REESE LIBRARY 
 
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 | 
 
 UNIVERSITY OF CALIFORN 
 
 x Keceired.... ^.l~S*U? G^tf M.S'. 
 Accessions No.2r.*&? / Shelf No.... 
 

 
CHAMBERS^ EDUCATIONAL COURSE 
 
 ELECTKICITT 
 
 EGBERT M. FERGUSON, PH.D., F.R.S.E. 
 
 OF THE EDINBURGH INSTITUTION 
 
 REVISED AND EXTENDED BY 
 
 JAMES BLYTH, M.A., F.R.S.E. 
 
 PROFESSOR OF MATHEMATICS AND OF NATURAL PHILOSOPHY 
 
 S COLLEGE, GLASGOW 
 
 " 
 
 OF Til: 
 
 W. & R. CHAMBERS 
 LONDON AND EDINBURGH 
 
 1882 
 
Edinlurgh : 
 Printed by W. & R. Chambers. 
 
PEEFACE 
 
 TO THE NEW EDITION. 
 
 THE well-merited success and popularity of Dr Ferguson's 
 work on Electricity has led the publishers to issue a new 
 edition adapted, by alterations and extensive additions, to 
 the present state of scientific investigation, and current 
 methods of studying the subject. The book aims at giving 
 a popular and accurate account of the chief experimental 
 facts of the science of El&ct^&ifc^ ^ind Magnetism, and of 
 the exact laws which have been deduced from them. It 
 is designed to meet the requirements of students at science 
 classes, science colleges, and technical institutes, as well as 
 Teachers and private pupils ; and as an introduction to 
 electrical science as a whole, should be valuable to those 
 engaged in telegraphy, telephony, electro-metallurgy, and 
 the other practical applications of Electricity. 
 
 The work has been revised and largely re-written for the 
 present edition ; and a considerable amount of new matter 
 added. This was rendered necessary, both from the recent 
 increase of our knowledge of the subject, and also from the 
 fact that certain modern ideas and methods of explanation 
 such as Potential required to be introduced. In the experi- 
 mental part of the subject, constant reference has, of course, 
 been made to Faraday's researches, and to such works as 
 those of Wiedemann and Mascart. In the theoretical 
 explanation, equally constant reference has been made to 
 
4 PREFACE. 
 
 the writings of Sir William Thomson and Professor J. 
 Clerk- Max well. The adopted systems of practical and 
 absolute units have been given, and the most approved 
 methods of measuring electrical and magnetic quantities 
 explained. 
 
 An attempt has been made to give the leading mathe- 
 matical formulae connected with the subject, as far as that is 
 possible with the aid of only elementary mathematics. 
 Care has been taken to include important recent inven- 
 tions, and special chapters on the Practical Applications of 
 the subject have been given. In this way it is hoped that 
 the work will be found of service not only to those students 
 who wish to obtain an experimental and elementary theo- 
 retical knowledge of the subject ; but also to those who are 
 engaged in practical work, and who aim at being practical 
 electricians. 
 
 2d October 1882. 
 
CONTENTS. 
 
 PAGE 
 
 PART I. MAGNETISM..... 11-60 
 
 CHAP. i. Magnetism 11 
 
 n. Terrestrial Magnetism 33 
 
 in. Chronology of Magnetism 59 
 
 PART IL FRICTIONAL OB STATICAL ELECTRICITY 61-163 
 
 CHAP. iv. General Phenomena. 61 
 
 v. Dynamical Principles 74 
 
 vi. Electrical Quantity and Density 83 
 
 vii. Induction. 92 
 
 vm. Potential 103 
 
 ix. Friction Electric Machines .117 
 
 x. Accumulators 129 
 
 XL Electroscopes and Electrometers 143 
 
 xii. Terrestrial and Atmospheric Electricity 155 
 
 PART III CURRENT ELECTRICITY 164-330 
 
 CHAP. XIIL Electro-motive Force, Current, Resistance, 
 
 and Electrical Units 164 
 
 xiv. Voltaic Batteries ...175 
 
 xv. Current Resistance, Ohm's Law 192 
 
 xvi. Measurement of Resistance 204 
 
 xvii. Physiological, Heating, Luminous, and 
 Electrolytic Effects of the Galvanic 
 
 Current 218 
 
 XVIIL Contact Force and Thermo-electricity 229 
 
 xix. Electro-magnetism and Magneto- electric 
 
 Induction ...245 
 
6 
 
 CONTENTS. 
 
 PART III. continued PAGE 
 
 CHAP. xx. Galvanometers 273 
 
 xxi. Current Induction 280 
 
 xxii. Electro-magnetic and Magneto-electric In- 
 duction Apparatus 301 
 
 PART IV. PRACTICAL APPLICATIONS or CURRENT 
 
 ELECTRICITY 331-406 
 
 CHAP. XXIIL Electro-metallurgy 331 
 
 Electric Light 334 
 
 Exploding Gunpowder at a distance 340 
 
 Electric Clocks 343 
 
 xxrv. Machines for converting Mechanical Work 
 
 into Electricity, and conversely 346 
 
 xxv. Electric Telegraph 369 
 
 xxvi. Telephone 390 
 
 Electrical Storage of Energy 400 
 
 XXVIL Electro-optics 402 
 
CENTIMETRE-GEAMME-SECOND (C. G. S.) SYSTEM 
 OF UNITS. 
 
 FUNDAMENTAL UNITS : 
 
 Unit of Length One Centimetre. 
 
 Unit of Mass One Gramme. 
 
 Unit of Time One Second. 
 
 The Centimetre = 0-3937 inch. 
 
 The Metre = 100 Centimetres. . . = 39-37 inches. 
 
 The MiUimetre... = T V Centimetre.... = 0-03937 inch. 
 
 The Gramme = 15432 grains Troy. 
 
 The Kilogramme = 1000 Grammes = 2-2 pounds Avoird. 
 
 The Milligramme = urnr Gramme. 
 
 DERIVED UNITS : 
 
 Velocity. The unit of velocity is the velocity of one centi- 
 metre per second. 
 
 Acceleration. The unit of acceleration is the acceleration of 
 one centimetre-per-second per second. 
 
 Gravity. g. = 981-1. 
 
 Force. The one of force One Dyne is that which, acting on 
 one gramme for one second, gives it a velocity of one centimetre 
 per second. 
 
 Work. The unit of work One Erg is the work done in 
 overcoming one dyne through one centimetre. 
 
 Heat. The unit of heat One Caloric is the heat required to 
 raise the temperature of one gramme of water from to 1 C. 
 Dynamical equivalent of one Caloric, that is, Joule's Equivalent 
 = 42,000,000 Ergs. Hence J = 42,000,000 (C. G. S.). 
 
 Since paragraph 187 was printed, a slight change in the names 
 of the Practical Electrical Units has been agreed upon by the 
 International Congress of Electricians at Paris. 
 
 Instead of the Weber, the name Coulomb is adopted, so that 
 the Coulomb = the unit of quantity = ^ C. G. S. 
 
 The na'me Ampere is given to the practical unit of current, so 
 that the Ampere = the unit of current = tV C. G. S. 
 
UNIVERSITY 
 
 ELECTRICITY. 
 
 Part I -MAGNETISM. 
 
 CHAPTER L 
 
 1. MAGNETISM is the influence in virtue of which certain 
 bodies called magnets have the peculiar property, among 
 others, of attracting iron. No substance is totally unaffected 
 by a magnet ; in iron the effects are most marked. Magnets 
 are either natural or artificial. Natural magnets consist of 
 the ore of iron called magnetic, familiarly known as load- 
 stone, the chemical composition of which is given by the 
 formula Fe 3 4 . This ore, although capable of becoming 
 magnetic, only occasionally occurs naturally magnetised. 
 The loadstone appears to have been first discovered in 
 Magnesia, in Asia Minor, hence the name magnet. Arti- 
 ficial magnets are, for the most part, straight or bent bars 
 of tempered steel, which have been magnetised by the action 
 of other magnets, or by the galvanic current. 
 
 2. The power of the magnet to attract iron is by no means 
 equal throughout its length. If a small 
 iron ball, suspended by a thread, be 
 placed in succession opposite different 
 parts of a bar magnet (fig. 1), it is 
 powerfully attracted at the ends, but 
 not at all in the middle, the magnetic 
 force increasing with the distance 
 from the middle of the bar. The ends 
 of the magnet where the attractive 
 power is greatest are called its poles. 
 The greater strength of the magnetic 
 power at the poles of a magnet may also be shewn by 
 dipping it in iron filings, when a tuft of filings adheres to 
 each extremity, and the middle is left bare. By causing a 
 
 Fig. i. 
 
12 ELECTRICITY. 
 
 magnetic needle moving horizontally to vibrate in front of 
 the different parts of a magnet placed vertically, and counting 
 the number of vibrations, the rate of increase of the magnetic 
 force with the distance from the centre may be found exactly, 
 as will be afterwards shewn. 
 
 Fig. 2 gives a graphic view of this increase. NS is the 
 magnet; the lines riN, aa, &c. represent the strengths 
 at the points N, a, &c. of the magnet ; and the curve of 
 
 Fig. 2. 
 
 magnetic strength, na'M.a'n', is the line formed by the extremi- 
 ties of all the upright lines. It will be seen from the figure 
 that the forces exerted at corresponding points on opposite 
 sides of M, the centre of the magnet, are exactly equal ; that 
 for some distance on each side of the middle point the force 
 is nothing, and that it increases with great rapidity towards 
 the ends. The centres of gravity of the areas MnNn and 
 Mn'Sn' may be shewn to be the poles of the magnet, which 
 must therefore be situated near, but not at its extremities. 
 The Magnetic Axis of a magnet is the line joining the poles. 
 
 3. If fine iron filings be strewn on a sheet of stiff drawing- 
 paper under which there is a strongly magnetised bar, and 
 the paper be gently tapped, the particles will arrange them- 
 selves in curved lines, crowded" together at the poles, and 
 
MAGNETISM. 
 
 13 
 
 farther apart as we recede from them (fig. 3, a). The lines are 
 called lines of magnetic force. The space through which a 
 magnet exercises a finite force has been named by Faraday 
 its Magnetic Field. The effect apparently produced by 
 the magnet ought to be referred to the mediate action of 
 the magnetic field, rather than to the direct action of the 
 magnet, since, as will be shewn later, the same effects may 
 be produced without the presence of a magnet. In other 
 words, the presence of a magnet produces a condition of stress 
 in the medium or ether in its neighbourhood. This condition 
 of stress manifests itself in various ways (such as by the 
 deflection of small magnets, &c.), which are usually explained 
 as being caused by the magnet. But as the same condition 
 of stress and the consequent effects can also be produced by 
 a current of electricity, it is considered better to attribute the 
 apparent action of the magnet to the action of the magnetic 
 
 Fig. 3. 
 
 field. A line of magnetic force is such that its direction at 
 any point is that of the resultant force exerted there, and the 
 magnetic field may be so mapped out that the number of 
 lines in unit of area at any place gives a measure of the 
 intensity of the magnetic force there. If we place, at any 
 point in the field, a small needle, free to turn about an axis, 
 
14 ELECTRICITY. 
 
 it will always take up a position tangential to the line of 
 force passing through its centre. And if it were moved 
 always in the direction in which it is pointing, its centre 
 would trace out a line of force. Fig. 3, a, shews the lines 
 of force in the neighbourhood of a single bar magnet ; 6, 
 of two magnets with like poles adjacent ; c. of two magnets 
 with unlike poles adjacent ; d, of a single pole. 
 
 A uniform magnetic field is one in which the lines of force 
 are parallel to and equidistant from each other, such as any 
 small space in the field at some distance from the poles. 
 Any station on the earth's surface unaffected by the presence 
 of magnetic matter in the neighbourhood is also a uniform 
 field the direction of the force being that of the dipping 
 needle there (sect. 35). 
 
 4. If between the magnet and the ball in fig. 1 a sheet of 
 pasteboard, or any other material not containing iron, be inter- 
 posed, the action would not be lessened. It is the peculiarity 
 of magnetic action that it is transmitted through all sub- 
 stances not decidedly magnetic with equal facility. Most 
 substances are thus, so to speak, magnetically transparent. 
 
 5. A magnet has, then, two poles or centres of magnetic 
 
 force, equal in strength but of 
 opposite properties. To shew this, 
 let a magnet, NS (fig. 4), be sus- 
 pended by a stirrup of paper, M, 
 hanging from a cocoon thread (or 
 any fine thread without torsion). 
 When the magnet is left to itself, it 
 takes up a fixed position, one end 
 pointing northwards, and the other 
 south. The north pole cannot be 
 made to stand as a south pole, and vice versd; for though 
 disturbed, the magnet, as soon as it is released, returns to its 
 original position. Here, then, is a striking dissimilarity in 
 the poles, by means of which we are enabled to distinguish 
 them as north pole and south pole. If we now try the effect 
 of another magnet upon the suspended one, we shall find 
 that the north pole of the suspended magnet is attracted by 
 one of the poles of the second magnet and is repelled by the 
 
MAGNETISM. 15 
 
 other, and similarly with the south pole ; where the one pole 
 attracts, the other repels. If, now, the second magnet be 
 hung like the first, it will be found that the pole which 
 attracted the north pole of the first magnet is a south pole, 
 and that the pole which repelled it is a north pole. Poles of 
 the same name are called like poles ; of opposite names, unlike 
 poles. We thus learn, that each magnet has two poles, the one a 
 north, and the other a south pole, alike in their power of attract- 
 ing soft iron, but differing in their action on the poles of another 
 magnet, like poles repelling, and unlike poles attracting, each 
 other. On this account a magnet is said to be Polarised. 
 
 6. When a small magnetic bar, or needle, as it is called 
 (fig. 5), is delicately balanced by means 
 
 of a small inverted agate cup on a 
 
 fine hard point, it may be used as a 
 
 magnetoscope to indicate whether a S 
 
 piece of iron or steel is magnetised 
 
 or not. If the poles of the needle are 
 
 attracted equally by either end of the 
 
 iron or steel it is not magnetised ; but 
 
 if one pole is attracted and the other Fig. 5. 
 
 repelled, the piece of iron or steel under examination is 
 
 magnetised. 
 
