direc- 
 tion as to tend to bring its lines of force into the same path and 
 direction as the lines of force of the cur- 
 rent. Sometimes the student forgets the 
 direction of the current's lines. In such 
 a case let him remember that if the cur- 
 rent flows from South to North and Over 
 the needle, the north end of the needle 
 will be turned toward the West, the com- 
 bination being remembered by the initial 
 letters, SNOW. 
 
 If we suppose the magnet to be 
 fixed, and the conductor carrying the 
 current to be movable, then the con- 
 ductor will move because of the strife 
 toward parallelism of their lines of force. 
 Lodge illustrates this by a beautiful ex- 
 periment. Send a strong current through 
 a vertically suspended gold thread (such 
 as is used upon military garments). 
 Alongside the thread place, vertically, an 
 electro-magnet (Fig. 361). Upon excit- 
 ing the magnet the thread will wind itself 
 around the magnet. Reverse the cur- 
 rent and it will unwind and then rewind 
 itself in the opposite direction. Com- 
 plete parallelism of the lines of force is, of course, impossible, 
 F ogo but the experiment well illustrates 
 
 the tendency. 
 
 The movement of a needle under 
 the influence of a current furnishes 
 a convenient means of determining 
 the direction in which the current 
 is flowing. 
 
 650. Solenoids. If a wire 
 which carries a current be bent in- 
 to a circle, all the lines of force will 
 emerge from one side of an imag- 
 inary disc bounded by the loop 
 (Fig. 362) and bending around the 
 wire will enter the opposite side. 
 The loop, because of the current, will be magnetically equivalent 
 
412 
 
 ELECTRICITY AND MAGNETISM. 
 
 FIG. 363. 
 
 to a disc magnet having north polarity on one side and south, 
 polarity on the other. In the diagram an isolated north pole 
 
 placed above the surface of the 
 page would be attracted to- 
 ward >, as though it were a 
 south magnetic pole. If the 
 wire is coiled into the shape 
 indicated in Fig. 363, it is 
 termed a solenoid or helix. 
 Upon passing a current, the 
 lines of force, from their mut- 
 ual action, take the paths indicated in the figure. A solenoid, 
 when traversed by a current, has 
 the same magnetic effect as a bar 
 magnet whose axis coincides with 
 the axis of the solenoid. Sole- 
 noids exhibit all the properties 
 of magnets attract pieces of soft 
 iron, attract and repel magnets 
 or other solenoids, and, if sus- 
 pended by non-restraining quick- 
 silver contacts, as in Fig. 364, will turn into the earth's magnetic 
 meridian. 
 
 FIG. 364. 
 
 FIG. 365. 
 
 651. Ampere's Theory of Magnetism. Because of the 
 
 like actions exerted by sole- 
 noids and magnets, Ampere 
 concluded that the perma- 
 nent magnetism of steel 
 owed itself to circular mole- 
 cular currents of electricity, 
 as shown in Fig. 365. He 
 showed that the resultant 
 of these many molecular 
 currents was equivalent to 
 surface solenoidal currents, 
 as indicated in Fig. 366. In the interior of the magnet cur- 
 rents on contiguous molecules are running in opposite directions, 
 and accordingly neu- 
 tralize each other's FIG. 366. 
 magnetic effects. Half 
 of the currents on the 
 surface molecules are 
 not neutralized, and the combined effect is the same as a surface 
 solenoidal current. 
 
MAGNETO-MOTIVE FORCE. 
 
 413 
 
 FIG 367. 
 
 It should be remembered that looking at the north end of 
 a magnet, end on, the amperian currents run counter-clockwise. 
 
 652. Electro-magnets. We have seen (Art. 611) that when 
 a piece of iron is placed in a magnetic field, it becomes an induced 
 magnet and it adds lines of force to the field. Now, if an iron 
 core be inserted into a solenoid, it becomes a magnet under the 
 influence of the solenoid's field, and, because of its much greater 
 permeability than air (Art. 612), adds many lines of force to the 
 field. Such a combination is termed an electro-magnet. An electro- 
 magnet differs from an ordinary one in that the instant the excit- 
 ing current is removed the electro-magnet loses its magnetism. 
 
 The intensity of the field which a given solenoid can produce is 
 limited only by the strength of the current traversing it. If the 
 current strength is doubled, the strength of the field is doubled. 
 The iron core, upon being inserted, multiplies the strength of the 
 field by a certain factor (the permeability of the core, see Art. 
 612). Now, if the permeability of iron were constant, there would 
 be scarcely any limit to the strength 
 which could be given to an electro- 
 magnet. But as the iron reaches the 
 point of saturation its permeability 
 decreases toward unity. As it is, 
 electro magnets can be made many 
 times more powerful than permanent 
 magnets. 
 
 A common form of electro-mag- 
 net is schematically shown in Fig. 
 367. The solenoid with its core is 
 bent into the form of a horseshoe. 
 An actual magnet would be wound 
 with many more turns of wire, which must, of course, be insulated 
 from the core. Upon passing a current, a heavy weight can be 
 suspended, and this will detach itself as soon as the current is dis- 
 continued. 
 
 653. Magneto-motive Force. In the practical construction 
 of electro-magnetic apparatus it is often desirable to obtain a 
 maximum number of lines of force in a given region. This region 
 is to be occupied by some movable armature or object, to be sub- 
 jected to the field's influences. Let us consider how this can be 
 obtained when this region is the space between the poles of an 
 electro-magnet. Evidently by increasing the number of lines gen- 
 erated by the current and adding as many lines as possible to these 
 by proper selection of materials and shape of the electro-magnet. 
 
414 ELECTRICITY AND MAGNETISM. 
 
 The number of lines originally produced will increase with the 
 current strength which flows through the solenoid or coil. It 
 will also increase with the number of the loops of the wire in the 
 coil for each loop will add the same number of lines to those 
 already traversing the axis of the coil. Accordingly we must 
 employ as strong a current and as many turns of wire as pos- 
 sible. Eemembering that the magnetic permeability of a sub- 
 stance is the same as its conductivity toward lines of force, it is 
 desirable that all the space which is traversed by lines of force, 
 except the portion which is to be employed for the movement 
 of the object to be subjected to the field's influence, should be 
 occupied by a substance of maximum magnetic permeability, i.e., 
 by the best soft iron. 
 
 Now we can obtain a law for the flow of lines of magnetic force 
 exactly like Ohm's law (Art. 641) for current flow. Call the source 
 of the lines the magneto-motive force (M. M. F.) ; call the reciprocal 
 of the conductivity the magnetic resistance (E) ; then the magnetic 
 flux or number of lines which pass through the axis of the coil 
 
 M. M. F. 
 
 *= R 
 
 Evidently the M. M. F. is a function of the current strength (c) 
 and the number of loops (n) made by the coil wire. It can be shown 
 mathematically that if. c is expressed in amperes, and N is to be 
 
 obtained in absolute units, the M. M. F. = - n c. The magnetic 
 
 resistance is subject to the same law as electrical resistance (Art. 
 639). Increase the length / of the path to be travelled by the 
 lines and the resistance is increased. It is decreased by increas- 
 ing the cross-section q, and decreases with increase of magnetic 
 permeability /A, so that the resistance 
 
 E = - l - 
 
 /x q 
 
 Introducing these values in the equation for the flux, we obtain 
 
 10 
 M 
 
 This formula is of great importance and has been of great service 
 in the designing of efficient electro-magnetic machinery, e.g., dy- 
 namos and motors. To understand the application of it, let us 
 refer to Fig. 367. The region where maximum flux is desired is 
 the bottom of the horseshoe where the armature and the weight 
 attached to it are suspended. The flux will be increased by 
 increasing the current (c), the number of turns of wire (n), the cross- 
 sections (q) of the core, the armature and the air gaps between tLe 
 
THE TELEGRAPH. 415 
 
 armature and the poles, by increasing the permeability (/*) of the 
 core and armature, and by decreasing the average lengths (I) of the 
 core, the armature, and the air gaps. 
 
 When it is considered that the permeability of iron is much 
 greater than that of air, it will be seen that the force of attraction 
 would be greatly lessened if a piece of the iron core were removed 
 from the top. The force exerted by a horseshoe electro-magnet 
 is much greater than that exerted by two parallel straight electro- 
 magnets corresponding to the two legs of the horseshoe. 
 
 654. The Morse Telegraph System. The fact that an 
 electro -magnet loses its magnetism as soon as the exciting current 
 is discontinued, was made use of by Professor Morse in the construc- 
 tion of his system of electric telegraph. In this system an oper- 
 ator at one station can, by making and breaking a current of elec- 
 tricity which traverses a wire to a second station, produce or de- 
 stroy, at will, the magnetism of an electro-magnet in the second 
 station. This electro-magnet is a part of an instrument called a 
 register, which will be described later. According as the magnet 
 is excited for a longer or shorter interval, the register marks upon 
 a moving band of paper a series of dashes or dots. These may be 
 combined so as to serve as an alphabet. 
 
 The Morse circuit has four elements : A battery to produce a 
 current ; a key to manipulate the current ; a register or sounder to 
 record the current thus manipulated ; and a line to convey the 
 current. 
 
 The battery generally employed is a modification of the Dan- 
 iell's type, called the Gravity Battery (Art. 635). Dynamos are, 
 however, rapidly supplanting them in the large telegraph systems. 
 
 The key for manipulating the current consists of a lever, B 
 (Fig. 368), and anvil, C, both of brass, and insulated from each 
 
 FIG. 368. 
 
 other. The anvil is connected to one terminal of the line, say 
 from the battery, and B to the other terminal, where it leaves for 
 the receiving station. The end of B is depressed by the finger of 
 
416 
 
 ELECTRICITY AND MAGNETISM. 
 
 the operator on the insulating button F, and is raised by the spring 
 E, when the pressure is removed. The former movement closes 
 the circuit, the latter opens it, and by a succession of these the 
 message is sent. When the key is not in use, the brass bar K, 
 hinged to the base of B, is pressed into contact with C. This 
 closes the circuit so that other operators on the line may have a 
 continuous circuit when they desire to send a message. When not 
 in use, the line is traversed by a current. 
 
 The register for recording the message on paper is constructed 
 as follows : 
 
 The lever E is furnished with a style e (Fig. 369), directly over 
 which is a groove on the surface of a solid brass roller c. Between 
 c and e is a long paper ribbon E R. Attached to E is a soft iron 
 armature A, placed above the magnet M, and furnished with a. 
 
 FIG. 369. 
 
 spring s to raise it as far as the screw i allows when it is not at- 
 tracted by M. When the circuit is closed, A is attracted and e 
 rises and forces the paper into the groove, producing a slight ele- 
 vation on its upper surface. The ribbon is pulled along at a uni- 
 form rate in the direction of the arrow by clockwork (not shown 
 in the figure), so that when the circuit remains closed for a little 
 time, a dash is marked on the paper by e ; when it is closed and 
 instantly opened, the result is a dot or rather a very short dash. 
 Spaces are left between these whenever the circuit is opened. 
 Combinations of these dots, dashes, and spaces, all carefully regu- 
 lated in length, compose the letters of the alphabet. Spaces are 
 also left between the letters, and longer ones between words. 
 
 By lengthening the circuit wire, it is evident that the person 
 who sends the message at n p, and the one who receives it at E, 
 may be miles apart, and the transmission will be almost instanta- 
 neous, owing to the rapid passage of the current. 
 
 It has been found that the ear is sufficiently accurate to allow 
 of the dispensing with the register, as used by Morse. Instead of 
 
THE RELAY. 
 
 41T 
 
 It a sounder is employed. In this the end of the lever L' (Fig. 370), 
 instead of being furnished with a style, is made to strike against 
 
 FIG. 370. 
 
 ihe two screws, N' t 0'. The downward click is a little louder than 
 the upward one, and so the beginning and end of each dot or 
 dash are distinguished from each other. Many operators learn 
 from the first to read by the ear, and have never used a register. 
 
 For a line it was at first supposed that a complete metallic cir- 
 cuit was necessary, hence a return wire was employed. But this 
 was rejected when it was found that the earth could be used as a 
 part of the circuit, as shown in Fig. 371, in which the dotted line 
 and arrow beneath the surface are not intended to convey the idea 
 that a current actually flows from one earth-plate to the other, but 
 
 FIG. 371. 
 
 that a complete circuit is formed, the earth acting the part of an 
 infinite reservoir of electricity. S and S f are the terminal stations, 
 and s is one of the way stations which may occur anywhere along 
 the line. At every station both a key, (7, and sounder, 1, are in- 
 troduced into the circuit, so that messages can be both sent and 
 received. 
 
 655. The Relay. When a telegraph line is very long, its 
 ^resistance is high and the leakage, because of insufficient iusula- 
 
 UNIVERSITY 
 
418 ELECTRICITY AND MAGNETISM. 
 
 tion, is great. Hence a current sufficiently strong to satisfactorily 
 operate a register or sounder cannot be economically sent through 
 it. Accordingly use is made of a relay. In this instrument (Fig. 
 372) the line current entering at W and leaving at W" excites the 
 electro-magnet M. This attracts the armature A of the delicately 
 adjusted lever L. The adjustment is obtained by regulating the 
 tension exerted by the spiral spring s. During the passage of a 
 current along the line, the lever L plays lightly to and fro, but 
 with insufficient strength to act as a register or sounder. It can, 
 however, be made to act as a key for a separate local circuit in the 
 receiving office. One terminal of this local .circuit, which contains- 
 a sounder and battery, is connected by the binding-post I with the' 
 
 lever L. The other, through n, is connected with the screw N. 
 When the distant operator closes his key the armature A causes 
 the lever L to close the local circuit at N. When the distant 
 operator opens his key, the spring s opens the local circuit. Thus 
 the moving lever of a relay acts as a key for a local circuit. 
 
 Evidently the relay may be used for repeating a message on 
 another long circuit. 
 
 656. Duplex Telegraphy. In the Morse system just de- 
 scribed evidently but one message can traverse the wire at the 
 same time. If two could simultaneously traverse it, the earning 
 capacity of the line would be doubled. This feat can be accom- 
 plished, and is termed duplex telegraphy. A simple duplex system, 
 employing the principle of Wheatstone's bridge (Art. 646), is 
 shown in Fig. 373, which represents two stations connected by 
 the line wire L L'. C L R is a W'heatstone bridge, modified to 
 suit the conditions of the case, I the sounder, R resistance coils, k 
 a key working upon the centre and having forward and back con- 
 
DUPLEX TELEGRAPHY. 
 
 419 
 
 tacts at a and c, b the battery, and E the earth connections. The 
 same letters, accented, represent like parts at the second station. 
 
 FIG. 373. 
 
 When not in use the keys make back contact by the action of a 
 spring. The ratio of the resistance C R and R E 3 is made equal to 
 that of C L and the line wire L L', including the back contact earth 
 connection at the second station. When thus balanced any current 
 arriving at C, which, dividing, passes through C L L' and C R E 3 , 
 will maintain the points L and R at the same potential. 
 
 If now, a' being closed, a be closed, a current will flow through 
 a and k to <7, where it will divide, one part going to earth through 
 R and E 3 , and the other through L L'. As the potentials were 
 made equal at L and R, no current will pass through the indicator 
 /; that part of the current which flows through L L' divides at L', 
 part going through C' k' a' to E", and part through /' (giving 
 signal) and R' to E'. Thus the closing of a gives a signal at /' 
 but none at I. 
 
 If now the second operator should close his key while a was 
 closed, a current from b' would flow through c' and k' to C', where 
 it would divide, part going to earth through R' and E' (joining 
 the current already flowing through from L L'), and part would 
 flow to L' and oppose the current from the other station; this 
 opposing current will have the same effect as increased resistance 
 in the line wire L L', and hence the balance C L R will be dis- 
 turbed, the potential of L rising above that of R, and resulting in 
 a current from L through / to R, giving a signal at /. Thus the 
 register at each station will respond to the key of the other, and 
 only to that, whether one or both operators be signalling. 
 
 The above explanation of the principle of this particular mode 
 of sending simultaneous messages in opposite directions on a 
 single wire, does not pretend to describe the actual arrangement 
 of wires or earths in use. For a full description of the various 
 modes of duplex and quadruple! telegraphy the student is referred 
 to works on practical telegraphy. 
 
420 
 
 ELECTRICITY AND MAGNETISM 
 
 657. Atlantic Telegraph Cable. This cable stretches a 
 distance of 3,500 miles, and from the nature of the case is a con- 
 tinuous wire, so that it cannot be advantageously worked by the 
 Morse apparatus. The indicator employed is a sensitive galva- 
 nometer needle, which is made to oscillate on opposite sides of the 
 zero point by the passage through it of currents in opposite direc- 
 tions. But to reverse the direction of the current throughout the 
 whole length of ' the cable is a slow process. For the cable is an 
 immense Ley den jar, the surface of the copper wire (amounting to 
 425,000 sq. feet) answering to the inner coating, the water of the 
 ocean to the outer", and the gutta-percha between the two to the 
 glass of an ordinary jar. A current passing into it is therefore de- 
 tained by electricity of the contrary kind induced in the water, and 
 no effect will be produced at the farther end until it is charged. 
 
 This very circumstance, at first considered a misfortune, is 
 now taken advantage of in a very simple and ingenious manner to 
 facilitate the transmission of signals. The current is allowed to 
 pass into the cable till it is charged then, urithout breaking the 
 circuit, by depressing a key for an instant, a connection is made 
 between it and a wire running out into the sea ; that is, between 
 the inner and outer coatings. This partially discharges it, and 
 the needle at the other end is deflected. When the key is raised 
 the discharge ceases, the current flows on as before, and the 
 needle is deflected in the opposite direction. 
 
 658. Electric Bells. The ordinary electric house bell con- 
 sists of an electro-magnet, which moves a hammer backward and 
 
 FIG. 374. 
 
 forward by alternately attracting and releasing it, so that it beats 
 against a bell. The arrangements of the instrument are shown in 
 
GALVANOMETERS. 421 
 
 3?ig. 374. A current from a battery (usually of the Leclanche 
 pattern), after traversing the electro-magnet E t enters a spring 
 attached to the armature and bell-hammer. It leaves the spring 
 by an adjustable screw, C, and returns to the battery. When it 
 flows it excites the magnet which attracts the armature and causes 
 the hammer to hit the bell. In moving toward the magnet the 
 contact at G has been broken, and the magnet losing its magnetism 
 allows the armature to spring back so that the contact is renewed. 
 This operation is repeated, the current repeatedly making and 
 breaking itself. One of the wires from the battery to the bell is 
 cut at the point P, and a push button is inserted. This is shown 
 in section to the right. An insulating knob, P, when pressed, 
 brings a spiral spring, which is connected with one end of the cut 
 wire, into contact with the other end. The circuit being closed 
 thus, the bell commences to ring. 
 
 659. Galvanometers. These instruments are employed in 
 the laboratory for the determination of nearly all electrical magni- 
 
 FIG. 375. 
 
 tudes. They serve to detect the presence of electrical currents 
 and to determine their strengths and directions. The principle of 
 their action is electro-magnetic. Suppose a magnetic needle (Fig. 
 375), free to move about a pivot, to lie in the direction of the 
 earth's magnetic meridian. Suppose further, that it be surrounded 
 by a coil of wire, whose windings are parallel to the axis of the 
 needle. If, now, an electrical current be sent through the coil, it 
 will develop magnetic polarity in the coil so that, e.g., its east side 
 will be equivalent to a north pole and its west side to a south pole. 
 The needle will, under this influence, tend to place itself in an east 
 and west direction. It will not quite attain this direction, for it is 
 influenced by the earth's magnetism at the same time, and this 
 tends to keep it in the meridian. Upon reversing the direction of 
 the current, the polarities of the sides of the coil become reversed, 
 and the needle turns so that its poles project from opposite sides 
 
422 ELECTRICITY AND MAGNETISM. 
 
 of the coil. The side toward which the north end of the needle 
 turns determines the direction of the current in a given galvano- 
 meter. The angle through which the needle is deflected deter- 
 mines the strength of the current flowing. 
 
 TANGENT GALVANOMETEKS. If the wire of a galvanometer be 
 wound on the circumference of a ring, whose diameter is at least 
 twelve times the length of the needle at its centre, the strengths of 
 currents causing different deflections will be proportional to the 
 tangents of the corresponding angles of deflection. Such an in- 
 strument is called a tangent galvanometer. The reason for having a 
 large diameter for the coil is that those of its lines of force, which 
 are cut by the short needle in its excursions, are then straight and 
 perpendicular to the earth's lines. The magnet's pole is thus 
 moved under the influence of two forces, which act continuously at 
 right angles to each other. The law of the tangents then follows. 
 
 REFLECTING GALVANOMETERS. In refined laboratory measure- 
 ments the determination of a needle's deflection, by observing the 
 movement of a pointer over a divided scale, is inaccurate and in- 
 convenient. Instead, a small mirror is attached to the magnet and 
 the deflections are measured by the different divisions of a sta- 
 tionary divided scale, which are reflected from the mirror into a 
 stationary telescope. The arrangement is shown in Fig. 319. 
 
 A method, much used in England, is to have the mirror reflect 
 a ray of light from a small hole in an opaque chimney of a lamp 
 upon a stationary scale. The method is very inconvenient, as it re- 
 quires the observations to be made in a darkened room. The ac- 
 curacy to be obtained is not as great as by means of a telescope 
 and scale. 
 
 BALLISTIC GALVANOMETERS. In many determinations it. is re- 
 quired to measure currents which last but for an instant, or to 
 measure, q uantities of electricity. The difficulties connected with 
 these determinations are much lessened if the time required by 
 the galvanometer needle to make a single oscillation be very great, 
 as compared with the time occupied by the electricity in passing. 
 Thus galvanometers whose needles have periods of from five to 
 twenty-five seconds are used, and are called ballistic galvanometers. 
 
 DIFFERENTIAL GALVANOMETERS. These instruments are supplied 
 with two sets of coils, which are so placed that they will produce 
 the same electro-magnetic effect upon the single needle, providing 
 they be traversed by currents of the same strength and direction. 
 By means of this instrument a current in one coil may be brought 
 to a given strength by being made to neutralize the effect upon 
 the needle from another current, which is of constant (the required) 
 strength and passes through the other coil in an opposite direction. 
 
CHAPTER VII. 
 
 FIG. 376. 
 
 ELECTRO-DYNAMICS. 
 
 660. Movement of Conductors Carrying Currents. In 
 
 the preceding chapter it has been shown that a conductor carrying 
 an electrical current, and placed in the vicinity of a magnet, tends 
 to move the magnet, so that the lines of force from each may be- 
 come parallel, or, if the magnet be stationary, the conductor strives 
 to move, to attain the same end. As might be expected, two 
 neighboring conductors, while traversed by currents, tend to move 
 so as to render their lines of force parallel. 
 
 Without any knowledge of the existence or properties of lines 
 of force, Ampere, in 1821, arrived, by experiment, at the following 
 laws, which could easily have been predicted by such a knowledge. 
 
 661. Parallel Currents. 
 
 1. If galvanic currents flow through parallel wires in the same 
 direction, they attract each other ; if in opposite directions, they 
 repel each other. These ef- 
 fects are shown by suspend- 
 ing wires, bent as in Fig. 
 376, so that their lower ends 
 may dip into four separate 
 mercury cups, a, b, a', b', by 
 means of which connection 
 between the wires C and D 
 land the battery may be 
 readily made. The sus- 
 pending threads should be 
 
 two or three feet long, and the mercury cups should be large 
 enough to allow considerable lateral movement of the wires. If 
 simultaneous currents be sent through the two wires G and D, in 
 the same direction, the wires will move toward each other; if 
 currents be sent through the wires in opposite directions at the 
 same time, they will separate more widely. 
 
 Hence, when a current flows through a loose and flexible helix, 
 each turn of the coil attracts the next, since the current moves in the 
 same direction through them all. In this way a spiral suspended 
 above a cup of mercury, so as to just dip into the fluid, will vibrate 
 up and down as long as a current is supplied. The weight of the 
 helix causes its extremity to dip into the mercury below it ; this 
 closes the circuit, the current flows through it, the spirals attract 
 
424 
 
 ELECTRICITY AND MAGNETISM. 
 
 each other, and lift the end out of the mercury ; this breaks the 
 circuit, and it falls again, and thus the movement is continued. 
 
 2. If currents flow through two wires near each other, which 
 are free to change their directions, the wires tend to become paral- 
 lel to each other, with the currents flowing in the same direction. 
 Thus, two circular wires, free to revolve about vertical axes, when 
 currents flow through them, place themselves by mutual attrac- 
 tions in parallel planes, as in Fig. 377, or in the same plane, as in 
 
 FIG. 378. 
 
 Fig. 378. In the latter case, we must consider the parts of the 
 two circuits which are nearest to each other as small portions of 
 the dotted straight lines, c d and ef. 
 
 It appears, therefore, that galvanic currents, by mutual attractions 
 and repulsions, tend to place themselves parallel to each other in such 
 a manner that the flow is in the same direction. 
 
 The force exerted between two parallel portions of circuits is 
 proportional to the product of the current strengths, to the length 
 of the portions, and inversely proportional to the distance between 
 them. The force exerted by each current acts in a direction per- 
 pendicular to the direction of the current. 
 
 662. Currents not Parallel. Currents, both of which flow 
 toward a common point, or both of which flow away from a common 
 point, attract each other. 
 
 If one of two currents flows toward, and the other away from a 
 common point, the two currents repel each other. 
 
 These cases are evident deductions from the preceding para- 
 graph. Suppose the two currents (Fig. 379) to flow in A and B 
 as though they came from <?, then the tendency of the wires A and 
 E is towards parallelism, and as we suppose the currents to flow 
 from the direction C, the wires must tend to move toward each 
 
ELECTRODYNAMIC ROTATION. 
 
 other in order to become parallel. The same effect would be pro- 
 duced if the currents in A and B were to flow towards C. But if 
 the current in A flows from 
 
 the direction C7, and that in B FIG. 379. 
 
 towards the point C, then the 
 tendency of the wires to be- 
 come parallel, with the cur- 
 rents flowing in the same 
 direction, causes B to revolve 
 
 about C as a centre till it reaches the position B' y and then the 
 condition that the currents shall flow in the same direction will be 
 fulfilled. It is not necessary that we should regard A and B as ly- 
 ing in the same plane. 
 
 A sinuous current produces the same effect as a straight cur- 
 rent having the same general direction and length. If a conductor, 
 having one portion sinuous and the other straight, be bent as in 
 Fig. 380, so that the current may flow from a to b through the 
 
 FIG. 380 
 
 FIG. 381. 
 
 straight part, and from b to c through the sinuous part, the two- 
 portions of the current thus flowing close together in opposite di- 
 rections, the joint electro-dynamic effect upon a movable conductor 
 parallel to a b will be inappreciable. 
 
 663. Continuous Rotation Produced by Mutual Action 
 of Currents. Suppose a continuous current to flow through a 
 
 wire A, as indicated in Fig. 
 381, and that a wire B, so 
 bent as to dip into the mer- 
 cury cup m at one end, and 
 into the annular mercury 
 trough n at the other, be 
 suspended at the middle, a 
 counterpoise, C, keeping it 
 balanced. 
 
 If, now, a current be made 
 to flow from the cup w, 
 through B, and thence out 
 again by means of the mercury contact in n, the wire B will rotate 
 in a direction opposite to that of the current in A ; for the current 
 in B, and that in the part of A to the right of n, are both flowing 
 towards n and hence attract, while the current in B and that part 
 
426 
 
 ELECTRICITY AND MAGNETISM 
 
 of the current in A immediately to the left of n are flowing in 
 directions to cause repulsion. 
 
 A beautiful experiment, illustrating continuous rotation, is to 
 place a round, shallow dish, containing mercury, on the pole of a 
 vertical, straight electro-magnet. Excite the magnet and dip the 
 terminals of a circuit, carrying a strong current, into the mer- 
 cury at the centre and side of the dish respectively. A portion of 
 the mercury carries the current from the centre to the edge of the 
 dish. In doing so it is made to rotate by the action of the lines of 
 force from the magnet. As soon as it has rotated a new portion 
 of the mercury is made to carry the current. This, in turn, gives 
 way to another portion, and the whole body of mercury is soon set 
 into rapid rotation. Centrifugal force, resulting from the rotation, 
 causes the mercury to heap up around the edges of the dish, and 
 to be depressed at the centre. 
 
 FIG. 382. 
 
 664. Electro-dynamometer. This instrument, invented by 
 Weber, is used for measuring the strengths of electrical currents. 
 Its action depends upon the electro-dynamic attractions discussed 
 in Art. 661. The principles of its construction are shown in the 
 crude apparatus represented in Fig. 382. This consists of a fixed 
 hollow coil of wire, in the centre of which 
 is suspended another smaller coil. The 
 suspension is made by means of two fine 
 parallel wires, placed one or two milli- 
 metres from each other. The upper ends 
 of these wires are connected to two in- 
 sulated binding-posts, and the lower ends 
 are connected with the terminals of the 
 suspended coil. The suspension is so 
 arranged that, when no current is pass- 
 ing through the dynamometer, the planes 
 of the two coils are perpendicular to each 
 other. If, now, a current of electricity 
 be sent through the apparatus (in the fol- 
 lowing order through the external coil, 
 down one suspension wire, through the 
 inner coil and up the other suspension 
 wire), the suspended coil will turn and 
 strive to cause a parallelism of the planes 
 
 and currents of both coils. The turning force of the currents is 
 resisted by an increasing force exerted by the twisted wire sus- 
 pension. With a certain current the coil will be deflected a 
 certain amount i.e., until the two opposing forces are equal. 
 
INDUCED CURRENTS. 427 
 
 With a stronger current the deflection will be greater. Thus the 
 magnitude of the deflection can serve as a measure of the current 
 strength. 
 
 A peculiarity of the electro-dynamometer is that it serves to 
 measure alternating currents, i.e., those which change their direc- 
 tion, perhaps, several thousand times per minute, equally as well 
 as continuous currents. A change in the direction of flow of the 
 main circuit changes the direction in both coils. This does not 
 alter the direction of the deflection. 
 
 CHAPTER VIII. 
 
 ELECTRO-MAGNETIC INDUCTION. 
 
 665. Currents of Electricity Produced by Induction. 
 It has been shown that when a current of electricity flows through 
 a conductor the air or other dielectric which surrounds the con- 
 ductor is traversed by lines of force. The presence of these lines 
 indicates that the dielectric is under some sort of a strain. To pro- 
 duce this strain energy must have been expended by the current 
 when it commenced to flow. During the short time that the strain 
 is being produced there is an opposition to the exciting current, 
 which, is equivalent to a current in an opposite direction. Now, it 
 is reasonable to suppose that, if lines of force or a magnetic field 
 be produced by some agency around a closed circuit which is 
 primarily traversed by no current, a current will be produced in 
 this circuit. The direction will be opposite to that which would 
 be necessary to create the field, and will last only for the time nec- 
 essary to produce the strain. Furthermore, upon destroying the 
 field it is reasonable to suppose that the energy which it represents 
 will appear as a current in the same direction as one which could 
 produce the field. These suppositions are substantiated by experi- 
 ment, as was first shown by Faraday. The currents are called 
 induced currents (not to be confounded with induced electro- 
 static charges), and those currents whose directions are the same as 
 a current which could produce the field are termed direct currents, 
 while those in an opposite direction are called inverse currents. 
 