 7. The fact of the freely suspended magnet taking up a 
 fixed position, has led to the theory, that the earth itself acts 
 much in the same way as a huge magnet, with its north and 
 south magnetic poles in the neighbourhood of the poles of 
 the axis of rotation, and that the magnetic needle or sus- 
 pended magnet turns to them as it does to those of a neigh- 
 bouring magnet. All the manifestations of terrestrial mag- 
 netism give decided confirmation of this theory. It is on 
 this view that the French call the north pole of the magnet 
 the south pole (pole austral), and the south the north pole 
 (pole boreal) ; for if the earth be taken as the standard, its 
 north magnetic pole must attract the south pole of other 
 magnets, and vice versa. In England and Germany, the 
 north pole of a magnet is the one which, when freely 
 suspended, points to the north, and no reference is made to 
 its relation to the magnetism of the earth. Clerk Maxwell 
 
16 ELECTRICITY. 
 
 and others use the term Boreal to indicate the magnetism 
 near the north pole of the earth and the south end of a 
 magnet, and Austral that of the south pole and north end. 
 
 8. It might be thought that, by dividing a magnet at its 
 centre, the two poles could be insulated, the one half contain- 
 ing all the north polar magnetism, and the other the south. 
 When this is done, however, each half becomes a complete 
 magnet the broken end of each having a new pole oppo- 
 site to and weaker than the original pole of the piece. 
 This and other facts mentioned in sect. 27 prove that we 
 can never have one kind of magnetism unless associated with 
 the same amount of the opposite magnetism. 
 
 9. Nature of Magnetism. To explain the phenomena of 
 magnetism several theories have been propounded. One of 
 these attributes the power of a magnet to the presence in 
 it of two fluids called respectively the northern and the 
 southern fluid. The molecules of either of these two fluids 
 attract those of the other kind, but repel their own. The 
 fluids are confined to the molecules of the magnetic sub- 
 stance, and are always in equal quantities that is, every 
 substance has always equal north and south magnetism. In 
 a non-magnetised piece of iron the fluids in each molecule 
 are supposed to be thoroughly mixed. To magnetise it 
 the fluids in every molecule must be separated and concen- 
 trated at its two ends the more complete the separation, 
 the stronger is the magnetisation. In such a substance 
 as soft iron the separation is effected only during the 
 presence of the magnetising agent. In steel again the separa- 
 tion is effected with difficulty, but continues in consequence 
 of the coercive force (sect. 11). 
 
 A more recent theory suggests, that all substances capable 
 of becoming magnetic consist of particles, each of which is a 
 permanent magnet ; that these infinitesimal magnets have their 
 poles turned in all the different directions, so as to neutralise 
 each other when the whole is not magnetic ; that magnetisa- 
 tion has the effect of bringing the poles of these particles 
 round so as to lie in the same direction ; that this coin- 
 cidence of poles in the case of soft iron takes place only when 
 the iron is under the influence of a magnet or of an electric 
 
MAGNETISM. 17 
 
 current ; that in the case of steel it takes place permanently ; 
 and that the intensity of magnetisation depends upon the 
 completeness of the coincidence. This way of conceiving of 
 the composition of a magnet is both simple and satisfactory, 
 and agrees with the fact that there is a limit to the magneti- 
 sation of a magnet. Ampere's theory of the electric consti- 
 tution of a magnet, which will be afterwards described, 
 introduces an entirely different view of it. 
 
 It may be noticed here that the magnetism of which a 
 substance is capable depends in some way on the closeness 
 of its particles. For the most magnetic substances, as iron 
 and nickel, have apparently their particles most densely 
 packed, as is seen by the ratio of their specific densities to 
 their atomic weights. Again, wherever a body is compressed 
 in one direction more than in any other, it shews magnetic 
 properties strongest in that direction, notably in crystals. 
 The change produced by rise of temperature goes to 
 strengthen this view (sect. 26). 
 
 10. Magnetic Induction. When a short bar of soft iron, ns 
 (fig. 6), is suspended from one end, S, of the magnet, NS, 
 
 Fig. 6. 
 
 it becomes for the time powerfully magnetised. It is found to 
 possess a north and a south pole, like a regular magnet, as may 
 be seen by testing with the small magnetic needle (fig. 5) ; and 
 if its lower end, s, be dipped into iron filings, it attracts them 
 as a magnet would do. When it is taken away from NS, the 
 great mass of the filings fall off, and nearly all trace of 
 magnetism disappears. Actual contact between the magnet 
 and the bar is not necessary to produce these effects. Any 
 piece of soft iron placed in a magnetic field exhibits magnetic 
 properties, which it loses to a greater or less extent when 
 
18 ELECTRICITY. 
 
 removed. For example, an ordinary soft-iron poker held 
 in the direction of the earth's magnetic force is found to 
 possess, in the Northern Hemisphere, a north pole at its 
 lower end and a south pole at the upper : this is proved 
 by the upper end always attracting the marked or north 
 pole of a needle and repelling the south pole. If the 
 poker be inverted, we find that the end which before was 
 a south pole, is now a north pole. This shews that the 
 magnetisation produced is not permanent. In such cases the 
 bar and poker are said to be magnetised by induction, and 
 the action is called magnetic induction. If the inducing 
 magnet be strong enough, the induced magnet, ns, when in 
 contact, can induce a bar like itself, placed at its extremity, 
 to become a magnet ; and this second induced magnet may 
 induce magnetism in a third ; and so on, the action being, how- 
 ever, weaker with every additional magnet. As was pointed 
 out in sect. 3, the explanation of this and similar phenomena 
 should be referred to the action of the magnetic field. 
 
 11. Coercive Force. If a steel bar be used for this experi- 
 ment, a singular difference is observed in its action ; it is 
 only after some time that it begins to exhibit magnetic pro- 
 perties, and then they are feebler than in the soft-iron bar. 
 When the steel bar is removed, it does not part instantly with 
 its magnetism, as the soft-iron bar, but retains it permanently. 
 Steel therefore, in the first instance, resists the assumption of 
 magnetism ; and, when assumed, resists its withdrawal. This 
 is said to be due to a coercive force. The harder the temper 
 of the steel, the more is the coercive force developed in it. 
 This resistance offered to magnetisation and demagnetisation 
 differs very much in different substances, and in any one 
 substance is greatly affected by such processes as hammering, 
 &c., and in the case of iron and steel by the temper. For 
 example, steel when soft is almost as easily magnetised as 
 soft iron ; but hard steel, in virtue of its great coercive 
 force, is the best substance to make permanent magnets of. 
 If, when the poker is held in the position above described, a 
 few sharp blows are given to it with a hammer, it retains 
 some of its magnetic power, and the poles are no longer 
 reversed when the poker is inverted. It is in this way 
 
MAGNETISM. 19 
 
 probably that tools become magnetised. On the other hand 
 a steel magnet loses some of its magnetism when hammered, 
 and it is probably for this reason that a magnet is weakened 
 by a fall. Whenever large masses of iron are stationary for 
 any length of time, they are sure to give evidence of mag- 
 netisation, and it is to the inductive action of the earth 
 acting for ages that the magnetism of the loadstone is 
 attributed. It is this force also, in the loadstone, which 
 enables it to retain its magnetism. The polarised condition 
 of iron under induction seems to indicate that a substance 
 which is attracted by a magnet must itself become mag- 
 netic. The attraction between a magnet and soft iron is 
 thus essentially the same as that between two magnets. 
 Hence we may conclude that magnetic attraction and repul- 
 sion take place only between bodies which are magnetised either 
 permanently or temporarily. 
 
 12. The magnetisation induced by a given magnetising force 
 depends upon the substance acted on. Iron is capable of by 
 far the most intense magnetisation, and next to it come 
 nickel and cobalt. In these the magnetisation is in the 
 direction of the magnetising force ; such substances are called 
 Paramagnetic, Ferromagnetic, or Magnetic. In bismuth the 
 induced magnetism bears a very small ratio to the magnetis- 
 ing force, and is in the direction opposite to the magnetising 
 force. It and similarly affected substances are called Diamag- 
 netic. All substances, when subjected to a sufficiently 
 powerful magnetising force, are found to be either Para- 
 magnetic or Diamagnetic. 
 
 13. Faraday was the first (1845) to shew that all bodies 
 are more or less affected by 
 
 magnetic influence, and his 
 beautiful researches on the 
 subject have opened up a 
 new field in the domain of |^_ ^ 
 
 science. He found that the 
 
 magnetism of bodies was 
 
 manifested in two ways Fig. 7. 
 
 either in being attracted 
 
 by the magnet, as iron ; or in being repelled, like bismuth. 
 
20 ELECTRICITY. 
 
 When a needle or slender rod of iron is suspended between 
 the poles of a magnet, as in fig. 7, being attracted by them, it 
 takes up a position of rest on the line ab, joining the two 
 poles. When a substance behaves itself in this manner, it is 
 said by Faraday to be paramagnetic, and to place itself axially, 
 ab being the axis. A rod of bismuth, on the other hand, being 
 repelled by the poles of the magnet, conies to rest in the 
 line cd, at right angles to ab. Bismuth and the like sub- 
 stances, he calls diamagmtic, and they are said to place them- 
 selves equatorially, cd being the equator. These terms, being 
 both definite and graphic, have been universally adopted. 
 Magnetic is the term, used by Faraday to indicate magnetism 
 of either sort, although in general language it is understood 
 to refer to paramagnetic bodies, such as iron, &c. Para- 
 magnetic bodies, then, are those which manifest the same 
 properties with regard to the magnet that iron does ; and 
 diamagnetic bodies are those which, like bismuth, shew oppo- 
 site but corresponding properties ; so that in circumstances 
 where paramagnetic bodies place themselves axially, diamag- 
 netic bodies place themselves equatorially ; and where the 
 former are attracted, the latter are repelled, and vice versd. 
 A. paramagnetic substance, not in the elongated form, but in 
 a compact shape, such as that of a ball or a cube, is attracted 
 by either pole of the magnet, when suspended near it ; a ball 
 or cube of a diamagnetic, on the other hand, experiences, 
 when so placed, repulsion. They may also be distinguished 
 by the fact that paramagnetic bodies tend to place themselves 
 where there are most lines of force in unit space, and 
 diamagnetic bodies where there are fewest lines of force. 
 
 14. The paramagnetism of iron, nickel, and cobalt becomes 
 manifest in the presence of magnets of ordinary power ; 
 but the magnetism of most other substances is so feeble 
 as to be developed only under the influence of the strongest 
 magnets. Electro-magnets are selected for investigations on 
 the magnetism of bodies, as they can be made of a strength 
 far outrivalling that of permanent magnets. Fig. 8 repre- 
 sents an electro-magnet which may be employed for this 
 purpose. The soft-iron horse-shoe, PPP, enveloped towards 
 its extremities in the coils of insulated copper wire cc, 
 
MAGNETISM. 
 
 Fig. 8. 
 
 which communicate with a galvanic battery by the wires w, 
 is fixed in an upright 
 wooden frame. The 
 ends or poles of the 
 magnet rise slightly 
 above the table or board 
 which forms the upper 
 part of the frame. In 
 order conveniently to 
 suspend substances be- 
 tween the poles, and to 
 protect them while under 
 observation from cur- 
 rents of air, a glass 
 frame of simple con- 
 struction (fig. 9) is made 
 to fit the table. The 
 upper plate of the frame 
 admits a wooden ring, into which an upright glass tube is 
 fitted. The thread by which the needle is suspended is 
 wound round a slender movable 
 bobbin at the top, so that it can 
 be elevated or lowered to the 
 proper position. To modify and 
 direct the action of the magnet, 
 two pieces of soft iron (fig. 7) are 
 made to rest on the end faces ; these 
 are pointed at one extremity, and 
 flat at the other, so that the force 
 of the magnet may be concentrated 
 in the points when they are turned 
 towards each other, or diffused over 
 the opposite flat surfaces when their 
 position is reversed. 
 
 15. To observe the effect of the magnet on liquids, Faraday 
 placed them in long tubes of very thin glass, and suspended 
 them as in the case of solid needles. It was found that 
 some arranged themselves axially, and others equatorially. 
 The attraction and repulsion that liquids experience in the 
 
 Fig. 9. 
 
22 ELECTRICITY. 
 
 presence of the magnet has been well shewn by Pliicker. 
 A large drop of liquid is placed in a watch-glass (figs. 10, 11), 
 and laid upon two poles of the shape shewn in the figures. 
 If the liquid be paramagnetic, the surface becomes depressed 
 at the interval between the poles, and heaped up over the 
 
 Fig. 10. Fig. 11. 
 
 extreme edges of them (fig. 10). A diamagnetic liquid, on 
 the other hand, shews a depression at each edge of the poles, 
 and a heaping up at the centre (fig. 11). 
 
 16. The magnetic nature of flames and gases has also been 
 studied. When the flame of a candle is brought between the 
 poles of a magnet, it is repelled by them, and thrown out 
 horizontally into an equatorial position. To ascertain the 
 magnetism of gases, Faraday inflated soap-bubbles with them, 
 and their para- or dia- magnetism was exhibited by their being 
 attracted or repelled by the poles. He ascertained the same by 
 causing the gases to flow out from glass tubes in the presence 
 of the poles, when the magnetic character of the gas was 
 shewn by its choosing an axial or equatorial means of egress. 
 
 17. The following lists include the more common sub- 
 stances in the order of the intensity of magnetisation of 
 which they are capable : 
 
 Paramagnetic. Iron, nickel, cobalt, manganese, chromium, 
 titanium, palladium, paper, sealing-wax, peroxide of lead, 
 plumbago, red-lead, sulphate of zinc, shell-lac, vermilion, 
 charcoal, proto- and per- salts of iron, salts of manganese, 
 oxygen, air. 
 
 Diamagnetic. Bismuth, antimony, zinc, tin, cadmium, 
 sodium, mercury, lead, silver, copper, gold, arsenic, uranium, 
 tungsten, rock-crystal, mineral acids, alum, glass, litharge, 
 nitre, phosphorus, sulphur, resin, water, alcohol, ether, sugar, 
 starch, wood, bread, leather, caoutchouc, hydrogen, carbonic 
 acid, coal-gas, nitrogen. 
 