 666. Methods of Producing the Inducing Field. Inas- 
 much as induced currents are produced by any variation in the 
 strength of the field around the conductor which carries them, 
 they can be produced either by varying the strength of the field 
 
428 
 
 ELECTRICITY AND M AG N ETISM. 
 
 FIG. 383. 
 
 current or by moving the conductor into fields of various strengths, 
 For the sake of clearness suppose that we are supplied with the 
 
 apparatus represented in 
 Fig. 383. c is the primary 
 coil of wire which produces 
 the field, and is traversed 
 by a current from the bat- 
 tery. The secondary coil, in 
 which induced currents are 
 to be produced, is repre- 
 sented at d. Its terminals 
 are connected with a gal- 
 vanometer, which indicates 
 the presence and direction 
 of the induced currents. 
 Now suppose that c be 
 placed inside of d. Upon 
 starting the current in c an 
 inverse current will be in- 
 duced in d, and upon 
 
 stopping it a direct current will be induced. Permitting the cur- 
 rent in c to flow, increasing or decreasing its strength will produce 
 inverse or direct induced currents respectively. If the current 
 strength in c be maintained constant, removing the coil c will pro- 
 duce a direct current, and replacing it an inverse induced current. 
 Induced currents may also be produced by magnets. Consider 
 a magnet to be the equivalent of a solenoid traversed by a current 
 (Art. 651). Dispensing with the battery we have the apparatus in- 
 
 FIG. 384 
 
 FIG. 385. 
 
 dicated in Fig. 384 An inverse current will be induced by the in- 
 troduction of the magnet into the secondary coil, and a direct cur- 
 
SELF-INDUCTION. 429 
 
 rent upon removing it. An inverse current may also be induced by 
 strengthening the field of a magnet which is stationary within the 
 secondary, by bringing a piece of iron near to it. In this case the iron 
 becomes a magnet by induction, as shown in Fig. 385, and adds its 
 lines of force to the field. Direct induced currents will follow the 
 removal of the iron. 
 
 It is well to remark that, as motion is merely relative, it is im- 
 material whether a magnet be placed in a secondary coil or the lat- 
 ter be placed around the magnet. 
 
 The facts which have been mentioned may be summed up in a 
 single law : 
 
 Inverse induced currents always result from an Increase in the 
 number of lines of force which pass through the circuit, and Direct 
 induced currents always result from a Decrease in the number of 
 these lines. 
 
 667. Lenz's Law. If two conductors, A and B, in one ofwhich f 
 A, a current is flowing, be made to change their relative positions, then 
 a current will be induced in B in a direction which will cause a mu- 
 tual action in tlte two conductors tending to oppose their motion. 
 Thus, if A and B be brought nearer together an inverse current will 
 flow in B, and currents flowing in opposite directions repel each 
 other ; and if A and B be caused to move apart, then a direct sec- 
 ondary current ^Yill flow in B, and currents flowing in the same 
 directions will attract each other. This statement of the results of 
 experiments will aid the memory in regard to the directions of the 
 primary or secondary currents. 
 
 663. Self-induction. Whenever a current is started in a coil 
 of wire, lines of force are created which increase in number from 
 zero to a maximum. Owing to the increase, they induce cur- 
 rents in the coil which are opposite to the direction of the original 
 current. "Upon stopping the original current the lines of force 
 decrease in number and thus induce a direct current in the coil. 
 The induction in such a case is termed self-induction, and the cur- 
 rents are termed extra or self-induced currents. 
 
 The existence of self-induced currents may be demonstrated 
 by the Wheatstone bridge combination (Art. 646). Let three of 
 the arms of the bridge be made up of resistances without self-in- 
 duction (Art. 645), the fourth arm consisting of an ordinary unifilar 
 coil. For the purpose of increasing the self-induction of this fourth 
 arm, insert a piece of soft iron in the coil. Obtain a balance in the 
 bridge by employing a constant purrent. When a balance has 
 been obtained the galvanometer will show no deflection. If . the 
 
430 ELECTRICITY AND MAGNETISM. 
 
 current be now stopped, the current induced in the fourth arm will 
 cause a deflection of the galvanometer needle. 
 
 669. Coefficients of Mutual and Self-induction. It can 
 be proved mathematically that the electro-motive force induced in a 
 closed circuit is equal to the rate of variation of the number of lines 
 of force which pass through it. 
 
 If in a short interval of time dt, the number of lines of force N 
 increases a small amount dN, then the electro-motive force 
 
 v dN 
 
 E = ~w 
 
 will be induced in the circuit which surrounds these lilies. In case 
 two coils, a primary and secondary, be fixed in position, and the 
 strength of the current in the primary be increased by an amount do 
 in the short time dt, then the electro-motive force 
 
 w nr dc 
 
 E= ~ M dt 
 
 will be induced in the secondary during that time. M is a constant 
 which is called the coefficient of mutual induction between the two 
 coils. Its value depends upon the shape and number of windings 
 of wire around the respective coils and their relative positions. It 
 is numerically equal to the number of absolute lines of force which 
 would be sent through either coil when an absolute unit current of 
 electricity was sent through the other coil. It makes no difference 
 which coil be chosen as a primary in determining M. 
 
 If it be supposed that the two coils be made to coincide, i.e., 
 that there be but one coil, then the electro-motive force of self- 
 induction 
 
 The constant L is called the coefficient of self-induction, and is 
 equal to the number of absolute lines of force which a coil would 
 send through itself if it were traversed by an absolute unit of current. 
 
 670. Induced Currents from the Earth. If a coil (whose 
 terminals are connected with a sensitive galvanometer) be placed 
 so that its axis is parallel with the axis of a dipping-needle (Art. 
 621), it will be pierced by a maximum number of the earth's lines 
 of magnetic force. If it be now turned through 90 around an 
 axis perpendicular to its own axis, the number of the lines piercing 
 it will decrease to zero, and the galvanometer will indicate that a 
 current is being induced by the rotation. 
 
 Continuous variations in the strength of the earth's magnetism 
 sometimes induce currents of considerable strengths in long tele- 
 graphic circuits. Such currents are known as earth currents. 
 
OF THE 
 
 (UNIVERSITY 
 
 INDUCTION CfrJ4 1 Sj n iAx' 431 
 
 671. Arago's Rotations. In 1824 Arago observed that the 
 collations of a magnetic needle were reduced in number by sus- 
 pending a copper plate above it. This observed phenomenon soon 
 led him to the discovery that if a horizontal copper disc be made 
 to rotate rapidly, a magnetic needle suspended above it would ro- 
 tate also. This effect may also be produced with other metals 
 though in less degree. 
 
 If a disc of copper be set spinning on an axis, between the 
 poles of a powerful electro-magnet whose circuit is broken, the axis 
 of the disc being parallel to the lines of force, the rotation con- 
 tinues with slight loss of velocity for a long time ; but if the circuit be 
 suddenly closed the rotation is at once checked, or possibly stopped. 
 If such a disc be kept in rapid rotation by a suitable band and 
 pulley, after the circuit is closed, the disc will be heated by the 
 action of the magnet. 
 
 These effects were explained by Faraday as being due to cur- 
 rents induced in the mass of metal. Thus let a needle, N S (Fig. 
 386), be suspended above a metal disc A B. The magnetic cur- 
 rents flow around the needle as indicated in 
 the figure, the currents below the needle from FlG - 
 
 right to left as shown by the dotted arrow, and 
 those above from left to right, as shown by the 
 full arrow. Now suppose the disc to be ro- 
 tated in the direction from A to B ; the por- 
 tions of the currents around 2V 8 which are 
 nearest to the disc will induce in that part 
 of the disc towards A currents whose direc- 
 tions are such as to resist the motion of the 
 disc, according to Lenz's law (Art. 667), that is to say, currents 
 will flow in the disc from left to right ; while in that part of the 
 disc towards B, which is moving away from N, the induced cur- 
 rents are from right to left, and so resist the motion of B away 
 from N. 
 
 If the needle had been moved, the disc remaining fixed, the 
 same analysis of the motion might be made, and we should find 
 that the disc would resist the motion of the needle. A copper col- 
 lar or frame is sometimes used to coil the galvanometer wire upon, 
 in order to reduce or damp the oscillations of the needle, and bring 
 it more quickly to rest. 
 
 672. Induction Coils. These instruments serve to trans- 
 form currents of low E. M. F. into alternating currents of high E 
 M F. Their forms and sizes are many, and only their principle 
 need be mentioned here. A continuous current of low E. M. F. is 
 passed through a primary coil made of a few turns of coarse insu- 
 
432 
 
 ELECTRICITY AND MAGNETISM. 
 
 FIG. 387. 
 
 lated copper wire (Fig. 387). The centre of the coil is filled witb 
 a core of soft iron wires. Before passing through the coil the cur- 
 rent traverses some sort 
 of a current - breaker, 
 e.g., the one shown in 
 the cut acts upon the 
 same principle as the 
 breaker of the electric 
 bell described in Art. 
 658. By means of this 
 breaker the current in 
 the primary is rapidly 
 made and broken. Al- 
 ternating currents are thus induced in a secondary surrounding 
 coil, which is wound with many turns of .very fine insulated wire. 
 The E. M. F. of these induced currents is great because the co- 
 efficient of mutual induction is great. This is owing to the large 
 number of turns of wire in the secondary and to the presence of 
 the iron core. Both conspire to cause a large number of lines of 
 force to pierce the circuit during the short interval required to 
 make the circuit of the primary. 
 
 The function of the induction coil, as here given, is often re- 
 versed, in which case it becomes what is termed a transformer. 
 Transformers are much used in the commercial distribution of 
 rapidly alternating currents for lighting and other purposes. Al- 
 ternating currents of high E. M. F. and low current strength are 
 received from a main line into the finer wire coil of an induction 
 coil. The thick wire coil of the transformer is connected with the 
 customer's home circuit, and delivers to it currents of great strength 
 but at low potential. 
 
 673. The Telephone. This instrument for reproduction of 
 sound at a distance by means of electric currents is shown in sec- 
 tion in Fig. 388, in which a a' is a disc or diaphragm of thin soft 
 iron, the circumference of 
 
 which is firmly clamped FIG. 388. 
 
 between the mouth guard 
 m m' and the case n ri, 
 upon the centre of which 
 the sound-waves from the 
 mouth impinge, as at E t 
 and communicate to it vi- 
 brations corresponding to 
 
 the simple or composite sounds uttered. These vibrations of the 
 disc cause a continual variation in the distance of the disc fron> 
 
BLAKE TRANSMITTER. 
 
 433 
 
 the end of a bar magnet, b. Around the end of the magnet near- 
 est to the diaphragm a a' is a coil, c c', of fine insulated copper 
 wire, the ends of which are connected with binding-posts, d d\ 
 From these posts are carried wires to another precisely similar 
 instrument at the station with which communication is to be held. 
 "When a word is spoken into the instrument at E, the vibrations 
 communicated to the disc a a' cause variations in the magnetic 
 field of the bar 6, and these variations induce electric currents 
 which flow in the coil c c', and thence through the connecting 
 wires to the coil in the instrument held to the ear of the listener, 
 and these currents in the last-named coil produce variations in 
 the strength of the magnet of the receiving instrument, causing 
 precisely the same vibrations in its diaphragm as were originally 
 set up in the first. The vibrations of the diaphragm are trans- 
 mitted through the air to the ear ; and though no sound has been 
 transmitted from one station to the other, the words spoken into 
 one instrument are distinctly delivered by the other. The sound 
 vibrations are the cause of electric currents, and these in turn 
 finally produce sound vibrations again. 
 
 To such perfection of action have these instruments been 
 brought, that not only can the spoken words be heard, but the 
 peculiar characteristics of voice are so faitkfully reproduced that 
 by these the speaker may be recognized. 
 
 674. The Blake Transmitter. The electro-motive forces 
 generated by the moving diaphragm of the Bell telephone are 
 not sufficiently large to produce 
 satisfactory results on long lines. 
 Therefore an instrument termed a 
 transmitter is substituted for the 
 telephone at the sending end of 
 the line. A common and very 
 satisfactory form of transmitter 
 is one designed by Francis Blake. 
 It is represented in Fig. 389, and 
 its action depends upon the prin- 
 ciple that the electrical resistance 
 offered by a carbon contact varies 
 greatly with the pressure exerted 
 upon it. 
 
 The sound to be transmitted 
 is received in the mouth-piece M, 
 which causes it to set the diaphragm D into corresponding vibra- 
 tions. Touching the rear of the diaphragm is a platinum or car- 
 'bon point, which is attached to a piece of watch-spring, aud which 
 
 FIG. 389. 
 
434 ELECTRICITY AND MAGNETISM. 
 
 is in connection with one terminal of a battery, B. (This battery- 
 is brought into circuit only as the transmitter is to be used.) The 
 point forms a loose contact, C, with a carbon button, which is also 
 mounted upon a spring. The current from the battery flows 
 through this contact to the rest of the circuit. As the diaphragm 
 vibrates it causes the point to exert correspondingly different 
 pressures upon the button. The resistance of the circuit is thus 
 varied, and this results in variations in the current which are the 
 electrical counterparts of the sound vibrations. 
 
 A Bell receiver, placed in the same circuit with the battery and 
 transmitter, will yield, besides the transmitted sound, a disagreeable 
 " sizzling " noise. To obviate this an induction coil, /, is intro- 
 duced. The varying current from the battery and transmitter is 
 passed through the primary of a small induction coil, and the line 
 wires, with their receivers included, are connected with the second- 
 ary coil. In this case the currents on the line flow in opposite 
 directions to what they would, if connected directly with the trans- 
 mitter circuit. This, however, is of no consequence. 
 
 The springs of the transmitter, which bear the carbon button 
 and platinum point, are fastened to one piece of brass, but are insu- 
 lated from each other. The amount of pressure at the contact is 
 regulated by a screw, whose end tits the bent end of the brass 
 holder. The holder is supported by pliable spring bands which- 
 are attached to the case of the transmitter. Although this method 
 of adjustment is simple and appears crude, the delicacy of it is- 
 marvellous. 
 
 675. Dynamos. These machines are for converting mechani- 
 cal energy into electrical currents. A discussion of the principles 
 of their construction is here out of place, and the student is re- 
 ferred to some one of the many technical treatises on the subject. 
 The principle of their action may be described. 
 
 The dynamo has two essential parts a movable * conductor, 
 called an armature, and a magnet, in whose field the armature 
 moves. The armature, by its motion, varies the number of the 
 field lines which pass through it, and is therefore traversed by in- 
 duced currents. 
 
 Fig. 390 (taken from S. P. Thompson's " Dynamo-Electric Ma- 
 chinery ") represents an ideal dynamo in its simplest form. N and 
 S are the poles of a field electro-magnet. The lines of force pass 
 between the poles and pierce the looped conductor C, which forms 
 the armature. The armature, in the position indicated by the con- 
 
 * In some machines the armature is stationary and the field magnets are- 
 movable. 
 
DYNAMOS. 
 
 435 
 
 tinuous lines, is pierced by a maximum number of the field lines ; 
 upon, turning through 90, coming then into the position indicated 
 
 FIG. 390. 
 
 by the dotted lines, it is pierced by none of the lines. During 
 the whole quarter revolution there has been a decrease in the num- 
 ber of lines passing through the loop. An induced current, flow- 
 ing in a certain direction, has accompanied the movement. During 
 another quarter revolution the number of penetrating lines will be 
 on the increase, but they now pass through the loop in an oppo- 
 site direction to what they did before, and hence the induced cur- 
 rents which result from the increase are in the same direction, 
 referred to the conductor, as during the first quarter revolution. 
 During the next two quarter revolutions the induced currents will 
 flow in an opposite direction. Thus by continuous revolution the 
 armature is traversed by currents which reverse their directions 
 twice each revolution. 
 