MAGNETISM. 23 
 
 18. The nature of the medium in which, the body under 
 examination moves, exerts a powerful influence on the nature 
 and amount of the magnetism it exhibits ; thus, if a glass tube 
 be filled with a solution of the proto-sulphate of iron, and sus- 
 pended in air between the poles, it will place itself axially. It 
 will do the same if made to move in water, or in a more dilute 
 solution of the proto-sulphate of iron. It will be indifferent 
 in a solution of the same strength, but it will place itself equa- 
 torially in a stronger solution. In short, the same substance 
 may appear paramagnetic, indifferent, or diamagnetic, accord- 
 ing to the nature of the medium in which it moves. As a 
 general rule, a body shews itself paramagnetic towards one 
 less paramagnetic than itself, indifferent towards one equally 
 magnetic, and diamagnetic towards one more paramagnetic 
 than itself. The same takes place, mutatis mutandis, with dia- 
 magnetic substances. This has given rise to the theory, that 
 there is no such thing as diamagnetism per se, and that bodies 
 are diamagnetic only in media of greater paramagnetic power 
 than their own. This view of the case is, however, rendered 
 highly improbable by some of Verdet's experiments in con- 
 nection with magnetic action on polarised light, which prove 
 that magnetic and diamagnetic bodies do possess opposite 
 properties. 
 
 19. Form of Magnets. Artificial magnets are generally 
 either bar magnets or horse-shoe magnets. Powerful magnets 
 are often made of several thin bars of steel placed side 
 by side with their poles lying the same way, a*nd bound 
 together by a brass screw or frame. Three or four bars 
 
 Fig. 12. 
 
 may be put up into a bundle, and these again into 
 bundles of three and four (fig. 12). Such a collection of 
 magnets is called a magnetic magazine or battery. A magnet 
 of this kind is more powerful than a solid one of the same 
 mass and size, because thin bars can be more strongly and 
 
ELECTRICITY. 
 
 regularly magnetised than thick ones. But the joint strength 
 of the compound magnet is much less than the sum of the 
 strengths of its components, for the reason mentioned in 
 sect. 25. Fig. 13 represents a horse-shoe magnetic magazine. 
 The central lamina protrudes slightly beyond the others, and to 
 it the armature (sect. 20) is attached, and by this means the sus- 
 taining power of the magnet is much increased. The horse-shoe 
 magnet is the most suitable for lifting ; the bar magnet, for 
 other purposes, such as counteracting the directive action 
 of the earth's magnetism. A natural magnet is shewn in 
 
 Fig. 13. 
 
 Fig. 14. 
 
 fig. 14. It is a rectangular block of magnetic iron ore, with 
 pieces of soft iron, NN and SS, bound to its poles by a brass 
 frame encircling the whole. These pieces of iron apparently 
 concentrate and so very much increase the effective power 
 of the magnet. The lower ends of the soft-iron bars act as 
 the poles, and support the armature, A. 
 
 20. Magnetic Armatures or Keepers are pieces of soft iron 
 that are placed at the extremities of magnets to preserve 
 their magnetic power. When magnets are allowed to 
 remain any length of time without such appendages, they 
 lose considerably in strength in consequence of the dis- 
 turbing influence of terrestrial magnetism ; but when 
 they are provided with them, their magnetism is kept in 
 
MAGNETISM. 25 
 
 a state of constant activity. The reason of this is to be 
 attributed to magnetic induction. The horse-shoe magnet, 
 NHS (fig. 13), magnetises by induction the armature sn, so as 
 to have the south pole s next to N, and the north pole n at 
 the opposite extremity. The pole S, by virtue of its mag- 
 netic affinity, powerfully attracts the north pole n, thus 
 formed, and adds its own inducing influence to heighten the 
 magnetic condition previously induced in the armature by 
 the pole N. The armature, from the combined action of both 
 poles of the horse-shoe magnet, is thus temporarily converted 
 into a powerful magnet, with its poles lying in an opposite 
 direction to that of the primary poles. The original magnet 
 is, in consequence, brought into contact with one of its own 
 making, which shields it from terrestrial disturbance. At 
 the same time the keeper diminishes greatly the influence 
 of the magnet upon surrounding objects. The attachment 
 of the armature to the magnet is greater when its contact 
 with the magnet is made by a rounded edge instead of a 
 plane surface. It is due to the mutual attractions of the 
 magnet and armature that a much greater weight can be 
 sustained by the armature thus placed, than what the single 
 poles can together sustain. Two bar magnets may be armed in 
 the same way by laying them at some distance apart parallel 
 to each other, with their unlike poles towards the same parts, 
 and then connecting their extremities by two pieces of soft 
 iron (fig. 17). When a magnet, such as a compass-needle, is 
 free to take up the position required by the magnetism of the 
 earth, the earth itself plays the part of an armature. 
 
 21. Magnetisation By Magnets. In sects. 10 and 11, 
 certain circumstances were mentioned in which pieces of 
 iron and steel become magnetised. Several other processes 
 have been invented by which iron and steel bars can be 
 permanently magnetised. They may be classed under two 
 heads, according as other magnets or the galvanic current 
 is employed. In single touch, the bar to be magnetised, 
 which for shortness we shall call A, is stroked ten to 
 twenty times in the same direction, along its entire length 
 and on both sides, with one pole of the magnetising bar. The 
 magnetising bar will be called B. Or this may be done to 
 
26 
 
 ELECTRICITY. 
 
 one half of A with one pole of B, and then to the other 
 half with the other [pole each stroke beginning at the 
 centre of A. In every case B must be carried back to the 
 beginning of a new stroke, in an arch. The new magnet 
 has, at the end where B is raised, a pole opposite to the 
 magnetising pole of B. In divided touch (fig. 15), the latter 
 
 process is carried on simultaneously with two magnets, Bs, 
 equally inclined to A, at about 30, and prevented from touch- 
 ing. In double touch, two Bs inclined to A at about 15, and 
 
 Fig. 16. 
 
 Fig. 17. 
 
 prevented from touching by a piece of wood, are drawn 
 together backwards and forwards along the whole length of 
 A, beginning and ending the operation at the centre of A. 
 Divided touch gives the best results. 
 
MAGNETISM. 27 
 
 For horse-shoe magnets, Hoffer's method is generally 
 followed. The inducing magnet (fig. 16) is placed vertically 
 on the magnet to be formed, and moved from the ends to the 
 bend, or in the opposite way, and brought round again, in an 
 arch, to the starting-point. A soft-iron armature is placed at 
 the poles of the induced magnet. That the operation may 
 succeed well, it is necessary for both magnets to be of the 
 same width. 
 
 By the Galvanic Current The bar to be magnetised is 
 placed with soft-iron armatures on its extremities, in the 
 interior of a short thick coil of insulated wire, connected with 
 a galvanic battery. The circuit should be completed when 
 the coil surrounds the centre of the bar, which is then moved 
 backwards and forwards always to the 'ends as in double 
 touch. The process is finished by breaking the circuit when 
 the centre of the bar is again at the coil. The magnetism 
 induced in this way is much weaker than that got when 
 the same strength of current is employed through the inter- 
 vention of an electro-magnet. Thick bars or horse-shoes of 
 the hardest temper can be easily magnetised with a strong 
 electro-magnet by rubbing each half of the bar or horse-shoe 
 on a different pole, beginning at the middle, after the method 
 of single touch. See ELECTRO-MAGNETISM. Electro-magnets 
 far transcend permanent magnets in power. 
 
 22. Saturation Point. Magnets, when freshly magnetised, 
 have sometimes more magnetism than they can retain per- 
 manently. In that case, they gradually fall off in strength, 
 till they reach a point at which their strength remains con- 
 stant. This is called the point of saturation. We may ascer- 
 tain whether a magnet is at saturation by magnetising it 
 with a more powerful magnet, and seeing whether it retains 
 more magnetism than before. The saturation point depends 
 on the coercive force of the magnet, and not on the power of 
 the magnet with which it is rubbed. When a magnet is 
 above saturation, it is soon reduced to it by repeatedly 
 drawing away the armature from it. After reaching this 
 point, magnets will keep the same strength for years 
 together if not subjected to rough usage. 
 
 23. As will be more fully described hereafter, a magnet, 
 
.28 
 
 ELECTRICITY. 
 
 when disturbed from its position of rest in the plane of the 
 magnetic meridian (sect. 28), is urged to return by a force 
 which depends, among other things, upon the moment of 
 the magnet. The moment of a uniformly and longitudinally 
 magnetised bar is the product of its strength into its length. 
 Coulomb measured the magnetic moments of magnets by 
 means of the Torsion Balance. It consists of a glass cylinder, 
 
 Fig. 18. 
 
 A, round or square, covered with a plate of glass, B, from the 
 centre of which rises a tube, C, terminated by a plate, D, 
 graduated on its margin (shewn on larger scale at E). 
 Through the centre of D passes a short rod provided with 
 an index, d, and terminating below in a hook to which is 
 attached a fine wire. This carries a stirrup in which the 
 needle to be experimented on is placed. When the wire 
 is without torsion, the index should point to zero. A 
 graduated strip of paper, e } e, is pasted on the cylinder on 
 a level with the needle. When an experiment is to be 
 made, the apparatus is so placed that, the magnetic axis (sect. 
 2) of the needle being in the plane of the magnetic meridian, 
 
MAGNETISM. 29 
 
 and the wire without torsion, the needle points to zero 011 e. 
 The index, d, is then turned through an angle, 9, and this has 
 the effect of deflecting the needle through an angle, ; con- 
 sequently the torsion on the wire is 6 a, and the force of 
 torsion is equal and opposite to the force tending to bring the 
 needle back to the meridian. This is, at any one place 
 and time, proportional to the magnetic moment multiplied 
 by the sine of a. Knowing the force necessary to twist 
 the wire through any angle, Coulomb determined by this 
 method the moments of different magnets. He found that 
 in cylindrical magnets of the same diameter, and in rec- 
 tangular magnets of the same breadth and thickness, formed 
 of the same steel, the moment was proportional to the length 
 of the magnet. 
 
 With the help of the Torsion Balance he also ascertained 
 the law of distribution of the magnetic intensity in magnets. 
 The curve representing this intensity is given in sect. 2, fig. 2. 
 
 24. Laws of Magnetic Attraction. Coulomb next investigated 
 the laws of magnetic attraction. A long thin magnet was placed 
 in the stirrup, and the instrument so arranged that the needle 
 was in the magnetic meridian, and pointed to zero on e, 
 while there was no torsion on the wire. A magnet identical 
 with the suspended one was then inserted through an aperture 
 in the glass plate, B, in a vertical position, so that one of its 
 poles was near and in the same horizontal plane with the 
 ' like ' pole of the suspended magnet. The latter was imme- 
 diately repelled, and when at rest, the repulsion between the 
 two poles is equal to the directive force of the earth added to 
 the force of torsion. These can be ascertained, and hence the 
 repulsion due to the mutual action of the magnets at a 
 distance equal to the chord of the angle of deflection can be 
 measured. By twisting the wire through any angle, the 
 distance between the poles is altered, and a new relation 
 found between the repulsion and the distance. The angle 
 through which the wire is twisted is equal to the sum of 
 the readings of the needle and index. 
 
 By inserting magnets of different strengths Coulomb found 
 how the repulsion varied with the strength of the repelling 
 poles. The law he discovered is that when magnets are so 
 
30 ELECTRICITY. 
 
 placed that two adjoining poles act on each other without 
 the interference of the opposite poles which happens very 
 nearly when the magnets are long, thin, uniformly magnetised, 
 and of hard steel their attraction or repulsionis in the straight 
 line joining the poles, and is proportional directly to the product 
 of the strengths of their poles, and inversely to the square of 
 the distance between them. 
 
 The strength of a pole is measured by comparing it with a 
 conventional standard pole of unit strength. Unit pole is 
 a pole which points north and which repels another similar 
 and equal pole placed at unit distance with unit force. (For 
 a discussion of unit force, see Chap. V.) A south pole is 
 reckoned negative. Hence if m^ and m 2 be the respective 
 strengths of two poles, and d be the distance between 
 them, and / the force, the above law may be expressed 
 
 / = * 2 . Thus, if the two poles are like, they will have 
 
 the same sign, and / will be positive, shewing that there is 
 repulsion. If one pole be a negative pole, / will be a negative 
 quantity, indicating that there is attraction. 
 
 The laws of magnetic attraction may also be proved by 
 causing a short and massive magnet, sn, to oscillate in a hori- 
 zontal plane under the combined action of the earth and the 
 pole of a fixed magnet, SN. The needle, sn (fig. 19), is sus- 
 pended by a torsionless thread, so that in 
 equilibrium it takes up a horizontal position 
 in the plane of the magnetic meridian, and 
 the number of oscillations is counted which 
 it makes in a given time in each of three 
 experiments first, under the action of terres- 
 trial magnetism alone ; second, under the 
 joint magnetic action of the earth and a thin 
 magnet so long that its N pole has no sen- 
 sible influence on the needle, when the 
 magnet is held vertically in the magnetic 
 meridian, so that its S pole is level 
 with and two inches from the north pole of the needle ; 
 third, when the horizontal distance from S to n is 
 increased to four inches. The force in each case is proper- 
 
MAGNETISM. 31 
 
 tional to the square of the number of oscillations, for 
 the oscillations being small follow the law of pendulum 
 motion. The number of vibrations in the three cases 
 is 10, 36, and 20 respectively. The action of the magnet 
 in each of the latter cases is evidently represented by the 
 difference between the joint effect and that due to the 
 earth alone ; this in the second case is 36 2 10 2 = 1196 ; 
 and in the third case is 20 2 10 2 = 300. The ratio of the 
 forces is thus nearly 4:1; the distances of the attracting 
 poles are in the ratio of 1 : 2. This shews that if the 
 distance of the attracting poles be doubled, the attraction 
 is reduced to one-fourth. Similarly, it is found that by 
 trebling the distance we reduce the attracting force to one- 
 ninth. In such a case the attraction is said to vary inversely 
 as the square of the distance. 
 
 The law of the action of magnets on soft iron by induction 
 was ascertained by Sir William Snow Harris in 1827. It 
 is as follows : The intensity of magnetism induced in the soft 
 iron is directly proportional to the inductive force, and inversely 
 as the distance. 
 
 In the measurement of magnetic forces, repulsion v effects 
 are preferred to those due to attraction, when that is 
 practicable ; because attraction may be wholly or partially 
 due to induction, whereas repulsion can only arise from 
 the original forces in the magnets. 
 
 25. The strength of magnets is ascertained by the process 
 described in sect. 24. A rough test of the strength of a 
 horse-shoe magnet is given by the mass its armature can 
 sustain against the attraction of the earth. Hacker found 
 that if m is the mass of the magnet in pounds, and a a 
 constant to be ascertained for the particular quality of steel, 
 then the mass W which can be supported by the magnet is 
 given by the formula W = a jj/ m 2 . In his experiments 
 a = 12-6. Hence, a magnet of 2 oz. can support a mass of 
 3 Ibs. 2 oz., whereas a magnet of 100 Ibs. sustains only 271 
 Ibs. Small magnets, therefore, are stronger for their size 
 than large ones. It may be thus explained : Two magnets 
 of the same size and power, acting separately, support twice 
 the mass that one of them does ; but if the two magnets 
 
32 ELECTRICITY. 
 
 be made into one by placing them side by side with their 
 like poles together, they no longer sustain the double of 
 what either can sustain singly, because the action of the north 
 pole of each induces a south pole in the other, and thus 
 both the north poles are weakened : similarly the south 
 poles are weakened, and the strength of the complex magnet 
 is diminished. The same explanation applies to the dimi- 
 nution in strength of a complex magnet composed of more 
 than two components. Now we may consider all large 
 magnets as composed of several small ones whose mutual 
 inductive action as above described renders the strength of 
 the whole magnet much less than the sum. of the strengths 
 of its elements. 
 
 26. Effect of Heat on Magnetism. A magnet loses in 
 power as it rises in temperature, and as it cools it acquires 
 again a portion of its lost strength, and the reverse takes 
 place when it is cooled below ordinary temperatures. When 
 it is raised to the same temperature several times, or when it 
 is kept a sufficient length of time at it, it reaches a condition 
 in which it suffers no further permanent loss by being again 
 heated up to the same temperature. The change of intensity 
 produced by ordinary changes of temperature is little, if 
 anything. At a white-heat, a magnet loses permanently all 
 trace of magnetism. When, however, it is again tempered and 
 magnetised, it resumes its magnetic properties. It is found 
 that soft iron, steel, and cast-iron, when temporarily magnetic 
 that is, when under induction are capable of a greater 
 intensity of magnetisation the higher their temperature, 
 until they reach a dull-red heat ; at that temperature it is 
 the same for each, shewing that there the coercive force 
 vanishes for these bodies. Beyond this, they become less 
 susceptible to the influence of the magnet, and at a white- 
 heat they are quite indifferent to it. The temperatures at 
 which other substances affected by the magnet become 
 indifferent to it, are different from that of iron. Cobalt is 
 attracted by the magnet at the highest temperatures, and 
 nickel loses this property at 662 F. 
 
S3 
 
 CHAPTEE 
 
 TERRESTRIAL MAGNETISM. 
 
 
 27. TJie Directive Action of Terrestrial Magnetism. The 
 action of the magnet is so allied with the magnetism of the 
 earth, that we cannot study the one apart from the other. 
 The action of the earth on a magnet is simply directive ; that 
 is, it determines the position of the magnet relatively to the 
 horizon, but produces no tendency to translation. This is 
 usually shewn by making the centre of a magnetic needle 
 rest on a piece of cork floating on water. The needle when eo 
 sustained comes round to a north and south position, but the 
 float remains at the same point on the surface of the liquid. 
 Another proof is that a needle has the same weight after as it 
 had before magnetisation. The explanation is that the mag- 
 netic poles of the earth are so far distant from the magnet, 
 that, practically, the north and south poles of the magnet 
 are at equal distances from either of them. Accordingly, 
 with whatever force the North Pole of the earth attracts the 
 north pole of the magnet, it repels the south pole with an equal 
 and parallel one, and hence its effect is reduced to that of a 
 couple. The same is true of the action of the South Pole. 
 The combined effect of the two couples is merely to deter- 
 mine the position in which the magnet will rest. 
 
 28. When a magnetic needle, uninfluenced by any body in 
 its neighbourhood, is supported at its centre, so as to be free to 
 turn in any direction, the needle takes up a definite position 
 in which its magnetic axis coincides with the direction of the 
 earth's magnetic force at that place. At most points on the 
 earth's surface, the needle so suspended points approximately 
 north and south. It is not horizontal, however, but is inclined 
 to the horizon, or dips the north pole being depressed in the 
 northern hemisphere, the south pole in the southern. In order 
 to determine accurately the direction of terrestrial magnetism 
 it is necessary to use two needles, one free to turn about a 
 vertical axis, and the other free to turn about a horizontal 
 axis. The former, capable of rotating in a horizontal plane 
 
34 
 
 ELECTRICITY. 
 
 only, assumes a definite position with reference to the horizon, 
 and, when disturbed, oscillates about it. The vertical plane 
 passing through the axis of the needle 
 in this position is called the magnetic 
 meridian ; and the angle between it 
 and the astronomical meridian is called 
 the magnetic declination. If NS (fig. 
 20) be the direction of true north 
 and south, and nCs be the position of 
 rest of the needle, the angle NCn is 
 the declination. It is east or west 
 according as the magnetic north lies 
 east or west of the true north. 
 "When the second needle is placed so that its axis is in 
 the magnetic meridian, it also assumes a definite direction, 
 generally inclined to the horizon. The angle which its 
 magnetic axis makes with the horizon is called the incli- 
 nation^ or the dip. If NS (fig. 21) be the position of 
 rest of a needle supported at its centre C, free to rotate 
 in a vertical plane, and the plane of the 
 paper be supposed to coincide with the 
 magnetic meridian, and if aCb be a 
 horizontal line, the angle NCa is the 
 dip. The intensity of the earth's mag- 
 netic field at any point is the force with 
 which unit pole would be acted upon 
 there. The declination, the inclination f 
 and the intensity are called the mag- 
 netic elements, and when they are known 
 for any place, the terrestrial magnetic 
 force is fully determined for that place. 
 29. Resolution of Total Magnetic Force. Let NS (fig. 22) be 
 a needle adjusted to move in a horizontal plane. It is repre- 
 sented as lying in the magnetic meridian. The north pole 
 of the magnet is attracted, and the south pole repelled, by 
 equal forces. The magnetic force of the earth, represented 
 by the lines NO and Sc, in magnitude and direction, 
 tends, when acting on N, to draw it down, when on S, to 
 send it up. The two equal and opposite parallel forces, 
 
 Fig. 2L 
 
TERRESTRIAL MAGNETISM. 
 
 35 
 
 NO and Sc, form with the needle a couple tending to 
 make it rotate. To keep the needle in a horizontal position, 
 the south end of it is made slightly heavier than the north 
 end. The forces, NO and Sc, may be resolved each into 
 two others acting vertically and horizontally that is, 
 
 \ 
 
 Fig. 22. 
 
 perpendicular to, and in the plane of, the needle's motion. 
 The construction is exactly alike, so far as magnitude is 
 concerned, at N and at S, but the direction of the components 
 is opposite. The vertical components of the earth's mag- 
 netic force, which are alone concerned in determining the 
 position of a needle moving in a vertical plane, are NB 
 and S&. These are counteracted by the counterpoise. NA 
 and Sa are the horizontal components, and they alone are 
 concerned in the motion of the needle in a horizontal plane. 
 NA and Sa, being equal and opposite, counteract each other. 
 Suppose, now, the needle moved from its position of rest to 
 that shewn by the clotted needle, N'S'. The earth's magnetism 
 must act on N' and S' as it did on N and S, and conse- 
 quently a similar resolution may be made. This resolution 
 takes place in planes parallel to the former, which are per- 
 pendicular to the circle or plane in which the needle moves. 
 The vertical components, N'B' and S'6', are counteracted as 
 before by the counterpoise, but the horizontal components, 
 N'A' and S'a', form a couple, tending to bring the needle back 
 
 c 
 
36 ELECTRICITY. 
 
 to its first position. They act, however, obliquely on the 
 needle, and to ascertain their effective force we must again 
 resolve them as in fig. 23 ; along the magnetic axis and a 
 
 Fig. 23. 
 
 line perpendicular to it in the plane of the needle. The parts 
 NT and S'/' being equal and opposite, counteract each other, 
 and the two effective parts, N'E and SV, alone make the 
 needle rotate. 
 
 Let (fig. 22) NO = T, the total intensity ; NB = I, the 
 vertical intensity ; NA = H, the horizontal intensity ; angle 
 ANC = i, the angle of dip ; then I = T sin. , H = T cos. i, 
 I = H tan. i. 
 
 INSTRUMENTS FOR ASCERTAINING MAGNETIC ELEMENTS. 
 
 30. Declinometer. Instruments for determining magnetic 
 declination are called declination needles or declinometers. 
 In these instruments two things are essential the means 
 of ascertaining the astronomical meridian, and a needle for 
 shewing the magnetic meridian. Fig. 24 represents a common 
 form of the declinometer. Upon a tripod provided with 
 levelling screws stands the pillar P, to which is fixed the 
 graduated azimuthal circle CC. The compass-box B, with the 
 vernier V, attached to it, moves on the azimuthal circle by 
 means of a pivot at the pillar P. Two uprights, U, U, are 
 fixed to the side of the compass-box, on the tops of which 
 rests the axis of the telescope, T. A graduated arc, A, is 
 fixed to the bottom of one of the uprights, and the angle of 
 
TERRESTRIAL MAGNETISM. 
 
 37 
 
 elevation of the telescope is marked by the vernier on the arm 
 E, attached to the axis of 
 the telescope. A level, 
 L, is also hung on the 
 axis of the telescope, for 
 adjusting it. Inside the 
 compass-box is another 
 graduated circle, F, the 
 line joining the zero- 
 points of which is 
 parallel to the direction 
 of the telescope line of 
 collimation. All the 
 fittings are of brass or 
 copper ; iron, of course, 
 being unsuitable. The 
 compass-box and tele- 
 scope move round as 
 one piece on an axis Fig. 21. 
 
 passing through the 
 
 centre of the azimuthal circle. When an observation is to be 
 made, the instrument is levelled, the needle is set free, and 
 the telescope is pointed to a celestial object whose position 
 with regard to the astronomical meridian is known at the 
 time of observation, or can be found by calculation. If the 
 telescope with the compass-box be then turned the proper 
 number of degrees on the azimuthal circle, until its axis 
 is in the astronomical meridian of the place, it is evident 
 that the reading of the needle on the inner circle will 
 give the declination. For example, if, when the telescope 
 is in this position, the north end of the needle stand at 
 the zero-point of the inner circle, the declination would 
 be ; but if it lie east or west of this point, the declina- 
 tion is shewn by the degree at which the needle stands. To 
 insure that the reading obtained is that of the magnetic axis 
 of the needle for the magnetic may not coincide with the 
 geometrical axis of the needle it is necessary to take two 
 readings one when the needle is in its usual position and 
 the other when it is inverted. In the two positions the 
 
38 
 
 ELECTRICITY. 
 
 magnetic axis has the same direction that of the magnetic 
 meridian and the deviations of the axis of figure are of equal 
 amounts but on opposite sides of 
 the magnetic axis. Hence the mean 
 of the readings is the true one, and 
 half the difference is the correction 
 which must be made in future 
 observations when the needle is 
 used in one position only. 
 
 31. A declinometer like the one 
 just described can only give the 
 declination approximately. To be 
 quite exact, the needle would 
 
 Fig. 25. 
 
 require to be very long, so as to allow the divisions of 
 the circle on which it moves to shew very small angles. 
 This, however, would be attended with the objection that 
 a very long needle is more difficult to move than a short 
 one, so that what we should gain in the number of 
 divisions on the circle we should lose in the sensibility 
 of the needle. Gauss's apparatus obviates this objection. 
 Fig. 26 gives a general idea of the action of his instru- 
 
 Fig. 26. 
 
 ment. NS is a magnetic bar, suspended in a stirrup by a 
 wire or a few untwisted filaments of cocoon silk sufficient to 
 sustain its weight, which is a few pounds. The silk is more 
 suitable than the wire, as its torsion affects the results to a 
 less extent. It is inclosed in a glass case (not shewn in the 
 figure), to shield it from currents of air. On the rod by 
 which the bar is suspended, a small mirror, M, is fixed, 
 the plane of which is at right angles to the magnetic axis 
 of the bar. A few yards from the bar, a theodolite, T, 
 
TERRESTRIAL 
 
 and a scale, S, about a yard long, are 
 above, the other as much below the mirro 
 sions of the scale may be seen reflected at the cross-wires 
 of the theodolite. A small plummet hangs down from the 
 object-glass of the theodolite, the thread of which stands in 
 front of the zero or middle point of the scale, which is 
 approximately perpendicular to the magnetic meridian. When 
 a magnetic bar is hung in this way it never keeps still, but 
 is constantly making small oscillations, like a pendulum. 
 The direction about which it is oscillating at any time is the 
 magnetic meridian at that time ; and the mean of the readings 
 taken when the needle is at the two extremities of its oscil- 
 lation gives the reading of the magnetic meridian. Suppose 
 that, as the result of such observations, we find that the 
 needle oscillates about a point, P, one inch from the zero, 
 and that the distance of the scale from the mirror is 15 feet. 
 We can easily learn from the trigonometrical tables that the 
 angle PMO is 19' 6", for 
 
 or we can obtain approximately the same result by con- 
 sidering that the arc is the same fraction of 360 as 1 inch 
 is of 2 x 3*1416 x 15 feet, the circumference of the circle. 
 It can be shewn by an easy geometrical construction that the 
 apparent angle is twice the angle that the mirjor or the 
 magnet describes, so that the real deflection of the needle 
 in this case is 9' 33". The observation thus obtained is as 
 correct as if a needle 30 feet in length had moved through 
 an angle 9' 33", or described an arc of half an inch on a 
 30-foot circle. To find the absolute declination at any time, 
 we have first to find, as above, the angle which .the magnetic 
 meridian makes with the zero position of the scale, which is 
 so placed as to coincide with the optical axis of the theodolite ; 
 then the angle which the optical axis of the theodolite makes 
 with the astronomical meridian. The sum of these, taken 
 with their proper signs, gives the absolute declination. To 
 obtain continuous observations, which are extremely valuable, 
 a lamp is substituted for the theodolite, and a small spot of 
 
40 
 
 ELECTRICITY. 
 
 light from it is reflected by the mirror to a cylinder rotating 
 uniformly round a horizontal axis by means of clockwork, 
 and covered with sensitised photographic paper. Wherever 
 the light falls a mark is made, and so a continuous line is 
 traced, by means of which we can tell the position of the 
 needle at any time. A self-recording system on this principle, 
 invented by Mr Brooke, is adopted in almost all observatories. 
 