 In order to lead the currents from the armature into a circuit 
 where they can be used, and in order to rectify them, i.e., cause 
 them to flow in the same direction, use is made of a commutator. 
 Fig. 391 represents a two-part commutator suited for our single- 
 loop armature. It consists in an insulating 
 cylinder, to be applied to the extremity of the 
 axis of the armature. Upon it is slid a metal 
 tube slit into two parts. To each part is con- 
 nected one of the ends of the loop, as shown in 
 Fig. 390. Against the commutator are pressed 
 two spring brushes, B B, which are connected 
 with the two terminals of the outside circuit 
 respectively. The commutator revolves with the armature, but 
 the brushes remain stationary. Both are so arranged that at the 
 instant the plane of the loop of the armature passes through 
 the vertical plane, the brushes will slide from one segment of the 
 commutator to the other. At this instant the induced current 
 reverses the direction of its flow, and the commutator, exchanging 
 
 FIG. 391. 
 
4:36 ELECTRICITY AND MAGNETISM. 
 
 the connections with the external circuit, causes the external cur* 
 rent to flow in one direction. 
 
 The E. M. F. which could be obtained from such an ideal dy- 
 namo would be very small. To increase it, the total number of 
 lines of force which are passed through or taken out of the circuit 
 in a unit time must be increased. There are three \vajs in which 
 this may be accomplished : the speed of revolution, the number of 
 loops in the armature, or the strength of the field may be increased. 
 It need not be considered here how this is carried out in practice. 
 
 The field magnets of a dynamo may be excited by currents from 
 an external source, by the whole of the machine's armature current, 
 or by only a portion of the armature current. The dynamos are then 
 termed separately excited, series, or shunt machines respectively. 
 
 When the field is furnished by permanent magnets the machine 
 is no longer termed a dynamo, but a magneto-electrical generator. 
 Such machines are not a commercial success except in the very 
 small sizes. 
 
 676. Electric Motors. The function of these machines is 
 the converse of that of dynamos. They are intended to transform 
 electrical energy into motion. The dynamo of the previous article 
 becomes an ideal motor by simply sending through it, from the ex- 
 ternal circuit, a current in an opposite direction. The commutator 
 accomplishes that the lines of force, due to the current flowing in 
 the armature, shall never become parallel to the field's lines. In 
 striving to secure such parallelism the armature revolves upon its 
 axis, and just as it is about to reach the goal the commutator re- 
 verses the direction of its lines, and it moves through another half 
 revolution to be again frustrated in its attempts. 
 
 CHAPTER IX. 
 
 ELECTRO-CHEMISTRY AND ELECTRO-OPTICS. 
 
 677. Electrolytes. Liquids may be divided into three classes, 
 depending upon their behavior towards the electrical current 
 those which do not conduct at all, as kerosene, turpentine, and oils 
 generally; those which conduct without decomposition, e.g., mer- 
 cury and molten metals ; those which are decomposed when they 
 conduct a current, e.g., solutions of acids or metallic salts and cer- 
 tain fused solid compounds. The liquids of the last class are 
 called electrolytes, and the process of decomposing an electrolyte by 
 
ELECTROLYSIS OF SALT SOLUTIONS. 
 
 43 r 
 
 FIG. 392. 
 
 means of an electrical current is termed electrolysis. The two 
 parts into which the electrolyte is decomposed are termed ions. 
 
 678. Electrolysis of Sulphuric Acid. If a current of 
 electricity flows into a solution of sulphuric acid (H 2 SO 4 ) in water 
 by means of an electrode, and if, after traversing the solution, it 
 flows out through another electrode, then it will, by its passage, 
 decompose the acid into two parts H 2 and SO 4 . The hydrogen 
 will appear, in the form of gas bubbles, at the electrode through 
 which the current makes its exit from the solution. The SO 4 will 
 endeavor to appear at the . electrode where the current entered, 
 but the water of the solution seizes upon it, and together they 
 form sulphuric acid, leaving, however, one portion of oxygen to 
 appear, as gas, at the electrode. The effect 
 
 of the passage of the current is to virtually 
 decompose water (H 2 O) into hydrogen and 
 oxygen, there .being twice as much of the 
 former as of the latter. 
 
 Hoffmann's apparatus for electrolyzing 
 sulphuric acid is shown in Fig. 392. The 
 dilute acid solution is poured into the funnel 
 F, and flowing into the two arms of the front 
 U-tube fills them, providing the stop-cocks 
 at their tops be opened. After filling, the 
 cocks are closed and a current is made to 
 pass between the two platinum electrodes E 
 E. The gases which are evolved at the elec- 
 trodes rise in the respective tubes above them 
 and displace the liquid. These gases are 
 subjected to the same pressure exerted by 
 the liquid in the funnel. Their volumes may be read off from 
 graduations on the tubes containing them. The gases may be 
 taken off through the cocks and their natures tested the oxygen 
 being made to relight a glowing taper and the hydrogen being 
 made to explode when mixed with air in a test-tube. 
 
 679. Metallic Salts. When the electrolyte is a metallic salt 
 solution the metal will be deposited at the electrode where the current 
 leaves the solution. The acid of the salt appears at the other elec- 
 trode. The metal may be deposited upon the surface of the 
 electrode in the form of a thin metallic film. In case the metal 
 has a strong affinity for the water of solution, e.g., sodium in water, 
 it will go into solution arid hydrogen will be evolved as a secondary 
 product. It is nevertheless true that Davy obtained metallic 
 .sodium and potassium by the electrolysis of strong caustic soda 
 
438 ELECTRICITY AND MAGNETISM. 
 
 and potash. These metals may be obtained by electrolysis, if a 
 mercury electrode be employed. They then appear in the form of 
 amalgams. 
 
 The character of a deposited metal often varies under different 
 current strengths or different concentrations of solution. Copper 
 may be deposited in the form of a black powder instead of an 
 even metallic film. Silver may appear in the form of crystals. 
 Platinum generally appears as a black, finely divided sponge. Tin, 
 from tin chloride, forms a beautiful " tree " of tin crystals, the 
 branches spreading out gracefully from the electrode. 
 
 680. Faraday's Laws. Faraday proved that a given quan- 
 tity of electricity always deposits the same weight of a given ion from 
 an electrolyte through which it passes. Thus a coulomb of elec- 
 tricity always deposits .001118 gram of silver on an electrode. It 
 makes no difference whether the electrolyte be molten silver iodide 
 or chloride, or whether it be a water solution of silver nitrate, sul- 
 phate, acetate, or cyanide. The passage of one coulomb is always 
 accompanied by the deposition of this much silver. The weights 
 of other chemical elements which a coulomb will deposit are in pro- 
 portion to their chemical equivalents This being so, it must be con- 
 cluded that a given quantity of electricity ruptures the same 
 number of molecular valencies, whatever the electrolyte may be. 
 
 681. Voltameters. From Faraday's laws it will be readily 
 seen that from weighing the amount of an ion, which is deposited 
 by the passage of a certain quantity of electricity, this quantity may 
 be determined. Thus, if a certain quantity deposits silver on an 
 electrode so as to cause it to weigh 1.118 gram more than before 
 the passage, it is evident that 1,000 coulombs have passed. If the 
 quantity passed in the form of a constant current, which lasted for 
 1 second, then the current strength was 1,000 amperes. For an 
 ampere means a strength of current which delivers 1 coulomb per 
 second, but in this case 1,000 coulombs were delivered in a second. 
 In general, if z the electro-chemical equivalent of the substance 
 deposited, i.e., grams per coulomb, c = the current in amperes, 
 t = time in seconds that the current was maintained, the weight 
 of the substance deposited 
 
 w c z t. 
 
 In case w and t are measured, the current strength may be de- 
 termined by the formula 
 
 w 
 
 c = ~t 
 
 Instruments for measuring current strengths in this manner are 
 called voltameters. The substances generally employed for depo- 
 
ELECTROPLATING. 439. 
 
 sition are copper from a solution of its sulphate, silver from its 
 nitrate, and hydrogen from dilute H 2 SO 4 . In the case of hydro- 
 gen weighing is difficult, hence the volume is measured and then 
 reduced to 760 mm. pressure and C. 
 
 A current of 1 ampere deposits in 1 minute, of 
 
 Hydrogen (at 760 mm. and C.) 6.942 cu. cm. 
 
 Copper 01969 gram. 
 
 Silver 06708 gram. 
 
 Zinc 02018 gram. 
 
 The Edison electrical companies place zinc voltameters in the 
 houses of their customers, and thus measure the quantity of elec- 
 tricity consumed. 
 
 682. Theory of Electrolysis. The most satisfactory ex- 
 planation of the phenomena of electrolysis is embodied in the the- 
 ory of Grotthuss, somewhat modified by Clausius. The molecules 
 of an ordinary solution are supposed to be in constant vibration in 
 all possible directions. Owing to collisions between the molecules, 
 or other causes, the constituent atoms are constantly leaving their 
 partners and combining with others to form new molecules. Every 
 molecule, having unit valency, is charged with the same quantity 
 of electricity half being positive and half negative. The positive 
 resides on one ion of the molecule and the negative on the other. 
 Now, upon subjecting the solution to a difference of potential be- 
 tween the electrodes, the direction of the molecular motions is 
 controlled, and ions, which by chance are isolated, will tend to 
 move towards one or the other electrode, according to the signs 
 of the charges which are upon them. If the impressed electro- 
 motive force is large enough to prevent recombination of these ions, 
 they will continue their movements towards the electrodes, and 
 will accumulate around them. Upon touching the electrodes they 
 impart to them their minute charges and the continuous accumula- 
 tion of these maintains a current in the circuit. 
 
 According to this theory, electrolytic conduction of electricity 
 is similar to the convection of heat in liquids. The transportation 
 of electricity is accompanied by a transportation of matter. 
 
 The remarkable connection between the results of the quanti- 
 tative work of Faraday and the chemical equivalents of the ele- 
 ments, points to electrolysis as a fertile field for the investigation 
 of the yet unknown nature of chemical affinity. 
 
 683. Electroplating. The principles of electrolysis are made 
 use of in the mechanic arts. Articles made of baser metals are 
 covered over with a thin deposit of silver or gold and are said to- 
 
 TTTCTTTT-TP-DOT 
 
440 ELECTRICITY AND MAGNETISM. 
 
 have been electroplated. The articles to be plated are suspended 
 in a bath from a metallic rod, which is in electrical communication 
 with the negative pole of a battery or dynamo (Fig. 393). The 
 
 bath consists of a solution 
 of some salt of the metal 
 which is to be deposited, 
 e.g., silver or gold cyanide. 
 The current from the posi- 
 tive pole of the dynamo en- 
 ters the solution by means 
 of an electrode, C, made of 
 the same metal as that which 
 is contained in the salt. 
 Upon passing a current, the 
 
 salt of the solution is decomposed the metal depositing on the 
 article to be plated, and the acid combining with the electrode C 
 to form new salt, thus maintaining the concentration of the solu- 
 tion. The articles to be plated must be thoroughly scoured and 
 cleansed before immersion in the bath. The character of the 
 results obtained depends much upon the character and concen- 
 tration of the baths and upon the magnitude of the currents and 
 electro-motive forces employed. Full details must be looked for 
 in technical books. 
 
 684. Electrotyping. If the object to be plated consists of 
 un impression, in wax or paper pulp, of the type from which a 
 page is printed, the impress'ion having been coated with fine plum- 
 bago to render it a good conductor, copper deposited upon it may 
 be removed, and having been stiffened by melted lead (or some 
 alloy) poured over its under surface, it may be used in the print- 
 ing-press instead of the .type. It is then called an electrotype 
 plate, and when not in use may be preserved indefinitely for suc- 
 ceeding editions, while the t} T pe of which it is a copy can be 
 distributed and used for other purposes. 
 
 685. Counter-Electromotive Force. If a current be sent 
 through a solution of alkaline zincate by means of two copper 
 electrodes, zinc will be deposited on one electrode and the other 
 will become oxidized. If the connections with the source of elec- 
 tricity be now removed and transferred to an electric bell, the bell 
 will ring. The bath and electrodes have been transformed into a 
 galvanic cell. The current which it gives is in a direction opposite to 
 that which caused the decomposition of the solution. Its E. M. F. 
 is about 79 volt, and is opposed to the original E. M. F. Had 
 ihe original E. M. F. been less than this amount, no plating of the 
 
STORAGE BATTERIES. 441 
 
 electrodes could have occurred. The E. M. F. developed in the- 
 solution is termed a counter-electromotive force. It occurs in nearly 
 all electrolytic actions, except when the electrodes are of the same 
 metal as that which is being deposited, e.g., copper in copper 
 sulphate. 
 
 The counter-electromotive force developed in the electrolysis 
 of dilute sulphuric acid is about 1.47 volt. Hence, to perform 
 the electrolysis, more than one Daniell's cell is necessary. 
 
 The counter- electromotive force constitutes the polarization of 
 a primary battery mentioned in Art. 634. 
 
 686. Storage Batteries. The copper electrodes in alkaline 
 zincate of the preceding article represent a very simple form of 
 storage battery or electrical accumulator. Upon sending a current 
 through it, the zinc is deposited and the battery is said to be 
 charged. Some of the electrical energy has been transformed into 
 chemical energy. The electrodes may be removed from the solu- 
 tion, packed away, and then be brought forward in the future and 
 be made to turn back their energy into electricity. The elec- 
 tricity proper has not been stored away, but the energy repre- 
 sented by it. 
 
 The first successful storage battery was constructed by Gaston 
 Plante in 1860. His electrodes were made of sheet-lead, and the 
 electrolyte was dilute sulphuric acid. In order to expose a large 
 surface of electrodes he made them of large sheets which he coiled 
 up into spirals, as shown in Fig. 394, the two plates being insulated 
 from each other by rubber bands between the spirals. 
 The object of the large surface was to increase the 
 capacity of the cell. The spiral form was conducive 
 to a small internal resistance. Upon the passage of a 
 current the acid was decomposed and hydrogen re- 
 duced one electrode to bright metallic lead, while 
 oxygen coated the other with peroxide of lead. 
 These two conditions of the electrodes rendered 
 them capable of giving an electro-motive force of two 
 volts. By repeated charging in alternate directions 
 the surfaces of both electrodes were rendered spongy, 
 thus exposing an increased surface to the action of 
 the ions and increasing the capacity of the cell accordingly. This 
 preliminary alternate charging was termed by* him "formation" of 
 the electrodes, and was performed at the expense of costly currents. 
 
 In order to reduce the time and expense of formation, Faure 
 used lead plates as a support and covered them with a paste 
 made of powdered oxide of lead mixed with sulphuric acid. This, 
 paste he kept in place by covering the sheets with felt. When the 
 
442 
 
 ELECTRICITY AND MAGNETISE. 
 
 FIG. 395. 
 
 -charging current was connected the oxide on one plate was changed 
 to a higher oxide, and on the other plate transformed into metallic 
 sponge. This idea of Faure was an excellent one, and is at the 
 foundation of the construction of all the commercial lead accu- 
 mulators. The percentage of energy recovered by discharge was 
 greatly increased. His method of keeping the paste in place by 
 felts was, however, soon abandoned, because fine lead needles soon 
 filled up the interstices of the felt, and thus made a metallic con- 
 nection between the electrodes. Holes were then punched in the 
 lead plates and the paste pressed into them. A large number of 
 the patents recently issued for accumulators refer to, methods of 
 making these holes and pressing in the paste, or to the shape of the 
 holes themselves after they have been punched. The shapes vary 
 from a slight depression on the surface to a hole completely 
 through the plate, and even further, to a hollow plate, with small 
 
 openings leading to the surface. 
 A great deal depends upon this 
 shape, for the paste changes its 
 volume during the process of 
 charging and discharging, and it 
 would tend to loosen itself from 
 some shaped openings and fall 
 to the bottom of the cell, while 
 in others it would tend to tighten 
 itself, and thus provide a better 
 contact. 
 