 32. The Mariner's Compass is also a declinometer, for it must 
 be always used with reference to the true north of the region 
 where it acts. It consists of a needle nicely poised on a point, 
 with a cross-bar of copper or brass at its middle. The needle 
 and bar support a card above, which is marked with thirty- 
 two equidistant points (as in fig. 27). The north and south 
 points of this card lie directly over the magnetic axis of the 
 needle, so that the card, and not the needle, indicates these 
 cardinal points to the observer. The whole is inclosed in a 
 brass or copper bowl. This is placed within a ring, which 
 
 moves by two pivots in 
 another ring, itself sup- 
 ported by two pivots at 
 right angles to the other 
 two. These two rings are 
 called the gimbals. The 
 compass- box and card 
 thus supported remain 
 always horizontal, what- 
 ever be the motion of 
 the vessel in which it is 
 placed. Inside the com- 
 pass-box a vertical black 
 line is marked, called 
 the lubber-line, which is 
 in the axis of the ship 
 
 or in the line of the ship's motion. The point of the card 
 that lies at the lubber-line shews how the ship is going. 
 
 33. The great difficulty connected with the use of the 
 mariner's compass arises from the disturbing influence of the 
 ship's magnetism, part of which is permanent and may be 
 considered constant, and part that due to the soft iron is 
 
TERRESTRIAL MAGNETISM. 
 
 41 
 
 temporary, and varies with the intensity and dip of the earth's 
 magnetism. This difficulty is particularly felt in iron vessels, 
 where the deviation of the needle is frequently so consider- 
 able as to render the compass almost useless. Various means 
 
 Fig. 28. 
 
 of obviating this have been suggested ; one of these is to 
 place bars of soft iron or magnets near the compass, in such 
 a position as to cause a contrary disturbance to that of the 
 iron of the ship. This is found to answer well in iron 
 ships plying between British and continental or North 
 American ports; but where the magnetic latitude changes 
 considerably, as in the Australian passage, such an arrange- 
 ment is found to be worse than useless, because the induced 
 magnetism of the vessel changing with the latitude causes an 
 ever-varying deviation of the needle. It has likewise been 
 
ELECTRICITY. 
 
 suggested to place a compass as a standard at the mast- 
 head, where it would be comparatively free from the attrac- 
 tion of the vessel, by which the ship's course might be shaped, 
 the ordinary compass being used merely to give immediate 
 direction to the steersman. Another course which is adopted 
 is to place a compass so high above the deck as to clear the 
 bulwarks, and allow the bearings of a distant object on shore 
 or a heavenly body to be taken while the ship's head makes a 
 complete circuit. In this way, the deviation caused by the 
 iron of the ship in all different positions may be ascertained, 
 and afterwards taken into account. 
 
 34. Sir William Thomson has recently invented a compass 
 
 (fig. 28) which is free from 
 most of the defects of those 
 in ordinary use. It consists 
 of a thin aluminium ring 
 connected by silk threads to 
 an aluminium boss, which is 
 supported on an aluminium 
 cup with a sapphire cap, 
 poised on an iridium point 
 (fig. 29). Small thin magnets 
 are fixed on two parallel 
 threads, and slung from the 
 aluminium rim by four silk 
 threads or fine copper wires ; 
 the card itself consists of 
 strong thin paper properly 
 divided, and the central parts cut away. Hence it is very 
 light the 10-inch compass being only one-twentieth of the 
 weight of ordinary cards of the same size friction in turning 
 is thus reduced, and the point of support lasts much longer. 
 Since most of its heavier parts are at the circumference, the 
 time of a vibration is increased, and the compass is thus ren- 
 dered much steadier. The corrections required on board ship 
 are easily applied. It is found in practice to be steadier, 
 quicker, and more accurate than any other compass. 
 
 35. Dipping Needle. The dip of the magnetic needle at 
 any place can be ascertained with great exactness by means of 
 
 Fig. 29. 
 
TERRESTRIAL MAGNETISM. 
 
 43 
 
 the dipping needle, fig. 30. It consists of a graduated circle, 
 AA, fixed vertically in the frame FF, and moving with it 
 and the vernier V, on the horizontal graduated circle HH. 
 This last is supported by a tripod furnished with levelling 
 screws. At the centre of the circle C, there are two knife- 
 edges of agate, supported by the frame, and parallel to the 
 plane of the circle. The needle, NS, rests on these knife- 
 edges by means of fine polished cylinders of steel, which 
 are placed accurately at the centre of the needle, and project 
 at right angles from it : so adjusted, the needle moves with 
 little friction. It is so made, moreover, that before being 
 magnetised it remains indifferently in any position ; after 
 magnetisation, therefore, the dip which it shews is wholly 
 due to the magnetic 
 influence of the earth. 
 It will be seen from fig. 
 22 (sect. 29) that when a 
 needle is capable of ver- 
 tical motion, the earth's 
 magnetism will swing the 
 needle round until it 
 coincides as nearly as 
 possible with the direc- 
 
 tion of the earth's mag- 
 
 netic force. When the 
 
 needle is in the mag- 
 
 netic meridian, the coin- 
 
 cidence is complete. The 
 
 moment of the couple 
 
 NO and Sc (fig. 22) is 
 
 in that case zero. When 
 
 the needle moves in a 
 
 plane at right angles to 
 
 the magnetic meridian, the vertical component alone can 
 
 affect its position, and makes it hang vertical. In this 
 
 case the moment of the couple NB and S& (fig. 22) vanishes. 
 
 Between these two positions the needle shifts from the 
 
 vertical position to that of the. direction of the dip, 
 
 and is always more inclined to the horizon than when 
 
44 ELECTRICITY. 
 
 in the meridian. We have thus two ways of finding the 
 meridian. When the needle points to 90 or is vertical, it is 
 at right angles to the meridian, except at the magnetic 
 equator (sect. 41) ; and by moving the vernier over 90, we 
 can place it in the meridian. Again, that plane in which 
 the inclination of the needle is least, is the plane of the 
 meridian, and the dip is the angle which it then makes with 
 the horizon. In making observations with the dipping needle 
 several sources of error have to be neutralised, such as devia- 
 tion of zero-point of vertical circle from horizontally, false 
 centering and deviation of axis of form from magnetic axis. 
 
 36. Intensity. The sources of error involved in working 
 with a magnet capable of rotation in a vertical plane only, are 
 so great, that to determine the intensity of terrestrial magne- 
 tism at any place, the practice is to determine the horizontal 
 component from which the total intensity can be obtained 
 when the dip is known. A magnet is suspended in a stirrup 
 by a silk fibre so as to be free to turn about a vertical axis. It 
 is then made to vibrate under the mutual action of its own 
 magnetism and the terrestrial magnetism of the place, and the 
 number of vibrations it makes in a given time is ascertained. 
 As this depends on the horizontal intensity so long as the 
 magnet and the thread remain exactly the same, the time the 
 magnet takes to make one vibration, is a measure of the hori- 
 zontal intensity in terms of the moment of the magnet. As 
 the moment of the magnet is liable to alter with a change of 
 temperature or of the inductive action of the earth, and from 
 other causes, the time of a vibration would alter with any 
 one of these. In order that a measure independent of the 
 moment of any particular magnet or of temperature or any 
 other circumstance, and therefore called absolute, may be 
 obtained the same magnet is employed to deflect a second 
 similar magnet from the plane of the magnetic meridian. The 
 apparatus is so arranged that the deflecting magnet is fixed 
 so as to be always in a line at right angles to and passing 
 through the centre of the deflected magnet. The distance 
 between their centres is known or can be measured, and the 
 angle between the magnetic axis of the deflected magnet 
 when at rest and the magnetic meridian gives a measure 
 
TERRESTRIAL MAGNETISM. 
 
 45 
 
 of the ratio of the horizontal intensity to the magnetic 
 moment of the deflecting magnet. The time of vibration in 
 the previous experiments gave a measure of the product 
 of these two quantities, and therefore the horizontal intensity 
 can be determined absolutely from the two experiments. 
 Thus, the average horizontal intensity at Kew for 1875 
 was 1'7915 metric units, which signifies that a south pole 
 one milligramme in mass, and of unit magnetic force, would, 
 supposing it were insulated and free to move in a horizontal 
 plane, acquire in one second a velocity southward of 1-7915 
 millimetres per second. Or we may express it by saying 
 that a mass of a milligramme acted on for one second by 
 a force equal to the horizontal intensity would acquire a 
 velocity of 17915 millimetres per second. In British units 
 expressed in feet, with the mass of a grain instead of a 
 gramme, the same quantity is 3*8855. 
 
 37. The horizontal intensity at any place is continually 
 undergoing changes. These are small in amount, and to 
 measure them a very sensitive arrangement is necessary. 
 This is obtained by the use of Gauss's 
 Bifilar Magnetometer, of which a rough 
 representation is given in fig. 31. It 
 consists essentially of a magnet sus- 
 pended by two wires. The line join- 
 ing their upper extremities is generally 
 not in the magnetic meridian ; and 
 if they were supporting a bar of 
 wood or copper, of dimensions similar 
 to those of the magnet, the wires 
 would be in a vertical plane which 
 would also intersect the supported 
 bar in the line, joining the points 
 to which the supporting wires were 
 attached. But the magnet, under the 
 influence of terrestrial magnetism, 
 tends to place itself as nearly in Fig- 31 - 
 
 the magnetic meridian as possible, 
 and consequently twists the wires out of the vertical 
 plane. This has the effect of raising the magnet, and 
 
46 ELECTRICITY. 
 
 thereby the tension of the wires is increased, which, with 
 any torsion given to the wires by the rotation of the magnet, 
 opposes the couple due to the horizontal intensity tending 
 to place the magnet in the magnetic meridian. The increase 
 of tension and the torsion corresponding to any position of 
 the magnet can be calculated, and hence by observing the 
 position which the magnet assumes at any moment, we have 
 a measure of the horizontal intensity. The sensitiveness of 
 the apparatus can be altered by changing the length of the 
 wires, their distance apart, &c. Like the declinometer, the 
 magnetometer has a mirror attached to it, and a scale, and 
 the position of the magnet can be photographically registered. 
 38. Magnetic Charts. The magnetic elements have been 
 ascertained with great care at different portions of the 
 earth's surface. The knowledge thus obtained has been 
 embodied in magnetic charts, in which lines are drawn 
 through those places for which the declination is the same ; 
 and similarly for the dip and intensity. The lines of equal 
 declination are called isogonic lines ; those of equal dip, 
 isoclinic ; and those of equal intensity, isodynarnic lines. As 
 the magnetism of the earth is subject to a slow secular vari- 
 ation, such charts are only true for the time of observation. 
 The chart fig. 32 was drawn up by Sir Edward Sabine for 
 the year 1840, and gives an approximate view of the lines of 
 equal declination for that year. The change since 1840 has 
 been small, so that an isogonic chart for the present time 
 would differ but slightly from it. The chart sufficiently 
 explains itself. Attention may, however, be given to one or 
 two points. The declination is marked on each line. Thus 
 the line passing through England, for instance, is marked 
 25, and that passing north-west of the British Islands 30. 
 At places through which these lines pass, the needle points in 
 a direction west of the true north, in the one case 25, in the 
 other 30 ; and at places between the two lines, including 
 Scotland and Ireland, the direction of the needle is interme- 
 diate. Thus in Dublin the declination was in 1840 about 27 
 30'. The westerly line of no declination cuts off the eastern 
 corner of South America, proceeds to North America, which 
 it traverses, and ends in the north at Boothia. The easterly 
 
TERRESTRIAL MAGNETISM. 
 
 47 
 
 Fig. 32. 
 
48 ELECTRICITY. 
 
 line of no declination enters Europe in the north of Kussici, 
 crosses the White Sea, the east of Eussia, Persia, and the 
 Arabian Sea ; then turns eastward, and cutting off the west 
 of Australia, passes southward. The untinted portion of the 
 chart between these two lines contains all places where the 
 declination was westerly. It includes the east of the two 
 Americas, the Atlantic Ocean, the whole of Europe and 
 Africa, and the west of Asia and Australia. The rest of the 
 earth, which in the chart is tinted, has an easterly declination. 
 An elliptic space in Eastern Asia, left white, has a westerly 
 variation, and forms an exceptional region in the eastern 
 magnetic hemisphere. 
 
 It will be seen that the lines converge in the north of 
 North America, and to the south of Australia. So far as 
 experience goes, and so far as the most matter-of-fact theory 
 (Gauss's) teaches, the convergence in both cases is towards 
 a point. The point in North America is called the north mag- 
 netic pole, and that to the south of Australia the south mag- 
 netic pole. At these points, then, all isogonic lines converge, 
 and a compass needle lies indifferently in any position. 
 
 39. According to the same theory, if the isogonic lines were 
 traced on a globe, instead of, as here, on a map in Mercator's 
 projection, they would form irregular curves, approximating 
 to circles, on the northern and southern hemispheres. Each 
 circle in the north would contain in its circumference the 
 north magnetic and geographical poles, the portion of the 
 circle on the one side of the poles being in the hemisphere 
 of westerly declination, and the other in the easterly. The 
 sum of the angles marked on the two portions would 
 amount to 180, the larger segment having the smaller 
 angle. The same conformation of circles would be visible 
 at the south pole. These two sets of circles proceeding 
 from both poles, would meet each other at the equatorial 
 regions, and when they began to overlap, would run into 
 each other, forming irregular curves passing through the 
 four poles. This conformation can be traced more par- 
 ticularly on the white part of the chart. In the North and 
 South Atlantic, the curves are seen approaching each other, 
 and proceeding from the region of the north and south poles. 
 
TERRESTRIAL MAGNETISM. 49 
 
 The last two circles that approach without touching are marked 
 20. The circles marked 15 would overlap ; but instead of 
 doing so, they run into each other, and make two continuous 
 curves, forming together a figure resembling the outline of 
 a sand-glass. The same union, with a less contraction in the 
 middle, is seen in the lines marked 10 and 5. 
 
 40. The isogonic lines, as seen from the chart, form a some- 
 what complicated system. This arises from the fact, that we 
 refer the indications of the needle to the geographical poles, 
 which are, so far as we know, arbitrary or extraneous as 
 regards terrestrial magnetism. Admiral Duperrey constructed 
 charts to shew the declination on a somewhat different 
 principle from that made use of in the isogonic chart. In 
 his chart lines are drawn so that the tangent at each point of 
 any one of them is the direction in which the needle points 
 at that place that is, the direction of the curve is everywhere 
 that of the magnetic meridian, and hence the lines are called 
 magnetic meridians. They are found to converge like the 
 lines of force of a bar magnet towards two points one in the 
 N. hemisphere, about 70 N. lat. and 98 W. long., and the 
 other in the S. hemisphere, about 75 S. lat. and 138 E. long. 
 On the same chart are drawn lines which always intersect the 
 meridians at right angles, and are called magnetic parallels, 
 and which also are approximately circles. . 
 
 41. The chart fig. 33, also by Sabine, represents the isoclinic 
 lines or lines of equal dip for 1840. In the upper part of the 
 chart, which is left white, the north end of the needle dips ; 
 and in the lower part, which is tinted, the south end of the 
 needle dips. The amount of dip is marked on each line. 
 Thus, the line passing through the centre of England is 
 marked 70. A dipping needle, at any place cut by the 
 line, is inclined 70 to the horizon. The line 75 passes 
 to the north of the British Isles. In Ireland and Scotland, 
 therefore, . the dipping needle has an inclination greater 
 than 70, and less than 75. The line marked is the 
 line of no dip ; at any station on it the dipping needle 
 is horizontal. This line is called the magnetic equator. 
 It will be seen that it is not coincident with the geo- 
 graphical equator ; it is not even a great circle of the earth, 
 
50 
 
 ELECTRICITY. 
 
 Fig. 33. 
 
TERRESTRIAL MAGNETISM. 51 
 
 but an irregular curve cutting the equator in two points, 
 one near the west coast of Africa, and the other in the 
 middle of the Pacific Ocean. The points on the earth's 
 surface where the dipping needle stands vertical, and where, 
 in consequence, as before mentioned, the compass needle lies 
 in any direction, are called the magnetic poles. The north 
 magnetic pole was found in Boothia Felix by Sir James C. Ross 
 at 70 5' N. lat. and 263 14' E. long. According to Gauss's 
 calculation, it should have been at the time (1831) some 
 3 north of this point. From observations made at Hobart 
 Town, the nearest station to it, the south magnetic pole 
 should lie in 66 S. lat. and 146 E. long. These points are 
 not diametrically opposite each other like the geographical 
 poles. If the lines of equal dip were drawn on a globe, they 
 would form round the magnetic poles a system of irregular 
 circles, somewhat resembling that of the parallels of latitude 
 round the poles of the earth. The irregularities of the 
 magnetic curves are to a certain extent attributable to the 
 irregular distribution of temperature, which greatly depends 
 on the distribution of land and water. 
 
 42. We do not add an isodynamical chart, as it would 
 engross too much space. Sir Edward Sabine's Dynamical 
 Chart, along with the isogonic and isoclinic charts, will be 
 found fully engraved and explained in Johnston's Physical 
 Atlas (new edition). From this chart we learn that the mag- 
 netic intensity is least in the vicinity of the magnetic equator, 
 and increases as we approach the magnetic poles. The lines of 
 equal intensity, though running much in the same direction 
 as the lines of equal dip, are neither coincident nor parallel 
 with them. The line of least intensity, itself not an isody- 
 namic line, runs nearly parallel to the magnetic equator, but 
 lies, except in the western half of the Pacific, a few degrees to 
 the south of it. We thus learn that the changes in direction 
 and intensity do not march together. We should fancy that at 
 that point or points on the earth's surface where the dipping 
 needle stood erect, we should be nearest to the centre of free 
 magnetic energy, and that there the force would be greatest ; 
 but this is not the case. The point in North America 
 where the intensity is greatest is situated to the west of 
 
 D 
 
52 ELECTRICITY. 
 
 Hudson's Bay, about 52 N. lat. and 92 W. long. But 
 this is not the only point of maximum force in the north 
 magnetic hemisphere. There is another, which was found 
 by Hansteen in 1828, in Eastern Siberia, about 118 E. long, 
 and 60 N. lat. This maximum point is weaker than the 
 American, in the proportion of 100 to 107 (Sabine). According 
 to Gauss, there can only be one maximum point in the 
 southern hemisphere, and it is stronger than either of the 
 other two. It lies north-east of the south magnetic pole, 
 and its intensity is 137 (Gauss) compared with 107, that 
 of the principal northern centre. At none of those points 
 does the dipping needle stand erect. This" want of coinci- 
 dence of the points of vertical dip and of maximum 
 intensity has led to some confusion in the use of the 
 term magnetic pole ; some writers meaning by it a point 
 of vertical dip, and others a point of maximum intensity. 
 In adopting the former definition, we are only adhering 
 to the popular meaning of the word, and to the opinion of 
 Gauss, perhaps the greatest authority on the subject. Some 
 of the best English authorities, however, attach to it the 
 latter meaning. 
 
 43. Although the total intensity increases as we go north- 
 wards or southwards from the line of least intensity, the hori- 
 zontal intensity diminishes. This arises from the fact that the 
 horizontal intensity depends partly on the dip ; the greater 
 the dip, the less the horizontal intensity (sect. 2.9). Hence, 
 the compass needle, which is affected by the horizontal in- 
 tensity only, oscillates more sluggishly as we leave the line 
 of least intensity. A dipping needle, for instance, oscillates 
 faster at London than at Calcutta, because the total intensity 
 which affects it is greater at London than at Calcutta ; but 
 with a compass needle it is the reverse, because the hori- 
 zontal intensity is greater at the latter than at the former 
 station. 
 
 44. Variations of the Needle. The magnetic elements do 
 not remain constant in the same place, but are subject to 
 continual small periodic variations. These are regular and 
 irregular. Under regular variations are included secular, 
 annual, and diurnal variations. The secular variations 
 
TERRESTRIAL MAGNETISM. 53 
 
 take centuries for their completion. The following list of 
 the declination and dip at London in different years will 
 give an idea of the secular variations for these elements : 
 
 Year. Declination. 
 
 1576 11 15' easterly. 
 
 1657 1662... 0', no declination. 
 
 1760 19 30' westerly. 
 
 1815 24 27' 18" westerly. 
 
 Maximum. 
 1850 22 29' 30" westerly. 
 
 Year. Inclination. 
 
 1720 74 42' 
 
 1780 72 8' 
 
 1800 70 35' 
 
 1830 69 38' 
 
 1850 68 48' 
 
 1865 68 9' 
 
 1875 (average)... 67 47' 
 
 1865 21 6' 
 
 1875 (average) 19 33' 
 
 From these observations it will be seen that in 1576, when 
 the earliest reliable measurement of the declination was made, 
 it was 11 15' easterly. This divergence from the true north 
 diminished till 1657 1662, when it pointed to the true 
 north. It then varied westward till 1815, when it stood 
 farthest from the true north. Since then the needle has 
 been veering eastward, and coming nearer to the north. At 
 present, the annual decrease of declination at London is 
 nearly 8'. At this rate it would take rather more than 
 eighty-four years before the compass needle shifts through 
 a whole point. The magnetic history of London does not 
 apply to other places ; each place, so far as haS been ascer- 
 tained, having a magnetic history of its own. Thus, in Paris, 
 the time of no declination was 1669 ; and of maximum 
 declination, 1814 ; the latter amounting to 22 34' west. At 
 the Cape of Good Hope the variations are in the opposite 
 direction ; for from about 1607, when the magnetic and 
 geographical meridians there coincided, the north end of 
 the needle has been pointing more and more west. At 
 present the declination is 32 W. At Hobart Town again 
 the declination is easterly and is increasing slowly. 
 
 From the observations of the dip, we find that it has 
 been gradually decreasing for the last hundred and fifty 
 years. The annual decrease of dip is at present about 
 2'-6. From the time observations have been taken of the 
 declination and dip until now, we are far from having 
 Completed a cycle of change in either, and it is matter of 
 
54 ELECTRICITY. 
 
 speculation how long that may take. Every place, accord- 
 ing to Barlow, appears to have its own magnetic pole and 
 equator. Magnetic intensity has been observed for so short 
 a time that little as yet is known of its secular variation. 
 The average total magnetic intensity at Kew, for 1875, was 
 10*276 British magnetic units (foot, grain, second), or 4-738 
 metrical units (millimetre, milligramme, second). At present, 
 the horizontal intensity is increasing in Europe, but that 
 may arise partly from decrease of dip. 
 
 45. The magnetic elements are subject also to changes, which 
 have a yearly and a daily period. In describing these shortly 
 we shall limit ourselves to the changes affecting declination, 
 as these are of most general interest. As regards the annual 
 variation of declination, it would seem to depend on the 
 position of the sun ; for we find that for places in the 
 northern hemisphere the declination is to the east of the 
 mean from May to October, reaching a maximum in August, 
 and is to the west of the mean from November to April, with 
 a maximum in February. In the southern hemisphere the 
 simultaneous variations are in the opposite direction. It will 
 be noticed that the maxima in each hemisphere occur at the 
 hottest and the coldest periods of the year. The range of 
 the annual variation at Greenwich is about 2' 25". The 
 extent of the oscillation varies from year to year, and seems to 
 depend upon the state of the sun's surface, as do probably all 
 magnetic phenomena. It is found that the years in which 
 the sun's spots attain a maximum are those in which the 
 declination range is a maximum, and the years of minima 
 also coincide. Balfour Stewart and others have shewn that 
 if curves be drawn one representing the condition of the sun 
 as regards sun-spots, and the other the declination range for 
 the same period every well-marked point in the former has 
 a corresponding point in the latter. One of the remarkable 
 features in these curves is that every declination point occurs 
 about six months later than the corresponding sun-spot point. 
 Moreover, it has been shewn that there is apparently some 
 connection between the positions of the planets Mercurv, 
 Venus, and Jupiter, and the magnetic conditions of the earth. 
 
 46. The mean diurnal variation for Kew is shewn in fig. 34 
 
TERRESTRIAL MAGNETISM. 
 
 55 
 
 (kindly furnished by Mr G. M. Whipple of the Observatory). 
 This irregular line indicates the course of the north end of 
 the needle. A rise of this line indicates a change of the 
 north end to the east, a fall a change to the west. The 
 interval between two horizontal lines corresponds to a deflec- 
 tion of the needle of 1'. The line marked o is the magnetic 
 
 2 13 1 
 
 4- 1 
 
 r 1 
 
 r, 1 
 
 7 1 
 
 8 1 
 
 9 20 2 
 
 ; 2 
 
 2 Z 
 
 * 
 
 1 1 
 
 
 
 
 
 
 t-^ 
 
 I 
 
 t ' 
 
 1 
 
 > 1 
 
 1 
 
 I 
 
 4-' E 
 
 V. 
 
 i> ,1 
 
 i ' I' 
 
 7'W 
 2' 
 
 ' 
 
 +,., 
 
 5'" 
 
 6' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 ' ' 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 ^ 
 
 
 
 
 fv- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^. 
 
 ^" 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 ' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 f 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 S 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Fig. 34. 
 
 meridian, or the mean daily position of the needle. The 
 interval between two upright lines corresponds to an hour. 
 The course begins at twelve at night, and ends at twelve 
 the following night. From the figure we see that at 
 twelve at night the magnet is 1??' east of tho, mean posi- 
 tion, and continues nearly in the same position, with only a 
 slight westerly deviation, till fifteen hours (three in the 
 morning), when it veers eastward. At twenty hours (eight 
 in the morning) it reaches its furthest east point. From 
 eight in the morning till ona in the afternoon, it makes a 
 sweep of 10' towards the west, and then stands about 6' to the 
 west of the mean. After one, it goes westward till midnight, 
 when it again begins the same course. The needle stands in 
 its mean position a little after ten in the morning, and a little 
 before seven in the evening. The course here described is 
 the average course for the year. Observations prove that the 
 extent of the diurnal range is different in different months. 
 In May, for instance, the average range between the extreme 
 points is 12', which is the maximum range for the year ; 
 
66 ELECTRICITY. 
 
 and in December, when it is a minimum, it is only 5' 28". 
 The diurnal changes here described for Kew are much the 
 same all over the north magnetic hemisphere. The range, 
 however, is different at different places, becoming less as 
 the equator is approached. At stations on the equator itself, 
 the variations do not vanish, as was formerly supposed, but 
 correspond to those in the northern hemisphere from the 
 vernal to the autumnal equinox, and with those in the 
 southern hemisphere during the remainder of the year. 
 They nearly vanish at the equinoxes. In the southern mag- 
 netic hemisphere the daily motions of the needle take place 
 much in the same way as in the northern hemisphere, only 
 the south pole takes the place of the north pole, and the 
 direction of the deflections is reversed. The correspondence, 
 and at the same time opposition, of the southern hemisphere 
 is also shewn from the time of maximum and minimum 
 range. When the sun is in the northern signs of the zodiac, 
 the range is a maximum in the northern, and a minimum in 
 the southern hemisphere ; and when the sun is in the 
 southern signs, the reverse takes place. 
 