 A modern commercial stor- 
 age battery is shown in Fig. 395. 
 The electrodes are made up of a 
 number of pasted plates, or grids 
 as they are called. The grids of 
 -one electrode are alternated with those of the other, and are all 
 
 connected by luas with com- 
 
 ' i . i FIG. 396. 
 
 mon cross-bars which consti- 
 tute the terminals of cell. 
 
 687. Capillary Elec- 
 trometer. This instrument 
 is for the measurement of 
 small differences ofr potential 
 not exceeding 1 volt. A simple 
 form is represented in Fig. 
 396. It consists of two up- 
 right test-tubes connected by a horizontal capillary glass tube of 
 about mm. internal diameter. 
 
LIGHT AND ELECTRICITY. 443 
 
 Into one of the test-tubes is poured mercury and into the other 
 ililute sulphuric acid. The heights of the two liquids are so arranged 
 that the dividing surface between them shall be in the horizontal tube. 
 Upon subjecting the two liquids to an electro-motive force, applied 
 at two platinum terminals fused into the bottoms of the test-tubes, 
 an electrolytic action will be started at the point of the capillary 
 tube where the acid meets the mercury. The surface tension will 
 be accordingly modified and the balance between the two columns 
 will be destroyed. To reproduce a balance the dividing surface 
 must move along the capillary tube in one direction or the other, 
 depending upon which liquid has the higher potential. The dis- 
 tance moved depends upon the potential difference and becomes 
 .a measure of it. 
 
 688. Light and Electricity. At the present time many in- 
 vestigators are experimenting upon the close relation between the 
 phenomena of light and those of electricity. Trustworthy results 
 point to the fact that electricity is the lurniniferous ether itself, as 
 was previously stated. A motion of the ether is unrestrained in a 
 perfect electrical conductor. In a dielectric only a limited dis- 
 placement of the ether particles is possible, except in case the 
 dielectric is ruptured. A displacement always subjects the enclos- 
 ing dielectric to a strain, and can be produced by a neighboring 
 conductor having an electrostatic charge or by its conveying an 
 electrical current. The displacement resulting from a current is 
 in a direction opposite to the current, and occurs through all the 
 dielectric which surrounds the current. Upon starting the current 
 the. displacements near the conductor occur before those at a dis- 
 tance. The velocity of propagation of the first impulse causing 
 displacement is the same as the velocity of light. 
 
 A full exposition of the ether hypothesis, and to what extent 
 it explains electrical phenomena is, of course, out of place here. 
 
 689. Double Refraction from Electrostatic Strain. 
 Kerr showed that the strain in a dielectric, caused by electrostatic 
 difference of potential, could be detected by means of polarized 
 light. He placed a block of glass between two Nicol's prisms 
 which served as analyzer and polarizer. Into opposite sides of the 
 glass were bored two holes, not quite meeting each other, but sep- 
 arated by about 2 mm. Into these holes were placed wires, which 
 were connected with the poles of a Holtz machine. Upon creating 
 n difference of potential between the ends of the wires the glass 
 was subjected to strain and exhibited to an eye placed at the an- 
 alyzing Nicol similar colors to those given by mechanically strained 
 glass. The glass was made doubly refracting. 
 
444: ELECTRICITY AND MAGNETISM. 
 
 690. Magneto-Optic Twisting of the Plane of Polarized 
 Light. Faraday discovered that the plane of polarization of a ray 
 of light which traversed a magnetic field in a direction parallel to 
 the lines of force was twisted by the field. One form of Faraday's 
 experiment is to place a straight electro-magnet between two Nic- 
 ol's prisms, which have been crossed so as to produce extinction of 
 light. Substitute for the iron core of the magnet a tube with 
 glass ends, which is filled with bisulphide of carbon. Before the 
 magnet is excited a ray of light from the polarizer passes through 
 the liquid and is brought to extinction by the analyzer. If, now, 
 the magnet be excited by an electrical current, the analyzer no 
 longer extinguishes the ray, and that it may do so must be rotated 
 through a certain angle. The plane of the ray has been twisted 
 or rotated by the magnetic field. The direction of the rotation is 
 the same as the direction of the exciting current. By reversing 
 the current the plane will be twisted in an opposite direction. The 
 amount of the rotation of the analyzer necessary to reproduce ex- 
 tinction of the ray is directly proportional to the length of the 
 tube and to the strength of the magnetic field, i.e., to the strength 
 of the exciting current. It also depends upon the nature of the 
 liquid in the tube. In general it may be said that substances of 
 high refractive indices have large rotatory powers. 
 
 As might be expected, rays of the different colors are rotated 
 through different angles. Hence, if complete extinction by large 
 rotations be desired, monochromatic light should be used. 
 
 691. Rotation of the Plane by Reflection. Kerr discov- 
 ered that the plane of polarization was rotated when the ray was 
 reflected from the polished pole of the iron core of an electro-mag- 
 net. In this case the direction of rotation was contrary to the 
 direction of the magnetizing currents. 
 
 692. Photo-Electric Properties of Selenium. Selenium, 
 when thoroughly annealed, offers a resistance to an electric current 
 which is dependent upon the degree to which it is illuminated. 
 An increase of illumination decreases the resistance. A piece of 
 selenium, whose resistance in the dark was 500 ohms, has been 
 known to decrease its resistance to 50 ohms upon exposure to 
 bright sunlight. 
 
 This peculiarity of selenium is made use of by Bell in the 
 construction of his photophone. This instrument is intended for 
 transmitting sounds to a distance by means of rays of light, which 
 are reflected from a mirror that is made to vibrate by the sounds. 
 Light of varying intensity is made thus to impinge upon a piece of 
 selenium, which is connected in circuit with a battery and a Bell 
 
POWER OF ELECTRICAL CURRENTS. 445 
 
 telephone receiver. The variations in the resistance of the selen- 
 ium, because of the varied illumination, cause variations of the cur- 
 rent in the receiver, which serve to reproduce the sounds. 
 
 Quite recently Shelford-Bidwell has exhibited an apparatus in 
 which selenium is made to light the gas as darkness comes on and 
 to turn it off as daylight appears. 
 
 Problems. 
 
 1. How much copper will be deposited by a current of 3 
 amperes in an hour ? 
 
 2. A current of 0.5 ampere is used for preparing pure silver 
 by electrolysis : how long must the current be allowed to flow in 
 order to obtain a deposit of 4 grams ? 
 
 3. What is the strength of a current which deposits a milli- 
 gram of copper per minute ? 
 
 4. It is found that a current of 1.868 ampere deposits 1.108 
 gram of copper in half an hour : what value does this give for the 
 electro-chemical equivalent of copper ? 
 
 5. What is the strength of a current which deposits 0.935 gram 
 of copper in 1 hour and 10 minutes. 
 
 CHAPTEK X. 
 
 THE RELATIONS BETWEEN ELECTRICITY AND HEAT, 
 
 693. Power of the Electrical Current. A current whose 
 strength is c carries in t seconds c t units of electricity from a 
 potential Fto one of V. The work which has to be expended in 
 doing this is c t (V F), as was shown in Art. 567. In this case 
 V F is equal to the electro-motive force E, which is sending the 
 current. Hence, representing the work by A, we have 
 
 A c t E. 
 
 If c, t, and E are measured in absolute units, the work is given in 
 ergs. 
 
 The power of the current P being the rate at which the work 
 is done, i.e., the work divided by the time required to perform it 
 is expressed by the formula 
 
 Expressing c and E in amperes and volts respectively will di- 
 
446 ELECTRICITY AND MAGNETISM. 
 
 vide the ergs per second by 10 7 . This gives the power in watts 
 (Art. 38). 
 
 E 
 Inasmuch as c = and E = c R, by Ohm's law, these values 
 
 may be substituted, and we have, further, 
 
 P = c 3 R. 
 
 694. Heat Developed in a Conductor. Whenever the 
 energy which is represented by a current is not expended in 
 doing external work, as in driving motors or decomposing electro- 
 lytes, it is transformed into heat. The conductor which carries 
 the current becomes heated. If a conductor of resistance, E, car- 
 ries a current c, then, by Ohm's law, the difference of potential 
 between its ends, E = c E. The energy represented by the cur- 
 rent is, as in the preceding article, 
 
 A c I .E = c 2 E t ergs. 
 
 This energy is transformed into heat. To express the heat in 
 gram-calories, Joule's mechanical equivalent of heat must be intro- 
 duced. Without going through with the transformations it is 
 sufficient to say that a current of c amperes flowing for t seconds 
 through E ohms communicates to the conductor carrying it 
 H c 2 E t 0.24 gram-calories. 
 
 695. Rise in Temperature of the Conductor. A long 
 thick wire could have the same resistance as a short thin one, but 
 a given current traversing them for a given time would produce 
 the same quantities of heat in each. The short thin wire, not 
 weighing so much, might have its temperature raised several hun- 
 dred degrees, while the thick wire would suffer a rise of a few de- 
 grees only. 
 
 In order to determine what rise in temperature will accompany 
 ra given quantity of heat imparted, account must be taken of the 
 (dimensions of the conductor, the specific heat of the substance of 
 -which the conductor is composed, and the temperature coefficient 
 of the conductor, i.e., the amount by which its resistance would in- 
 crease under a rise of one degree of temperature. A full considera- 
 tion cannot be considered in these chapters. It is well to know, 
 however, that, in different wires of the same material, traversed by the 
 same current, the rise in temperature is inversely proportional to the 
 fourth power rf their diameters. 
 
 A wire of given resistance, traversed by a given constant current, 
 will receive the same amount of heat each second that the current 
 flows. After a short time the temperature of the wire may rise to 
 

 c . 
 
 UNIVERSITY) 
 
 V^ ' OF J 
 
 HOT WIRE AMMETERS. 44.7 
 
 uch a point that it gives off to surrounding objects, by radiation 
 and conduction, just as much heat as it receives in every second. 
 The temperature then remains constant at this point as long as 
 the flow is maintained. 
 
 The heat effects mentioned may be illustrated by sending a 
 strong current through a chain, whose alternate links are made of 
 platinum and silver wire. The platinum links will be heated to 
 luminosity while the appearance of the silver remains unaltered. 
 The reason for this is that the platinum offers a much greater re- 
 sistance than the silver, and its specific heat is less. 
 
 Platinum wires, heated red-hot by currents, are much used by 
 surgeons for cauterization. They are much easier of manipulation 
 than the knife. 
 
 696. Hot Wire Ammeters and Voltmeters. The expan- 
 sion in length which a wire undergoes when its temperature is 
 raised to a certain point by a current which traverses it, can be made 
 a measure of the strength of the current* A given wire has a 
 definite length at a given temperature. Increasing the tempera- 
 ture increases the length. Every current produces a definite length 
 in the wire. Different current strengths correspond to different 
 lengths. A measurement of the length can thus be made a meas- 
 ure of the current strength. 
 
 A simple ammeter, whose action depends upon this principle, is 
 represented in Fig. 397. The current to be measured is passed 
 
 FIG. 397. 
 
 through a long and thin platinum or iron wire, one of whose ends 
 is clamped in a stationary binding-post. The other end passes 
 around and is fastened to a small metallic cylinder. This cylinder 
 turns upon a metallic pivot fastened in another binding-post. 
 The current having traversed the wire leaves it by this binding-post. 
 The wire is subjected to a constant strain, exerted by a spiral spring 
 attached to the periphery of a disc, which is fastened to one end 
 of the cylinder. The disc carries a radial pointer, whose end 
 moves over a graduated scale whenever the length of the wire is 
 ohanged by a change in temperature caused by a current. The 
 
448 ELECTRICITY AND MAGNETISM. 
 
 graduation of the scale is empirical, being determined by the assist- 
 ance of some other current measurer. 
 
 As the current strength is dependent upon the difference of po- 
 tential between the two binding-posts, it is evident that the instru- 
 ment may be graduated as ^voltmeter, i.e., will indicate the volts im- 
 pressed upon it. As it is not desirable that a large current should 
 flow through a voltmeter, the wire of such an instrument should have 
 a large resistance. The voltmeters of Cardew are constructed on 
 this principle. Sometimes a high resistance coil is inserted in 
 series with the wire, and then the voltmeter readings indicate the 
 fall in potential between the terminals of the spool and wire in 
 series. 
 
 Hot wire ammeters and voltmeters can be employed to meas- 
 ure currents and voltages which rapidly alternate their directions. 
 For the heat produced being dependent on the square of the cur- 
 rent strength is positive, whether the current flows in a positive or 
 negative direction. 
 
 697. Electric Welding. The welding together of two 
 pieces of metal, by means of the electric current, as done in the 
 
 Thomson process, depends upon the heat 
 produced. The pieces are pressed to- 
 gether and a powerful current (some- 
 times 50,000 amperes) is sent across the 
 juncture. The consequent heat renders 
 the metal plastic, and upon cooling a 
 most perfect joint is obtained. 
 
 698. The Electric Arc. If two 
 rods of carbon, traversed by a current 
 from a source of at least 40 volts electro- 
 motive force, be touched together at their 
 ends and then be separated by a few 
 millimeters' distance, an electric flame or 
 arc will be observed to pass over this dis- 
 tance. A brilliant light will accompany 
 it, the extreme brilliancy being at the 
 end surfaces of the rods. If allowed to 
 burn for a few moments the rods and 
 flame will present an appearance like that 
 represented in Fig. 398. The end of the 
 positive rod will have formed itself into a 
 sort of crater, while the end of the neg- 
 ative will have become pointed. If al- 
 lowed to burn for some time, the rods will be consumed, and, in a. 
 
THERMO-ELECTRICITY. 449 
 
 given time, about twice as much of the positive rod will be con- 
 .sumed as of the negative. 
 
 In order to form an arc it is necessary that the points be at 
 first in contact. When in loose contact the current encounters a 
 great resistance, and accordingly heats the points until a tempera- 
 ture is reached which is sufficient to vaporize the carbon. Carbon 
 vapor is a much better conductor of electricity than air, and 
 whereas an arc could not be maintained across an air space, yet it 
 can be across a space filled with this vapor. 
 
 The heat at the vapor portion of the arc is intense, being suffi- 
 cient to vaporize the most refractory substances, of which carbon 
 itself is the best example. The heat at the crater, though not so 
 intense, is the cause of greater illumination, because of being asso- 
 ciated with a solid instead of a vapor. 
 
 Recent investigations, concerning the fall of potential uloug the 
 arc, indicate that a large portion of the electrical energy repre- 
 sented by it is consumed in maintaining the heat of the crater. 
 
 699. Incandescent Electric Lamps. These lamps con- 
 sist of filaments of carbonized bamboo, paper, or silk, which are 
 heated to incandescence by the current. That the filaments may 
 not be consumed by combustion, they are sealed into glass bulbs, 
 from which the air has been exhausted. Although no oxygen is 
 present, the filaments become disintegrated by continuous use. 
 Particles of carbon escape from the surface of the filament and are 
 oftentimes deposited upon the interior of the bulb, causing a 
 brownish opalescent appearance. 
 
 700. Thermo-Electricity. Let two bars of bismuth (6) and 
 antimony (a) be soldered together as in Fig. 399. If, now, the 
 joint S be heated by a 
 
 lamp a current will flow FlG - '^- 
 
 across the heated June- s 
 
 tion from the bismuth to . ^ * - 
 the antimony, as will be "* 
 
 shown by the galvano- 
 meter G. 
 
 The electro-motive force of the current depends upon the metals 
 in contact at the heated junction. If any one of the metals given 
 below be joined with any one following it in the list, upon apply- 
 ing heat the current will flow across the junction from the former 
 to the latter : Bismuth, lead, platinum, tin, zinc, copper, iron, an- 
 timony. 
 
 The thermo-electro-motive force is proportional to the difference of 
 temperature between the junction and the rest of the circuit. 
 
450 
 
 ELECTRICITY AND MAGNETISM. 
 
 The E. M. F. of a single thermoelement is very small. If the- 
 junction of a copper-iron element be heated 1 C. above the tem- 
 perature of the rest of the circuit, the E. M. F. developed is about 
 fourteen millionths of a volt. 
 
 In some cases, e.g., with iron, a continued increase of tempera- 
 ture at the junction finally reverses the direction of the current. 
 
 701. Thermo-Electric Pile. If a series of bars of bismuth 
 and antimony be arranged, as in Fig. 400, and the junctions 
 
 marked 3 and 4 be equally heated, 
 no current will be indicated by the 
 galvanometer ; for the flow at 3 
 would be from the bismuth to the 
 antimony as indicated by the arrow, 
 while at 4 it would also be from b 
 to a, as shown, and these two cur- 
 rents would neutralize each other. 
 But if we heat only one set of junctions, the odd-numbered for 
 instance, then a current flows whose electro-motive force is pro- 
 portional to the number of heated junctions. 
 
 A set of twenty or thirty pairs, conveniently arranged so that 
 the alternate junctions may be simultaneously subjected to heating- 
 or cooling effects, is called a thermo-pile, and has been an impor- 
 tant instrument in investigations upon radiant heat. 
 
 702. Peltier Effect. Peltier discovered a phenomenon which 
 is the converse of that mentioned in the preceding articles. He 
 found that, if a current of electricity be sent through a junction of 
 dissimilar metals, the junction becomes heated or cooled according 
 to the direction of the current. For instance, if a current be sent 
 through a junction from bismuth to antimony, the junction will 
 absorb heat, i.e., become cooled. If the current be reversed the 
 junction will become heated. 
 
 The heat thus produced is not owing to the resistance of tbe 
 conductors. For the heat from resistance is not altered by a 
 change in the direction of the flow of the current. Cooling can 
 never result from ohmic resistance. Again, the heat of the Peltier 
 effect is proportional to the current strength simply, whereas the 
 heat from resistance is proportional to the square of the current 
 strength. 
 
 Problems. 
 
 1. An 11,000 watt dynamo develops an E. M. F. of 110 volts : 
 (a) What is the current strength in the mains ? (b) How many in- 
 candescent lamps, of 220 ohms hot resistance, will it light, provid- 
 
THE ELECTRICAL UNITS. 451 
 
 ing they are arranged in multiple arc? (c) How many gram-calo- 
 ries will be developed in each lamp per second ? (d) How many 
 watts will be consumed by each lamp? [ (a) 100 amperes. 
 
 A \ (b) 200 lamps. 
 m ' } (c) 13.2 calories. 
 L (d) 55 watts. 
 
 2. How much power is required to properly operate an arc 
 lamp which carries 10 amperes and has a difference of potential of 
 45.2 volts between its terminals ? 
 
 3. How many calories are developed per minute in a wire of 
 100 ohms resistance, traversed by 5 amperes ? 
 
 4. A wire of 2 ohms resistance placed in 100 grams of water is 
 traversed by a certain current, which, in 20 minutes, raises the 
 temperature of the water from 18 to 28 C.: what is the current 
 strength ? Ans. 1.32 amperes, nearly. 
 
 The Electrical Units. 
 
 Electrical magnitudes may be expressed in three different sets 
 of units. Two of them the absolute electrostatic and the absolute 
 electro-magnetic units are termed absolute because they are units 
 derived from the absolute units (Art. 4) of length, mass, and time, 
 viz., the centimetre, gram, and second. The third set are called 
 practical units, because they are the ones which are employed by 
 practical electricians. They are either decimal multiples or deci- 
 mal parts of the electro-magnetic units. 
 
 ELECTROSTATIC UNITS. 
 
 The Unit of Quantity of electricity is that quantity which, when 
 placed at a distance of one centimetre from a similar and equal 
 quantity, repels it with a force of one dyne (Art. 563). 
 
 The Unit Strength of Current flows in a circuit when a unit 
 quantity of electricity passes any section of the conductor in one 
 second. 
 
 The Unit Difference of Potential exists between two points 
 when it requires an expenditure of one erg of work to bring a 
 unit quantity of electricity from one point to the other against the 
 electric force. 
 
 The Unit of Resistance is offered by that conductor which, when 
 interposed between two bodies whose potentials are maintained at a 
 constant difference of unity, allows a unit current to pass along it. 
 
 The Unit of Capacity is possessed by that conductor which 
 requires that it be charged with a unit quantity of electricity in 
 order that its potential may be raised from zero to unity. 
 
 ELECTRO-MAGNETIC UNITS. 
 The Unit Strength of Current is such that, when flowing through 
 
452 ELECTRICITY AND MAGNETISM. 
 
 a conductor of one centimetre length which is bent into an arc of 
 one centimetre radius, it will exert a force of one dyne on a unit 
 magnetic pole situated at the centre. 
 
 The Unit Quantity of electricity passes in one second through a sec- 
 tion of a conductor which is traversed by a current of unit strength. 
 
 The Unit Difference of Potential (or of Electro-motive Force) exists 
 between two points when it requires the expenditure of one erg of 
 work to bring a unit of electricity from one point to the other 
 against the electric force. 
 
 The Unit of Resistance is offered by that conductor which, when 
 interposed between two bodies whose potentials are maintained at 
 a constant difference of unity, allows a unit current to pass along it. 
 
 The Unit of Capacity is possessed by that conductor which 
 requires that it be charged with a unit quantity of electricity in 
 order that its potential may be raised from zero to unity. 
 
 A little consideration will show that in the electrostatic and 
 electro-magnetic systems the definitions of all the units except that 
 for quantity are identical. Whereas the electrostatic unit of quantity 
 is determined from its exerting a dyne of force on another unit 
 quantity, the electro-magnetic unit of quantity is determined from 
 its exerting a dyne of force, when moving as a current, on a unit 
 magnetic pole. The electro-magnetic unit is about 3 x 10' times 
 the electrostatic unit. This numerical factor is the same as the 
 velocity of the propagation of light expressed in centimetres per 
 second. This fact, combined with certain mathematical relations 
 which exist between the two units, is of great significance in sus- 
 taining the ether theory of electricity. 
 
 PRACTICAL UNITS. 
 
 Many of the absolute units would be inconveniently large and 
 others would be inconveniently small for practical use. Therefore 
 the following units, based upon the electro-magnetic units, are used : 
 
 Electromotive force Volt = 10 8 electro-magnetic units. 
 
 Resistance Ohm = 10 9 " " 
 
 Current Ampere = 10 ~ l " ' 
 
 Quantity Coulomb = 10-' " " 
 
 Capacity Farad = 10- 9 " " 
 
 Even these units are not of a magnitude suited for the use of all 
 electricians. Thus a physician uses currents whose strengths can 
 be more easily expressed in thousandths of an ampere. The prefix 
 milli- is therefore used for "one thousandth " and a milliampere is 
 the thousandth part of one ampere. Capacities are best expressed 
 in millionths of a farad or microfarads. The high resistances 
 offered by insulations are conveniently expressed in megohms = 
 one million ohms. 
 
A COURSE IN ELECTRICAL 
 MEASUREMENTS. 
 
 INTKODUCTOKY. 
 
 To the Instructor. The student who carries out the exper- 
 iments outlined in the following course will become acquainted 
 with methods generally employed in determining electrical mag- 
 nitudes. The accuracy of the results which he may obtain is 
 largely limited by the care exercised in eliminating disturbing 
 conditions, and to a certain extent by the character of the appa- 
 ratus employed. It is possible, however, to make very accurate 
 measurements with quite ordinary apparatus. A laboratory should 
 possess a standard resistance coil, a standard thermometer, and 
 a set of standard weights. A cheap rheostat, if wound with wire 
 of negligable or known temperature coefficient and of small ther- 
 mo-electric power (e.g., manganin), can be calibrated with the aid 
 of the standard resistance and be made to yield accurate results. 
 Standard Weston voltmeters and ammeters are great conveniences. 
 The cheap D'Arsonval galvanometers sold by Queen & Co. may, 
 however, be used both as ammeters and as voltmeters. Observa- 
 tions should be made by means of a telescope and scale. Tele- 
 scopes which are entirely satisfactory may be made from ordinary 
 spectacle lenses. If the telescope be kept at a fixed distance from 
 the mirror of the galvanometer, a suitably sized copper wire 
 shunted between the galvanometer terminals will reduce it to a 
 direct reading ammeter independent of temperature variations, 
 but liable to slow alterations, owing to decrease in strength of 
 the magnets with the time. A high resistance of proper magni- 
 tude placed in series with the galvanometer transforms it into a 
 direct-reading voltmeter. High resistances of any magnitude 
 (approximate) may be purchased from the Dixon Crucible Co., of 
 Jersey City, for a few cents. They are of graphite and in form 
 of rods. Their ends can be copper-plated and copper wires can 
 be soldered to the plating. Adjustments can be made by scraping 
 
454 ELECTRICAL MEASUREMENTS. 
 
 away a portion of the plating. These galvanometers, if of high 
 resistance (1,000 ohms), may be used for all the work in this 
 course. When used as ballistic galvanometers, the period of os- 
 cillation is rather small, and, further, it must be constantly borne 
 in mind that the damping is dependent on the resistance of the 
 circuit. Some of the exercises require that electricity be taken 
 from the electric-lighting street circuit. These exercises are more 
 conveniently carried out in this manner, but may be performed 
 with the assistance of batteries. When the street circuit is of 
 constant potential, the amount of current employed is conven- 
 iently regulated by means of altering in number interposed elec- 
 tric lamps, coupled in multiple arc. 
 
 To the Student. Physical laboratory instruction, to be of 
 most value in education, should develop in the student : 
 
 1. A habit of observation of the phenomena of nature, both 
 ordinary and extraordinary. 
 
 2. The ability to accurately and truthfully record these obser- 
 vations in a note-book. 
 
 3. The ability to draw correct and logical inferences from the 
 noted observations, and 
 
 4. The ability to present in concise and perfect English the 
 observations and the results to be inferred from them. 
 
 In general, it is always advisable to use the greatest possible 
 accuracy of observation that is allowable with the apparatus em- 
 ployed. In some cases, however, when other observations of less 
 possible accuracy are to be combined in forming a final result, 
 less care may be taken. A single observation is no security against 
 blunders. A number of observations is, however, and, in addition, 
 diminishes the probable error of the mean. Errors of observation, 
 and all errors which are as liable to be above as below the true 
 value, can be diminished in this manner only. Instrumental 
 errors can sometimes be obviated by changing in each observation 
 the conditions of the experiment ; for example, in measuring the 
 length of an object by means of a scale, an error of the graduation 
 can be eliminated by placing the object upon different portions 
 of the scale. A large number of observations will increase the 
 accuracy of results. 
 
 In recording observations, truthfulness is paramount. Eecord 
 as an observation only that which has been observed. Several 
 students recorded in their note-books the length of an object as 
 observed to be 19 cms. because it extended from the to the 19 
 division of a scale. The scale had no division at 17 and was 
 faulty. The length of the object was 18 cms. The students- 
 
COMPARISON OF RESISTANCES. 455 
 
 should have noted what they observed, and not what they in- 
 ferred. 
 
 The record should always indicate the accuracy of an observa- 
 tion. If an ammeter which is readable to the hundredth of an 
 ampere should indicate a current of exactly 2 amperes, the record 
 should be 2.00, not simply 2. The two ciphers in the decimal 
 places, although of no numerical value, still -indicate the accuracy 
 of the observation, and to what extent the observation may be 
 relied upon. 
 
 Perfect freedom in the matter of drawing inferences is not com- 
 patible with a course of electrical measurements. Original research. 
 and investigation alone give this. Yet the failure of many experi- 
 ments to yield reasonable results upon first trial give to the student 
 the opportunity of inferring the causes of the failure, and it is ad- 
 visable that the student should unassisted determine these causes.. 
 
 The student is admonished : 
 
 1. To interfere in no other student's experiments. 
 
 2. To consider neatness and cleanliness as essential to good 
 work. 
 
 3. To disconnect all apparatus after use. 
 
 4. To arrange and adjust all apparatus so that the greatest 
 accuracy is obtained with the least inconvenience to the observer. 
 
 RESISTANCES. 
 
 Comparison of Resistances. It is not often that the de- 
 termination of a resistance in absolute measure is required. In 
 nearly all cases a resistance is measured only in so far as its ratio 
 to some known standard resistance is determined. Standard re- 
 sistances are made of German silver, platinoid, or manganin wire, 
 and are wound bifilar. These substances are chosen because of 
 their high resistivity, and because of their small variation in re- 
 sistance with the temperature. If the resistance of a conductor at 
 18 C. "be .#, then its resistance at any near temperature, t, may be 
 represented by the formula 
 
 where a is the temperature coefficient 
 
 For German silver a = 0.00024 to 0.0006. 
 
 For copper a = 0.004. 
 
 For carbon a = - 0.0002 to 0.0007. 
 
 For electrolytes a = 0.014 to - 0.030. 
 Attention is called to the fact that the resistance of metals in- 
 creases with a rise in temperature, while the resistance of carbort 
 and electrolytes decreases. 
 
456 ELECTRICAL MEASUREMENTS. 
 
 Rheostats or resistance-boxes are stamped with a normal tem- 
 perature. This means that, at the given temperature, the resist- 
 ance of all the coils in series is exactly equal to their nominal value. 
 The individual coils, however, may none of them have the exact 
 resistance with which it is stamped. A table of corrections should 
 accompany each box. By applying the correction and then cor- 
 recting for temperature, the exact resistance of any coil may be 
 obtained. 
 
 E.g. : The correction for a 100-ohm German silver coil is + 
 0.12 at the normal temperature 18.8, and the temperature coeffi- 
 cient is 0.00035. At 21.8 the resistance 
 
 = 100.12[1 + (21.8 - 18.8)0.00035] = 100.23 ohms. 
 
 Care must be taken that the resistance of a connecting wire be 
 not, through oversight, added to a resistance to be compared or 
 to a standard. If it must of necessity be added, its value should 
 be added or its influence considered. Bad contacts often add re- 
 sistance in unsuspected places. The ends of connecting wires 
 should be scraped and fastened firmly in the binding posts. The 
 plugs of a rheostat should be twisted in their respective holes. 
 
 Method of Substitution Two resistances are equal to each 
 other if, when one replaces the other in a given circuit, the current 
 strength remains unaltered. 
 
 Apparatus. Daniell cell, galvanometer, rheostat, and x. 
 
 Directions. Form a circuit of cell, galvanometer, and x. Note 
 deflection 0. Substitute for x such a resistance E l as to yield a 
 deflection O l slightly less than 0. Then substitute E^ so as to yield 
 2 slightly larger than 0. Then 
 
 Prove formula. Why is a Daniell cell used ? 
 
 What accuracy have you attained ? 
 
 This method is used in determining insulation resistances, 
 which are very large. 
 
 For measuring small resistances the galvanometer resistance 
 should be small. Why? 
 
 Direct Method (Ohm). I. Apparatus. Mirror galva- 
 nometer (shunted), Daniell cell, rheostat, and x. 
 
 Directions. Form a circuit of cell, connecting wires, and gal- 
 vanometer. Observe small deflection 6, which is proportional to 
 the current C. Insert x in circuit and observe O x , i.e., C x . Sub- 
 
PROJECTION OF POTENTIALS. 457 
 
 stitute for x a known resistance R and observe 2 , i.e., C 3 . Then 
 
 - 
 
 -c\ c x 
 
 -e e x 
 
 Evidently this method is good for measuring resistances while 
 a current is traversing them. What difference would this make 
 in the case of incandescent lamps ? An ammeter may be used in- 
 stead of a galvanometer and the currents be read off directly. 
 
 Prove the correctness of the formula. 
 