 47. The irregular variations are those which break in upon 
 the regular march of the diurnal variation without in the 
 main altering it. Instead, for instance, of the needle steadily 
 going westward from 8 A.M. to 1 P.M., as shewn in fig. 34, 
 it makes, when affected by irregular variation, deflections 
 eastward as well as westward, although it in the main 
 moves westward ; so that the line between these hours, 
 instead of being comparatively straight, would be an irregular 
 zigzag. These disturbances of the mean course are sometimes 
 considerable, amounting even to one or two degrees in extreme 
 cases. On some days the mean diurnal course is much dis- 
 turbed, on others very little ; but it is never quite free from 
 them. It has been found that places of the same longitude 
 have similar disturbances at the same time ; that those on 
 opposite sides of the globe, or differing by 180 of longitude, 
 have disturbances equal in amount but opposite in direction ; 
 and that those situated 90 west or east of the disturbed 
 regions have little or no disturbance. The appearance of 
 auroras is invariably accompanied by magnetic irregulari- 
 
(TERRESTRIAL MAGNETISM. 67 
 
 ties, and their effect extends far beyond the regions where 
 they are visible. Earthquakes and volcanic eruptions have 
 also a marked effect in this way. Humboldt gave the 
 name of Magnetic Storms to these irregular disturbances. 
 Sabine has found that the frequency of magnetic storms is 
 greatest every eleven years at the same time that the spots 
 on the sun are most numerous. 
 
 48. Theories of Terrestrial Magnetism. The earliest theory 
 was that suggested by Gilbert, in which it is supposed 
 that a magnet in the middle of the earth extended from one 
 magnetic pole to the other. On this supposition, the general 
 phenomena of terrestrial magnetism may be accounted for a 
 needle, both by declination and dip, must point to the poles. 
 This must always remain, from its simplicity, the popular 
 theory on the subject. In consistency with his theory, 
 Gilbert considered the north pole of the magnet to be 
 a south pole, as he took the north pole of the earth for 
 his standard north pole. If this theory were correct, the 
 magnetic equator would be a great circle of the earth, 
 and the magnetic poles would be 90 from it, which is far 
 from the case. It is only a rough approximation to a just 
 theory. 
 
 Halley endeavoured to supplement Gilbert's theory, by 
 supposing two magnets of unequal strength crossing each 
 other at the earth's centre to be the cause of terrestrial 
 magnetism. The theory of the two magnets or four poles was 
 ably defended by Hansteen. 
 
 Barlow considered that the earth acted on the needle as if 
 currents of electricity traversed it from east to west. He imi- 
 tated its action by wrapping a wire in parallel coils round a 
 wooden globe, and causing a galvanic current to pass through 
 it. Each turn of the wire represented a magnetic parallel, 
 and the two ends of the coil the magnetic poles ; and to com- 
 plete the analogy, the globe was movable on an axis, which 
 stood in the same relation to the ends of the coil as the astro- 
 nomical axis to the magnetic poles of the earth. When a 
 small needle was placed on the globe, its declination and dip 
 bore a striking resemblance to those of a needle similarly situ- 
 ated on the earth's surface. The objection to this theory is the 
 
58 ELECTRICITY. 
 
 difficulty of accounting for the origin of such currents in the 
 earth. To meet this, some suppose the earth to be a huge 
 thermo-electric pile ; as the heat of the sun falls on one side 
 of it, currents are there generated which travel round the 
 globe. But how, again, it may be asked, are the conditions 
 of thermo-electricity implemented by the materials of the 
 earth ? This question still remains to be answered. The close 
 connection between temperature and magnetism is shewn by 
 the diurnal variation of declination, the epochs of which 
 closely correspond with those of the daily temperature, and 
 by the fact that the isodynamic and isothermal lines manifest 
 a marked correspondence. Sir David Brewster has also shewn 
 that there are two centres of maximum cold in the northern 
 hemisphere, which are situated near to the two intensity 
 poles. 
 
 Gauss did not start from any simple supposition of one 
 or two magnets giving rise to the magnetism of the earth, 
 nor did he assert or deny its electric origin. Considering 
 the whole earth as magnetic, he aimed at determining 
 how it must act as a whole at the different points on its 
 surface. In order to make the equations he obtained theo- 
 retically, express the distribution on the earth, the magnetic 
 elements of eight stations at a sufficient distance from each 
 other on the earth's surface had to be ascertained and sub- 
 stituted in these equations. This done, from the longitude 
 and latitude of any station he considered himself prepared to 
 deduce its magnetic elements. The magnetic charts which he 
 sketched, though founded on the imperfect observations to 
 which he had access, are singularly in keeping with i'act, and 
 go far to establish the correctness of his reasonings. 
 
59 
 
 CHAPTER III. 
 CHRONOLOGY OF MAGNETISM. 
 
 49. The property of the loadstone to attract iron appears 
 to have been the only fact in the science of magnetism 
 known to the ancients. The compass is a comparatively 
 modern discovery ; it was certainly known in Europe in the 
 12th century, the first reference to it being made in a manu- 
 script poem by Guyot de Provins, now in the National Library 
 of France. The Chinese, according to some, were acquainted 
 with it as early as the 4th century. The discovery of the 
 change in declination at different places is generally attributed 
 to Columbus, and was one of the many important observa- 
 tions of his memorable voyage across the Atlantic. Robert 
 Norman, an instrument-maker in London, first discovered 
 the dip of the needle in 1576. He was led to it by finding 
 that needles nicely balanced before magnetisation had to be 
 slightly loaded on the south end, to keep them horizontal 
 after being magnetised. The first really important contribu- 
 tion to magnetism as a science was the Tractatus de Magnete 
 by Dr Gilbert of Colchester, physician to Queen Elizabeth. 
 It was published in 1600. He first used the word poles with 
 reference to magnets, and gave the first theory of terrestrial 
 magnetism, namely, that of the single magnet. Halley, the 
 astronomer-royal, published his theory of the four poles in 
 1683. In 1688 and 1689, at the expense of government, he 
 made two magnetic voyages, the results of which he embodied 
 in his charts of the lines of equal declination, published in 
 1701, which were the first magnetic charts ever published. 
 In 1722 the diurnal variation was discovered by Graham, the 
 celebrated instrument-maker of London. Canton determined 
 it in 1759. About the middle of the 18th century, armatures 
 began to be used, and various new processes of magnetisation 
 were found out. Knight in 1745 invented divided touch, which 
 was afterwards improved by Duhamel (sect. 21); and Mitchell 
 in 1750 double touch, afterwards improved by .ZEpinus (sect. 
 21). Brugman in 1778 discovered that cobalt was attracted and 
 that bismuth was repelled by the magnet. Coulomb in 1789 
 
60 ELECTRICITY. 
 
 discovered the law of the distribution of magnetism on a 
 magnetic bar, and the law of magnetic attractions and repul- 
 sions. The first inclination chart was published by Wilcke, 
 at Stockholm, in 1768. Humboldt inaugurated the present 
 system of careful observations of terrestrial magnetism by 
 taking comparative measurements of the magnetic elements 
 at Peru and Paris in 17991803. Hansteen's work on the 
 Magnetism of the Earth (sect. 48) was published at Chris- 
 tiania, 1819 ; in 1826 he published the first isodynamic charts. 
 Barlow in 1831 suggested the electric origin of terrestrial mag- 
 netism (sect. 48) ; and in 1833, introduced correcting plates 
 of soft iron for ships. In 1831, Sir James C. Ross came upon 
 the north magnetic pole. In 1835, stations were established 
 throughout Europe, and the observations were published by 
 Gauss and Weber, 1836. Duperrey's observations, 1822 
 1825. Gauss in 18331840 perfected his theory. In 1837, 
 Sir Edward Sabine published an isodynamical chart of the 
 whole globe. Diamagnetisin was discovered by Faraday, 
 1845. Observations were made in 1840 1854 at stations 
 throughout the British empire by British officers, under the 
 direction of Sir Edward Sabine. In 1855, Tyndall shewed 
 that a diamagnetic body assumed a polarity similar in action 
 but oppositely directed to that of a magnetic body when 
 under the action of magnetic force. 
 
 In recent years the advances made have been chiefly in 
 tracing the connection between terrestrial magnetism, the 
 condition of the sun's surface, and the positions of the 
 planets and moon, reference to which has been made in the 
 text. In 1876, Sir William Thomson invented a new 
 mariner's compass. 
 
61 
 
 Part IL-FRICTIONAL OR STATICAL 
 ELECTRICITY. 
 
 CHAPTER MU 3 
 GENERAL 
 
 50. Fundamental Fact of Electricity. More than two 
 thousand years ago it was known that when amber whose 
 Greek name is electron is rubbed with a woollen substance, 
 it acquires the property of attracting light bodies. Till com- 
 paratively recent times, not much more was known about 
 electricity the name given to the influence supposed to com- 
 municate this property of rubbed amber ; but during the past 
 hundred years or so, a very great increase has been made to 
 our knowledge of this branch of Natural Philosophy. 
 
 51. Electric Pendulum. The elementary facts of electricity 
 are illustrated by the electric pendulum (fig. 35). A glass rod 
 placed on a suitable stand supports a fibre of unspun silk, to 
 the end of which a pith-ball is 
 
 attached. If a tube of glass be 
 
 rubbed with a dry silk handker- 
 
 chief, and brought near the ball, 
 
 the ball is at first briskly attracted, 
 
 and after contact it is as briskly 
 
 repelled ; and if the tube be then 
 
 moved towards it, it moves off, 
 
 always keeping at a distance. 
 
 The ball being so affected, or 
 
 charged, as it is called, a rod 
 
 either of shell-lac or sealing-wax, 
 
 after being rubbed with flannel, 
 
 and brought into the neighbour- 
 
 hood, attracts it very briskly, and after contact repels it 
 
 exactly &* the gluss had done. If the glass tube be again 
 
 Fig. 35. 
 
62 ELECTRICITY. 
 
 taken up, and rubbed a second time, if necessary, the ball will 
 be affected by it as it was by the sealing-wax, being first 
 attracted, and, after contact, repelled. The same series of 
 attractions and repulsions would have taken place if we had 
 begun with the sealing-wax instead of the glass tube. From 
 these experiments we learn that when glass is rubbed with 
 silk, and sealing-wax with flannel, they, like amber, become 
 endowed with the property of attracting, and subsequently 
 repelling, light bodies, and are then said to be electrified or in 
 a state of electrification. Moreover, we see that although the 
 glass attracts the ball at first, it repels it immediately alter 
 contact. The same is true of the wax. Again, when the ball 
 is in a condition to be repelled by the glass rod, it is attracted 
 by the wax ; and when repelled by the wax, it is attracted 
 by the glass. What the one repels, the other attracts. 
 
 We may infer from these experiments, what will be fully 
 confirmed by later experience, that other bodies besides 
 amber possess its property : that there are two kinds of 
 electrification, with similar but opposite properties that 
 shewn by the glass, and that shewn by the wax. Also, that 
 the repulsion of the ball after contact with the glass or the 
 wax, is due to a communication of part of their electricity 
 to it ; and, that bodies with the same kind of electricity repel 
 one another. Lastly, since the ball, when electrified with the 
 same electricity as the glass, is attracted by the electrified 
 wax, and when electrified like wax, is attracted by electri- 
 fied glass, we see that bodies charged with unlike electricity 
 attract one another. 
 
 52. It was customary to distinguish these two kinds of 
 electricity as vitreous or resinous, according as the electrified 
 body behaved like the glass or the sealing-wax. As these 
 names seem to imply that only the one kind of electricity is 
 got from glass, whereas either kind can be obtained, it is 
 better to speak of the vitreous electricity as positive, and the 
 resinous as negative. These names have the advantage of 
 shewing the opposite characters of the two kinds of electrifi- 
 cation. They admit, moreover, of a very convenient con- 
 traction, namely, the algebraic + for yositivt, and for 
 negative. 
 
FRICTIONAL OR STATICAL ELECTRICITY. 63 
 
 We are taught by the above experiments, that bodies 
 electrified either positively or negatively, attract neutral bodies 
 and bodies with the opposite electrification, but repel those with 
 the same kind of electrification ; and that the electrical condition 
 can be communicated from one body to another. The former 
 of these statements is sometimes put thus Like electricities 
 repel one another, unlike electricities attract. A neutral or 
 unelectrified body is one which is not charged with electricity ; 
 the pith-ball, before any experiments were made with it, was 
 an instance of an unelectrified body. 
 
 53. Nature of Electricity. To explain electrical phenomena, 
 different theories have been proposed as to the nature of 
 electricity. It has not been positively decided yet what 
 electricity is, but the most favoured idea is contrary to its 
 being material. The best known theories treat it as a sub- 
 stance existing in the form of two fluids or one. In the 
 former, every non-electrified body has an enormous and 
 equal quantity of each of the electric fluids in it, and they 
 are then said to be neutral, fixed, or combined ; so great is 
 this quantity, that by no possible electrification can a body be 
 entirely deprived of either kind. These fluids have no mass 
 nor weight, nor any other properties of fluids, save that of 
 mobility, and attraction and repulsion. They are not, as in 
 the corresponding magnetic theory, confined to the molecules 
 of the body, and can be separated one fluid bejng drawn to 
 one part of the body, and the other to the opposite. They 
 may also pass from one body to another. The molecules of 
 either fluid repel like molecules, and attract those of the 
 other fluid, with a force varying inversely as the square of 
 the distance between them. A body is charged positively (or 
 negatively) by having an excess of the positive (or negative) 
 fluid, or a deficiency of the negative (or positive) one. The 
 excess of the one fluid in a body over the other is called the 
 Free Electricity. A positive electrification may be produced 
 in a conductor either by a transference of a quantity A of 
 positive electricity to it, or of an equal quantity of negative 
 electricity from it, or by a simultaneous transference of 
 positive electricity to it and negative electricity from it, the 
 Bum of these two quantities being equal to A. 
 