 II. Apparatus. Voltmeter, ammeter, constant voltage, and x. 
 
 Directions. Form a circuit as indicated in Fig. 401. Ob- 
 serve the amperes C in the ammeter A 
 and the volts E in the voltmeter V. 
 Let the resistance of the voltmeter be 
 E. Then 
 
 E 
 
 FlG - 401 - 
 
 x = 
 
 -J 
 
 
 Determine the probable error in your results. 
 
 III. Apparatus. Same as in II. 
 
 Directions. Form circuit as indi- FlQ - 402 - 
 
 cated in Fig. 402. Observe amperes G 
 in A and the volts E in V. Let R = re- 
 sistance of ammeter. Then 
 
 t 
 
 Projection of Potentials. Apparatus. High-resistance 
 sensitive galvanometer, a known resistance R, constant source of 
 E. M. F., and x. 
 
 Directions. Form a circuit of E. M. F. R, and x. From the 
 extremities of x lead off to galvanometer. Note the deflection 0. 
 Transfer the galvanometer connections to the extremities of R. 
 Note the deflection 9 l [R should be so chosen in respect to x 
 that and O l shall be nearly equal]. Then 
 
 This method is most often employed for comparing small resist- 
 ances. Before making this measurement draw a diagram of the 
 connections. 
 
 Resistivity. The resistivity of a substance is the resistance 
 which a cube of the substance, with faces of a sq. cm. would offer 
 
 UNIVERSITY 
 
458 
 
 ELECTRICAL MEASUREMENTS. 
 
 to a current entering one face and flowing out of the opposite face. 
 Hence the resistance of a wire, made of a substance of resistivity 
 />, whose length is I cms. and whose diameter is d cms. is 
 
 4J 
 
 P = 
 
 The resistance may be measured by the projection of potentials, 
 I by means of a cm. scale, and d by means of a micrometer screw. 
 
 TABLE or RESISTIVITIES. 
 
 Substance. Resistivity at C. 
 
 Silver (annealed) 1.504 x 1Q- 6 
 
 Copper (soft) 1.594 
 
 Aluminum 2.912 
 
 Platinum 9.057 
 
 Iron 9.716 
 
 German silver 20.93 
 
 Mercury .94.32 
 
 Zinc 5.626 
 
 A Weston 0-150 voltmeter combined with a source of constant 
 E. M. F. e. g., an incandescent street circuit of about 100 volts, 
 furnishes a convenient and quick method of measuring resistances 
 of from 5,000 to 100,000 ohms. 
 
 Directions. Form a circuit of the voltmeter and x in series, 
 connected with the street service. Take a reading of the volt- 
 meter 9. Suddenly short-circuit x and observe the new deflection 
 1 . Then, if E be the resistance of the voltmeter, 
 
 x = 
 
 E (O l - 0) 
 
 Prove the correctness of the formula. Measure resistances of 
 widely varying magnitude (lead-pencil marks on ground glass) , 
 and plot a curve with x as abscissae and error % in results as or- 
 dinates. 
 
 FIG. 403. 
 
 Method of Wheatstone's Bridge. 
 
 When a circuit is arranged as in Fig. 403, 
 there will be no current in the galvanom- 
 eter G, if the resistances a, b, E, and x 
 are so proportioned that a \ b = E \ x. 
 
 Apparatus. Resistances a and b, rheo- 
 stat E, galvanometer, source of E. M. F., 
 commutator, and x. 
 
WIRE BRIDGE. 459 
 
 Directions [a = b]. Connect apparatus as in Fig. 404. The 
 commutator c serves to quickly exchange 6 for a in Fig. 403, 
 and hence, if a be not exactly equal to b, 
 two values of E (E^ and J2 2 ) will be found FiG^404. 
 
 which produce an equilibrium in the bridge. 
 The true value of x will then be 
 
 .=*fi 
 
 x 
 
 2 
 
 Interpolation. In practice it is seldom 
 that a rheostat has sufficiently small units 
 to render it possible to effect an exact ad- 
 justment of the bridge. The value of x 
 may be determined, however, by interpola- 
 tion. Suppose that a resistance E in the rheostat nearly pro- 
 duces equilibrium. "When the commutator is in its two positions 
 1 and 2, suppose the needle's readings to be m, and m 2 divisions 
 respectively. Increase E by a small amount 8, and observe the cor- 
 responding readings n l and ?i 2 . Then 
 
 x = E+ _ \ 7* _ n] & 
 
 For measuring very large resistances, b should be made larger 
 than a (10, 100, or 1,000 times). E must then be multiplied by 
 
 the ratio - to get x. If x be small, a is made larger than b. In 
 a 
 
 these cases the commutator must be dispensed with, as well as 
 the increased accuracy which it affords. 
 
 Wire Bridge. In the bridge formula x = - E it is imma- 
 terial whether the absolute values of b and a be known or not, as 
 long as the ratio - be known. If b and a be together the resist- 
 ances offered by two portions of a stretched uniform wire, and 
 contact be made between a and b with the galvanometer by means 
 
 of a sliding knife edge, the ratio - will be equal to the ratio of 
 
 the two lengths of the wire comprised between the contact and 
 the two ends of the wire respectively. For the resistances offered 
 by two wires of the same material and cross section are propor- 
 tional to the lengths of the wires. 
 
 Apparatus. Stretched wire with sliding contact, galvanometer, 
 .standard resistance E } source of E. M. F., and x. 
 
460 
 
 ELECTRICAL MEASUREMENTS. 
 
 Directions. Connect as in Fig. 405. Slide the contact c along 
 the wire a b until the galvanometer shows 
 no deflection. Measure the lengths of a 
 and b. (The whole wire is usually made 
 1,000 units long, hence, if a be measured, 
 6 = 1,000 -a.) Then 
 
 FIG. 405. 
 
 , 
 
 a 
 
 By comparing Figs. 403 and 405 it will be noticed that the battery 
 and galvanometer have been exchanged. Why ? 
 
 Method of Mathiesen and Hockin. To compare the con- 
 ductivities of two substances. 
 
 Apparatus. Two wires of the same cross-section made of the 
 two substances, sensitive galvanometer, stretched wire with slid- 
 ing contact, and source of E. M. F. 
 
 Directions. Send a current through the stretched wire in 
 FIG 406 multiple arc with the two wires 
 
 1*1 1! \ wn ^ cu are * be compared, and 
 
 ft K v B R I which are arranged in series 
 
 with each other. Connect one 
 terminal of the galvanometer to 
 a point p t of one of the wires. 
 Connect the other terminal with 
 a point q 1 on the stretched wire, 
 
 so that no current flows through the galvanometer. Proceed sim- 
 ilarly with p a a , p s q 5 , and p t q 4 . Then 
 
 Resistances,^ Length q t g^ 
 Resistance p 3 p t Length q 3 q t 
 
 -4.9X933&: 
 
 Conductivity A _ Length 
 Conductivity B Length 
 
 Why? 
 
 BATTERY RESISTANCES. 
 
 Method of Ohm. Apparatus. Galvanometer of low resist- 
 ance G, rheostat, cell of internal resistance x. 
 
 Directions. Form a circuit of cell, rheostat, and galvanometer 
 in series. Adjust H in rheostat so as to give a proper deflection 0. 
 Add a resistance R f in the rheostat so that the deflection & is- 
 
METHOD OF MANCE. 
 
 461 
 
 about, half 0. Then, if the deflections be proportional to the cur- 
 rents, 
 
 x = Rf -~ ~ R + 0- 
 
 This formula results from 
 
 (1) 6 = 
 
 (2) 
 
 E 
 
 G + x + 
 E 
 
 ~ G + R + R +x 
 
 A Weston ammeter may be employed in place of the galvanome- 
 ter, and it yields quick results. 
 
 Method of Mance. Apparatus. Galvanometer, wire bridge 
 or two known resistances, rheostat, key, cell of internal resistance x. 
 
 Directions. Connect the cell in one 
 arm of the Wheatstone's bridge, and in FlG - 407. 
 
 the customary position of the battery 
 place a key and suitable resistance. Ma- 
 nipulate a, 6, or E so that the galva-< 
 nometer gives the same deflection whether 
 the key be closed or not. Then 
 
 *=!* 
 
 o 
 
 The magnitude of the galvanometer deflection may be regulated 
 by a copper wire shunted between its terminals. 
 
 This method is unreliable in its results. The E. M. F. of a 
 cell is somewhat dependent on the current. If the key circuit ia 
 of small resistance, the E. M. F. will be changed by the closing of 
 the key. 
 
 Method of Thomson. Apparatus. Galvanometer, rheostat, 
 
 shunt for galvanometer, cell of internal resistance x. 
 Directions. Connect the cell, plugged rheostat, 
 and shunted galvanometer in series. Adjust shunt 
 for a suitable deflection. Remove shunt of resist- 
 ance S and bring in circuit a resistance -R from 
 rheostat, so as to produce the same deflection as 
 before. Jf G be the galvanometer resistance, then 
 
 _ES 
 x Q. 
 
 FIG. 408. 
 
462 ELECTRICAL MEASUREMENTS. 
 
 The current C in the galvanometer is the same in each observa- 
 tion. In the first case 
 
 In the second case 
 
 fi 
 
 x + R + G 
 
 whence 
 
 G*S GS 
 Gx + Sx+ -=-, 
 
 G + S 
 
 Method of Beetz. Apparatus. Stretched wire of known 
 resistance per unit length provided with two sliding contacts, gal- 
 vanometer, shunted cell, double key, cell of internal resistance x. 
 
 Directions. Connect cir- 
 cuit as indicated in Fig. 409> 
 both cells tending to send a 
 current toward A. At A is a 
 key connecting both cell cir- 
 cuits with the stretched wire 
 Ap. Leaving p in place, shift 
 o until no deflection occurs in the galvanometer G, upon suddenly 
 closing the key at A. Shift p to a new position, p', and find a cor- 
 responding point, o', which shall produce an equilibrium. Repre- 
 senting the resistances of Ao, op, Ao', and o'p' by a, b, a', b', re- 
 spectively, we have 
 
 ab' - a'b 
 
 x = 
 
 a' -a 
 
 minus the resistance of the conducting wires. 
 
 Proof. Inasmuch as no current flows in G, the current C In 
 the stretched wire is the same as in the branch AEp. Hence 
 
 E = C (x + a + b), 
 
 if we neglect connecting wires. Also the difference of potential 
 V between A and o is 
 
 V= Ca. 
 
RESISTIVITY OF ELECTROLYTES. 
 
 In the second adjustment we have 
 
 E = G' (x + a' + V) 
 
 V= C'a' 
 E x + a + b x + a' + V 
 
 463 
 
 V 
 
 aV - a'b 
 
 This method gives the resistance of the cell E on open circuit. 
 It may also be used to determine the resistance of a cell which 
 has been previously short-circuited through a resistance. This 
 resistance can be thrown out at the moment of contact at A. 
 
 FIG. 410. 
 
 Method of Kohlrausch. Apparatus. Induction coil (of 
 low resistance secondary), cell to operate 
 it, telephone receiver, wire bridge, cell of 
 internal resistance x. 
 
 Directions. Connect the cell in one 
 of the arms of the Wheatstone's bridge. 
 Connect the secondary of the induction 
 coil with the sliding contact and the junc- 
 tion between R and x. Substitute a tele- 
 phone for the galvanometer of an ordinary 
 bridge combination. Adjust a and b so 
 that a minimum loudness is heard in the 
 telephone. Then 
 
 ft 
 
 Why can a telephone be used and not a galvanometer ? . 
 
 Resistivity of Electrolytes If a vessel containing an 
 electrolyte and supplied with platinized platinum electrodes be 
 substituted for the cell in Fig. 410, the resistance of the electrolyte 
 may be determined in the same manner as the internal resistance 
 of the cell. Owing to the high temperature coefficient of electro- 
 lytes the vessel should be placed in a water bath in order to main- 
 tain the temperature constant. The temperature of the electrolyte 
 may be obtained from a thermometer with its bulb submerged in 
 the electrolyte, if the vessel is of suitable shape. If the contrary 
 be the case, the temperatures of the bath and electrolyte may be 
 assumed alike. The resistance R of the electrolyte is dependent 
 on the size and shape of the vessel and on the position of the elec- 
 trodes. To obtain the resistivity it is necessary to substitute for 
 
464: ELECTRICAL MEASUREMENTS. 
 
 the electrolyte another of known resistivity p f and obtain its re- 
 sistance R r . Then the resistivity of the original electrolyte 
 
 As a standard solution saturated NaCl (specific gravity = 1.201) 
 may be used. Its resistivity at 18 is 4657 ohms. This decreases 
 0.104 ohm for each degree rise of temperature. 
 
 COMPARISON OF E. M. F.'S. 
 
 The Clark standard cell has an E. M. F. at the temperature t of 
 1.434 [i _ 0.001l5(* - 15)] volts. 
 
 It should never be short-circuited or closed through less than 
 10,000 ohms. For comparing the E. M. F. # of a cell with that of 
 the standard E s , by means of a tangent * galvanometer, we have 
 the following methods : 
 
 Method of Unequal Resistances and Deflections 
 Apparatus __ Galvanometer, resistance -box, standard cell, and 
 cell x. 
 
 Directions. Form a circuit of the standard cell and the rhe- 
 ostat with resistance R s > through the galvanometer whose reduction 
 factor is K. Observe the deflection 6 S . Substitute x for the stand- 
 ard and with a resistance R x note 6 X . Then, if JB S and B x be the 
 resistances of the standard and x and G of galvanometer, we have 
 
 and 
 
 . 
 
 whence 
 
 /q. - (B x +R x . x 
 
 -(B. + R.+ 0)to*.0.* 
 
 Consider whether you may neglect B s and B x . 
 
 Method of Equal Resistances. If you arrange so thai 
 3 X + R x + a = B 8 + R 8 + G, then (3) reduces to 
 
 * Small deflections obtained with a telescope and straight scale are propor- 
 tional to the tangents of the angular deflections of the needle. 
 
POLARIZATION. 465 
 
 Method of Equal Deflections. If K s and R x be so ad- 
 justed that 6 X 6 S , then 
 
 Method of Sum and Difference. Directions. Connect 
 both standard and x in series and with the total resistance of the 
 circuit R of such a [large] magnitude as to obtain a suitable de- 
 flection 0. Reverse one of the cells so that both tend to send cur- 
 rents in opposite directions. Note the deflection &. Then 
 
 E 9 + x tan. 6 
 
 _ 
 " 
 
 x tan. 0' 
 
 tan. - tan. & 
 tan. + tan. ff 
 
 Method of Wheatstone __ Directions. Form a circuit with 
 standard cell, suitable resistance, and galvanometer. Note deflec- 
 tion 0. Add R 8 to the circuit and note deflection &. Substitute 
 x for the standard and adjust resistance so as to obtain 0. Add 
 R x to get &. Then 
 
 Derive the formula. 
 
 Polarization. Apparatus. Two platinum electrodes in a 
 beaker of dilute H 2 SO 4 , Daniell cell, dead-beat low resistance 
 (shunted) galvanometer, key, watch with seconds hand, and rheo- 
 stat. 
 
 Directions. Form a circuit of key, cell, 1,000 ohms, beaker, 
 and galvanometer in series. Close key and note deflections every 
 thirty seconds for ten minutes. Take a reading at the instant of 
 closing, if possible. Remove the platinums and heat to a red glow 
 in a Bunsen burner. Replace and change the 1,000 ohms to 100 
 ohms. Repeat the operation of reading. Reduce the resistance 
 to 10 and then to ohms. Take readings every fifteen seconds 
 in the last two cases. Plot the four resulting curves with deflec- 
 tions for ordinates^and time for abscissae. What inferences can 
 be drawn from the results ? What causes polarization ? How is 
 it obviated in the Daniell, Bunsen, and Le Clanche cells ? Why 
 lieat the platinum ? 
 
466 ELECTRICAL MEASUREMENTS. 
 
 MEASUREMENT OF CURRENTS. 
 
 Reduction Factor of a Galvanometer The reduction 
 
 factor K of a galvanometer is such a constant that the current G 
 which passes through the galvanometer is expressed as a function 
 of the angular deflection <o of the needle by the equation 
 
 G = K tan. CD. 
 
 Apparatus. Telescope-reading galvanometer, standard Daniell 
 cell, rheostat, and meter rod. 
 
 Directions. Measure the voltage E of the cell and the re- 
 sistance G of the galvanometer. Then form a circuit of cell, 
 galvanometer, and resistance-box. Vary the resistances E in the 
 rheostat, noting the corresponding deflections 0. Measure the 
 distance d of the middle point of the scale from the galvanometer 
 mirror. [In the same units as those of the scale, e.g., milli- 
 metres.] Calculate the currents from E, G, and E's. Calcu- 
 late the <o's from the formula 
 
 A 
 
 tan. 2 a) - 
 d 
 
 Calculate the reduction factors K for the different currents and 
 make a table. Plot a curve with tan. o> for ordinates and G for 
 abscissae. 
 
 The currents may be read directly by inserting a Weston am- 
 meter, if the galvanometer be suited for moderately strong cur- 
 rents. 
 
 Reduction Factor of an Electro-dynamometer. If a 
 
 'current (7, flowing through an electro-dynamometer, needs a tor- 
 sion angle 6 to bring the needle back to zero, the reduction factor 
 K connects G and 6 by the formula 
 
 Why? 
 
 Apparatus. Electro-dynamometer, ammeter, lamp-board re- 
 sistance, street circuit. 
 
 Directions. Form a circuit of all the apparatus in series, and 
 varying the lamps in circuit, note C's by the ammeter and corre- 
 sponding e's of the electro-dynamometer. Calculate K in each 
 case and form a table. Plot a curve with 6's for ordinates an& 
 C's for abscissae. 
 
HEAT EFFECTS. 
 
 Electro-chemical Equivalents of Copper and Hydro- 
 gen. One coulomb [1 ampere for 1 second] theoretically disen- 
 gages 0.1157 cu. cm. of hydrogen [at 760 mm. and 0] at the 
 cathode of an electrolytic vessel containing dilute H 2 SO 4 , and 
 0.000328 gram of copper from a solution of CuSO 4 . 
 
 Apparatus. Hoffman H 2 SO 4 voltameter with cock at the bot- 
 tom, copper voltameter, Weston ammeter, lamp-board, street cir- 
 cuit, clock, thermometer, barometer. 
 
 Directions. Fill the voltameter with a dilute solution of chem- 
 ically pure H 2 SO 4 . Form a fresh deposit on the cathode of the 
 copper voltameter. Wash the cathode, dry it under an air-pump, 
 and weigh. Let the weight be 'w grams. 
 
 Form a circuit of ammeter, two lamps in multiple arc, volta- 
 meter in series. Close the circuit and note the time t. Allow the 
 current to flow until one tube of the voltameter is nearly filled 
 with hydrogen. Turn off current, noting time t'. Let the acid run 
 out of the lower cock of the voltameter until the level in the reser- 
 voir tube is the same as in the hydrogen tube. Bead off the cu. 
 cms. q of hydrogen. Note barometer height h. Take the tem- 
 perature t of hydrogen by placing the thermometer alongside the 
 tube. Eead the ammeter every thirty seconds that the circuit 
 is closed. Let the average current be C. Wash, dry, and weigh 
 [= w' grams] the copper cathode. C (t f t) coulombs, in passing 
 through the circuit, have deposited (w f w) grams of copper and 
 
 cu - cms - f hydrogen. 
 
 1 -f- 0.00367 t 760 
 
 Verify the theoretical equivalents, i.e., amount per coulomb in 
 each case. 
 
 Heat Effects. C amperes flowing through E ohms for t sec- 
 onds liberate C*Rtx gram calories of heat You are required to 
 determine x. 
 
 Apparatus. Calorimeter, distilled H a O, thermometer, bare 
 German silver coil, balance, ammeter, lamp-board resistance, and 
 clock. 
 
 Directions. Measure the resistance R of the coil. Submerge 
 the coil in q grams of H 2 O placed in the calorimeter. Place the 
 thermometer so that the bulb is in the centre of the coil. Con- 
 nect the lamp-board, ammeter, and coil in series. Close the cir- 
 cuit and note the time t l and temperature t. When the temper- 
 ature [the H 2 O being continually stirred] reaches about 30 [r= 2 ], 
 open the circuit, noting time t tj . Eead the ammeter and ther- 
 
468 
 
 ELECTRICAL MEASUREMENTS. 
 
 mometer every thirty seconds that the circuit is closed. If the 
 average current be C and the water value of the calorimeter be w, 
 
 (1 - t) (w + q) 
 G'B (t, - 
 
 It is well to have the original temperature of the water as 
 much below the temperature of the room as it will be above that 
 temperature at the close of the experiment. Plot a curve of tem- 
 perature and time. Explain its form. 
 
 CONDENSERS. 
 
 If a condenser of G farads capacity be charged with Q coulombs, 
 the two terminals will have a difference of potential of V volts de- 
 termined by the condition Q = C V. If a condenser charged suc- 
 cessively with Q lt Q 3 . . . units be discharged through the same gal- 
 vanometer yielding the [small] amplitudes of the first vibrations 
 6 lt a . . . then Q l : Q 3 : . . . = 6 l : a : . . . The deflections 6 are 
 termed "throws" or "kicks " 
 
 To Compare Capacities. Apparatus. Double key, stand- 
 ard condenser (7, condenser of capacity x, ballistic galvanometer, 
 
 and Daniell cell. 
 
 Directions. Connect up the stand- 
 ard as in Fig. 411. Close the key and 
 observe the throw 0. Substitute the 
 condenser of unknown capacity for the 
 standard. Observe the throw 0'. Then 
 
 The ratio of the E. M. F. of two cells may be easily determined 
 by means of the condenser. They are to each other directly as 
 the throws which they cause in the galvanometer when connected 
 successively with the same condenser as in Fig. 411. 
 
 To Determine the Internal Re- 
 sistance of a Cell by Means of a 
 Condenser. Apparatus. Condenser, 
 C, ballistic galvanometer, G, double 
 contact key, K, rheostat, E, and cell of 
 internal resistance x. 
 
 Directions. Form circuit as in Fig. 
 412, leaving out an infinity plug in the 
 rheostat. Press the key and release it. 
 Observe the throw 6 in the galvanom- 
 
 FIG. 412. 
 
MAGNETISM. 469 
 
 eter. Replace the infinity plug leaving a resistance R in the 
 rheostat. Again close and release the key observing the throw &. 
 Then 
 
 ,, '- 
 
 Prove that the formula is correct. 
 
 MAGNETISM. 
 
 Moment of Inertia. The moment of inertia K of. a cylinder 
 magnet I cms. long and of r cms. radius and weighing m grams, 
 referred to an axis perpendicular to the axis of the cylinder at its 
 middle point is 
 
 '--(+3- 
 
 measure I by a scale, 2r by micrometer screw, and m by a balance. 
 Calculate K. 
 
 Time of Oscillation of a Cylindrical Magnet. Appara- 
 tus. Cylinder magnet, suspension case, seconds striking clock. 
 
 Directions. Suspend magnet so that, when no torsion is ex- 
 erted by the suspension, the magnet sets north and south. Affix 
 a light paper pointer to magnet over a mark in the case. Set the 
 magnet in vibration by approaching another magnet. Starting 
 at any convenient time, mentally count the seconds as they are 
 struck by the clock and, in your note-book, record the exact times 
 of 50 successive passages of the pointer over the mark in the case. 
 (Instead of a pointer, a mirror may be attached to the magnet 
 and the passage of the zero point of a scale can be observed in a 
 telescope.) The seconds must be divided into 10 parts by esti- 
 mate. A little practice enables one to do this well. 
 
 Of the 50 observed times, cast away the first 5 and the last 5. 
 Divide the remaining 40 into 4 groups of 10 successive times. In 
 each group take the arithmetical mean of the 1st and 10th, 2d 
 and 9th, 3d and 8th, 4th and 7th, 5th and 6th. Take the mean of 
 the means of each group. You have then four absolute points in 
 time. The magnet made 20 oscillations between the 1st and 
 3d points and 20 between the 2d and 4th points. The time of 
 
 gd _ p 4*& _ 2<* 
 
 a single oscillation r = ^- = -- From K and r cal- 
 
 M = magnetic moment of the cylinder, 
 _ f. , , . , . . , * 
 
 H = earth s horizontal intensity. 
 
 culate MH 
 
 Determination of .Apparatus. Magnetometer, cylin- 
 rl 
 
470 ELECTRICAL MEASUREMENTS. 
 
 der magnet, rack to hold magnet in same horizontal plane as the> 
 needle of the magnetometer, meter rod. 
 
 Directions. Place rack so as to hold magnet in an east-west 
 direction with its middle point in the same horizontal plane as the 
 magnetometer needle and directly north of it. Place magnet at a 
 distance r cms. from the needle and read the deflection 6 of the 
 magnetometer needle. Reverse the magnet end for end and read 
 the deflection 6'. Average these readings. Repeat the operation 
 with the magnet at a shorter distance r' cms. from the needle, 
 obtaining an average deflection < (r should be equal to about 1.4 
 r'). Then 
 
 M r 5 tan. 6 / 6 tan. <fr 
 
 From the values of and ME determine M and H. Calculate 
 Jd. 
 
 M 
 
 the specific magnetism = - . 
 
 wt. in grams 
 
 Magnetization Curve of Iron or Steel. Apparatus. 
 Test ring*, T, wound with a primary and secondary coil, ammeter, 
 A, adjustable resistance, R, commutator, C, ballistic galvanometer, 
 G, and source of current, E. 
 
 Directions. Connect the apparatus as in Fig. 413. Adjust R 
 so as to yield the maximum current to be employed. With the 
 galvanometer circuit broken, cominutate a few times to get the 
 
 iron into a cyclic condition. 
 Close the galvanometer circuit, 
 and, commutating once, ob- 
 serve the throw of the galva- 
 nometer, 6, at the same- time 
 read the amperes, c, by the am- 
 meter. Repeat this operation with various currents. The mag- 
 netizing forces are proportional to the current strengths, and the 
 induction in the iron is proportional to the throws of the gal- 
 vanometer. If the current in the primary of N turns be c amperes 
 
 * The dimensions of the test ring and the number of turns of wire in the- 
 primary and secondary are dependent on the sensibility of the galvanometer 
 and the availability of current for the primary magnetizing coil. The fol- 
 lowing ring is suitable for a test with the cheap D'Arsonval galvanometers 
 mentioned before. The ring is annular, of rectangular cross-section, with 
 an internal diameter of 5 inches, an external diameter of 6 inches, and a 
 depth of 2 inches. If the primary be wound with one layer of No. 16 wire 
 (250 turns), 5 amperes will be the maximum current required. The second- 
 ary needs but 4 or 5 turns. 
 
MAGNETIZATION OF IRON. 471 
 
 and the arithmetical mean of the internal and external diameters 
 be d cms., the magnetizing force 
 
 If the throw 6 in the galvanometer connected with n turns around 
 the ring, whose cross- section is A square cms., results from a re-. 
 versal of the main current, c, then the flux density corresponding 
 to this Hia 
 
 D 100 r . 
 B -- kQ gausses, 
 A A.n 
 
 where r is the resistance of the galvanometer plus the secondary 
 coil, and k is the galvanometer coefficient, i.e., the micro-coulombs 
 of electricity which are necessary to cause a throw of 1 scale di- 
 vision in the galvanometer. To obtain the value of k it is neces- 
 sary to charge a microfarad condenser with a cell of E volts, dis- 
 charge it through the galvanometer, and immediately afterward 
 connect the terminals of the galvanometer by a resistance equal 
 to the resistance of the secondary coil on the ring. This latter is 
 necessary because the damping of a galvanometer is dependent 
 on the external resistance. The charge, discharge, and short cir- 
 cuit can be conveniently accomplished with the assistance of a 
 two-tongued top-and-bottom contact key. Plot a curve with B 
 for ordinates and H for abscissae. 
 
 Test Nail. This exercise is to determine the distribution of 
 force along a bar magnet. If a piece of soft iron be placed in the 
 field of a magnet, a pole, proportional to the field's strength, will 
 be induced. The force exerted will be proportional to the strength 
 of field x strength of pole, i.e., proportional to the square of the 
 field strength. 
 
 Apparatus. Bar magnet, piece of wood of the same size as the 
 magnet, soft iron armature, suspended from a spring whose elon- 
 gation may be measured on a graduated circular scale, meter 
 rod. 
 
 Directions. Determine the of the scale with the armature 
 resting upon the piece of wood. Substitute for the wood the 
 magnet and, using the just found, determine the extension of 
 the spring necessary to detach the armature from various points, 
 of the magnet. Kepresenting the distances of these points from 
 the middle of the magnet by Z>, and the extension by F, form a 
 
 fW 
 
 p and W -= 
 
 table of D, F, p and W -= Plot a curve of F and D. 
 
472 ELECTRICAL MEASUREMENTS. 
 
 CALIBRATIONS. 
 
 Rheostat. Apparatus. Wire bridge, galvanometer, rheostat, 
 1-ohm coil, and standard 100-ohm coil. 
 
 Directions. Determine the correction for the 500 division of 
 the bridge wire by balancing two 10-ohm coils against each other 
 and then, exchanging them, balancing them again. The mean of 
 the two bridge readings gives the electrical centre or 500 of the 
 wire. (500 mean) is the correction which must be applied in all 
 the subsequent readings. Now, assuming the auxiliary 1 ohm as 
 correct, determine the assumed correct value of the 1 ohm in the 
 rheostat. Compare these two 1 ohms with the 2-ohm coil, and 
 find its assumed correction. Similarly compare 3 with corrected 
 1 + 2 ; 4 with 3 + 1 ; 10 with 4 + 3 + 2 + 1; 20 with 10 + 4 + 
 3 + 2 + 1 ; etc. You thus obtain a table of assumed corrections, 
 which would be correct at the correct temperature for the assumed 
 standard 1-ohm coil. Now compare the 100 in the rheostat with the 
 standard 100 coil. From the actual correction for the 100, thus ob- 
 tained, subtract the assumed correction. Add -$ of this difference 
 to the assumed correction for the 10 ; T J 7 to the assumed correc- 
 tion for the 1 ; T 4 ff for the 40 ; etc. Make a table of corrections. 
 
 "Bridge Wire. From the known values of the resistances 
 the electrical position of any portion of the bridge wire can be 
 obtained. The bridge reading minus the electrical position = cor- 
 rection. Find the correction for every 50th division. 
 
 Ammeter. Apparatus. Standard ammeter, adjustable re- 
 sistance, current to the maximum capacity of the ammeter to be 
 calibrated. 
 
 Directions., Arrange all the apparatus in series. Adjust the re- 
 sistances so as to produce a current T ^ of the maximum range of the 
 ammeter to be calibrated. Read both the ammeters at the same 
 time. Eepeat this operation with different currents throughout the 
 range of the instrument. Plot a curve with the readings of the 
 standard for abscissae and those of the other ammeter for ordinates. 
 
 Voltmeter. Apparatus. Standard voltmeter, two adjust- 
 able resistances, E. M. F. to the maximum capacity of the voltme- 
 ter to be calibrated. 
 
 Directions. Connect the two resistsfhces in series with the 
 E. M. F. Connect both voltmeters in multiple arc with the ter- 
 minals of one of the resistances. By manipulating the resistances 
 impress various voltages on the voltmeters, making simultaneous 
 readings from the two instruments at each of the voltages. Plot 
 3, curve as in the case of the ammeters. 
 
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