64 ELECTRICITY. 
 
 The single-fluid theory supposes that all bodies are com- 
 posed of t\vo kinds of material particles one ordinary matter, 
 the other the electric fluid. The former has all the properties 
 of matter ; the latter has only mobility, and attraction and 
 repulsion. The particles of matter repel other particles of 
 matter, but attract the particles of the fluid with a force 
 varying inversely as the square of the distance between the 
 particles. The particles of fluid have similar properties ; but 
 the attraction between any given quantities of unlike mole- 
 cules is slightly greater than the repulsion between the same 
 quantities of like molecules when the other conditions are 
 the same ; consequently there is a slight resultant attraction 
 between an amount of matter in combination with an equal 
 amount of the fluid and another similar combination of matter 
 and fluid. When equal quantities of matter and fluid are 
 present in a body, it is non-electrified, and the matter and 
 fluid are then said to be combined. When more fluid than 
 matter is present, the body is positively electrified ; when 
 there is a deficiency of the electric fluid, the electrification is 
 negative. There may be an excess of the fluid in one part of 
 a body, and a deficiency in another, and then the former is 
 positive, the latter negative. 
 
 54. We may further illustrate the laws stated in sect. 52 
 by another very instructive series of experiments. A glass 
 vessel, A (fig. 36, a), in the form of a cylindrical or globular 
 bottle, is provided with a tightly-fitting cork, B. Through 
 B passes a metal (usually brass) rod, C, fixed by sealing-wax. 
 At its upper extremity the rod carries a metal disc, D, and 
 to its lower extremity are attached two rectangular pieces 
 of gold-leaf, E, three or four inches long by one broad, 
 hanging face to face. To keep the air dry, a dish con- 
 taining sulphuric acid is sometimes placed inside. Two 
 strips of gold-leaf or tinfoil are usually pasted on the inner 
 side of A, in such a position that the leaves, E, will touch 
 them when they diverge to a great extent. The apparatus 
 is called an Electroscope, for by its aid the kind of electricity 
 with which a body is charged, can be ascertained. 
 
 Having rubbed the glass rod briskly, bring it towards 
 the plate of the electroscope. As it approaches, the leaves 
 
FRICTIONAL OR STATICAL ELECTRICITY. 
 
 65 
 
 will diverge (fig. 36, &), shewing repulsion, which is due to 
 their being similarly electrified. While they are divergent, 
 touch the plate with the finger (fig. 36, c) ; the leaves will 
 immediately collapse. Kemove the finger, and then the glass 
 rod : the leaves will again diverge (fig. 36, d), owing to their 
 
 Fig. 36. 
 
 being again similarly electrified. Now bring the glass rod 
 near, the leaves collapse ; nearer still, they diverge again ; 
 remove the rod a little, they collapse ; remove it further, they 
 diverge again, and remain divergent, shewing that there is 
 now a charge in the electroscope. Bring the electrified wax 
 near, the leaves diverge still more. Take the wax away, they 
 resume their former divergence. If we begin with the wax 
 rod, we have a similar series of phenomena. The explana- 
 tion is this. At first the plate and leaves are unelectrified. 
 When the electrified glass rod is brought into the neighbour- 
 hood, it attracts the opposite electricity to the plate and repels 
 the like electricity to the leaves ; hence the leaves repel each 
 other. When the plate is touched by the hand, the, experi- 
 menter, and with him the earth, becomes electrically a part 
 of the electroscope, and the positive electricity is repelled by 
 the glass rod into the earth through the body. The negative 
 electricity is retained chiefly in the plate by the attraction of 
 the glass rod. When the finger and then the rod are removed, 
 the negative electricity spreads over the plate and leaves, and 
 
66 ELECTRICITY. 
 
 the leaves consequently again diverge ; when the glass rod is 
 brought near again, it attracts the negative electricity to the 
 plate ; there is thus no electricity in the leaves, and they 
 collapse ; when brought nearer, the rod separates more of 
 the neutral electricity in the plate and leaves, drawing the 
 negative electricity to the plate and repelling the positive 
 electricity to the leaves, which again diverge. When the 
 electrified wax is brought near, it repels the negative elec- 
 tricity in the plate and leaves to the lower extremities of the 
 leaves, and hence makes them diverge more than before. 
 
 55. This experiment shews that we can charge a body with- 
 out touching it with one already electrified, and we are then 
 said to charge it by induction. But it will be noticed that in 
 doing so we charge it with the opposite kind of electricity to 
 that possessed by the inducing body. The two bodies were 
 separated by air, which does not, as we see from this experi- 
 ment, allow the electricity of the glass to pass to the electro- 
 scope. In that capacity the air is called a Dielectric. We 
 see also how the electroscope may be used to shew whether 
 a charged body, A, is positively or negatively electrified. 
 Because, if we charge the electroscope inductively by the 
 glass rod, a body charged positively and brought near will 
 make the leaves collapse ; but if charged negatively, will 
 make them diverge. 
 
 56. These laws may be further illustrated by using two 
 electric pendulums placed near one another. Charge both 
 the balls with the glass or the wax, then they will repel each 
 other ; or charge one of the balls with the glass rod, and 
 then allow the other to touch it ; the first will communicate 
 a portion of its charge to the second, and they will repel each 
 other, but not so much as before. If they are charged, the 
 one with the glass rod and the other with the wax, they will 
 attract each other. We see from these experiments that the 
 effect is somehow dependent on the amount of electrification, 
 and hence we may speak of a quantity of electricity, which 
 we can measure by the effect it produces. 
 
 57. Conductors and Non-conductors. The electric pendulum 
 was described in sect. 51 as consisting of a glass stem with 
 a ball of pith attached to it by a silk thread. With a metal 
 
FRTCTIONAL OR STATICAL ELECTRICITY. 67 
 
 stand and a cotton thread or a wire, we could not make the 
 experiments described, because any electricity given to the 
 ball by contact would have instantly been conducted to the 
 ground by the wire and stem. The silk thread and the glass 
 rod offer resistance to the passage of the electricity, and 
 hence are called non-conductors. Bodies possessing this pro- 
 perty are often called insulators, since they may be used, as 
 in this case, to support electrified bodies without allowing 
 their electricity to escape. Copper, silver, and the metals 
 are the best conductors ; gases, paraffin, glass, vulcanite and 
 resinous substances are among the best insulators. It must 
 be observed that these terms are entirely relative. Every 
 substance conducts electricity more or less, and every sub- 
 stance resists the passage of electricity to a greater or less 
 degree ; there is no perfect conductor, and no perfect insu- 
 lator. When a substance is spoken of as being a conductor, 
 it is generally meant that it is a good conductor. (The name 
 Conductor is generally applied to bodies of good conducting 
 material, which are mounted on insulating stands for the 
 purpose of holding charges of electricity.) Good conductors 
 allow the electricity to move freely over and through them, 
 and if a charge be given to one part of a good conductor, it 
 is instantly spread over the whole surface. A charge given 
 to a bad conductor takes a long tjme to distribute itself, and, 
 in fact, in many cases is practically confined to the particular 
 portion of the body where it was originally put. 
 
 The following series classifies the more common substances 
 according to their conducting powers, beginning with the best, 
 and ending with the worst conductors : The metals, graphite, 
 sea-water, spring-water, rain-water; alcohol and ether, dry 
 wood, marble, paper, straw, ice at 32 F. ; dry metallic oxides, 
 fatty oils, ice at 13 F., phosphorus, lime, chalk, camphor, 
 porcelain, leather, dry paper, feathers, hair, wool, silk, 
 gems, glass, agate, wax, sulphur, resin, amber, gutta-percha, 
 caoutchouc, shell-lac, ebonite, water- vapour, gases. 
 
 An increase of temperature has in the case of the metals 
 the effect of lessening the conducting power, whilst it has 
 the opposite effect in almost all other substances. Glass 
 becomes a conductor at a temperature below that of boiling 
 
68 ELECTRICITY. 
 
 water, and wax, sulphur, amber, and shell-lac become so 
 when fused. 
 
 58. Insulation. When a conductor is placed on sup- 
 ports which prevent the electricity communicated to it 
 from passing into the ground, it is said to be insulated. 
 The insulating material usually employed in the construc- 
 tion of electrical apparatus is glass, which is hard, durable, 
 and easily worked, and, could its surface be kept dry, 
 would be one of the best non-conductors. In frosty and 
 in very dry weather, glass insulates well ; but at all other 
 times it becomes coated with a thin, scarcely visible, layer 
 of moisture, which very considerably impairs its insulating 
 power. In order to insure dryness, it is necessary to warm 
 electric apparatus before use. Water-vapour, in the form of a 
 gas, is non-conducting, and when it can be kept from con- 
 densing on the glass, does not affect its insulating power. 
 The deposition of moisture is much lessened by coating 
 the glass with shell-lac, which is done by painting the glass 
 when hot with shell-lac varnish. Green glass, which contains 
 no lead, is better adapted for the construction of electric 
 apparatus than flint glass, and does not condense moisture to 
 the same extent. Sir William Thomson has tested the insu- 
 lating power of glass by preserving charges of electricity in 
 hermetically sealed glass bulbs for years. Ebonite, a rigid 
 preparation of vulcanised india-rubber, is much superior to 
 glass as an insulator. It is of this substance that india- 
 rubber combs are made, which in dry and frosty weather 
 make the hair crackle with electricity. Even with the best 
 insulators, and with dry air, it is not possible to maintain 
 undiminished the charge which a body receives. There is 
 invariably a loss, arising chiefly from the particles of air or 
 dust becoming charged, and carrying off the charge ; and 
 partly, perhaps, from the insulators, even the best of them, 
 being imperfect non-conductors. In all exact experiments 
 it is necessary to ascertain the rate at which the charge 
 diminishes, and to take it into account in estimating results. 
 
 59. The term electrics used to be applied to those substances 
 which, when held in the hands and rubbed, become electric ; 
 and non-electrics, to those which do not. The distinction is 
 
FRICTIONAL OR STATICAL ELECTRICITY. 69 
 
 an unnecessary one, for if proper arrangements are made, it 
 can be shewn that all bodies become electrified when rubbed. 
 In the case of conductors held in the hand, the electricity is 
 no sooner excited than it is conveyed by the body, which is 
 a good conductor, to the ground ; while in the case of non- 
 conductors, it remains on their surface. When a metal 
 rod is rubbed with a silk handkerchief, no electricity 
 is shewn by the rod if it is held in the hand ; but if held 
 by a glass handle, it is at once seen to be electrified on 
 being brought near an electroscope. In the first case, the 
 hand conveys the electricity of the rod to the ground ; but 
 in the second, the glass prevents this discharge. The rod 
 is truly an electric in both cases ; non-electric is a term 
 applicable to very few, if any, substances. 
 
 60. In the description of the preceding experiments nothing 
 has been said about the condition of the rubbers. It is found, 
 when proper precautions are taken, that the silk handker- 
 chief employed to rub the glass acquires the negative 
 electric state, and the flannel rubber of the sealing-wax the 
 positive. This cannot, however, be clearly shewn when the 
 experiment is performed as above described, for the rubbers 
 are in each case held in the hand, which, being a con- 
 ductor, carries off a great portion of the electricity produced 
 on them, so that they give feeble, if any, evidence of 
 electrical excitement. As the rods are non-conductors, and 
 are held only by their extremities, the electrification of the 
 untouched portions suffers almost no diminution. If vulcanised 
 india-rubber cloth, however, be used instead of the silk 
 handkerchief, the rubbing side of the cloth shews negative 
 electricity. The opposite electricities of the rubbing sur- 
 faces are best shewn when the rubber as well as the rubbed 
 surface is insulated. When two similar discs one of glass, 
 the other brass covered with silk held by insulating handles, 
 are rubbed together, so long as they are kept touching, no 
 electricity is shewn : but when they are separated, the former 
 shews positive electricity, the latter negative electricity. 
 The negative and positive conductors of the electric machine 
 (sect. 142) illustrate the same principle. From the most careful 
 observations attending the production of electricity, we are 
 
70 ELECTRICITY. 
 
 led to conclude that when a quantity of one kind of electricity 
 is produced, as much of the opposite electricity is produced. 
 In no case is one electricity produced without an equal 
 quantity of the other. This will be more fully considered 
 later on. 
 
 61. It has been found by experiment that the relative nature 
 of the rubbing and rubbed surfaces determines the kind of 
 electricity which each assumes. Thus, if glass be rubbed with 
 cats' fur instead of with silk, its electricity is negative instead 
 of positive. This shews the impropriety of calling one 
 kind of electricity vitreous. In the following list, each 
 body, when rubbed with any one preceding it, is electrified 
 negatively ; with any one succeeding it, electrified positively : 
 cats' fur, smooth glass, linen, flannel, feathers, wood, paper, 
 silk, sealing-wax, shell-lac, ground glass. When two pieces 
 of the same material are rubbed together, the colder or 
 the smoother becomes electrified positively. An apparently 
 email difference in the nature of the surface or the temperature 
 or colour often entirely changes the position of the substance 
 in the above list. Where the temperature of the positive body 
 can be raised sufficiently, it is found that the relative posi- 
 tion of the two substances can be changed ; the one usually 
 electrified negatively becoming positively electrified, and 
 the other being negatively electrified. Metal filings rubbing 
 against a plate of the same metal produce negative electricity 
 in themselves, and positive electricity in the plate. When 
 a white silk ribbon is rubbed with a black one of the same 
 texture, the white one becomes positively electrified. When 
 two portions of the same ribbon are rubbed together, the 
 one longitudinally and the other transversely, the latter is 
 always negatively electrified. A plate of glass becomes 
 positively electrified when a stream of air is directed against 
 it from a pair of bellows. The amount of electricity deve- 
 loped is apparently not proportional to the amount of energy 
 expended in rubbing. 
 
 62. Processes of Electrification. There are other means of 
 developing electricity besides friction. In general, every- 
 thing that tends to disturb the molecular condition of bodies 
 tends to produce electricity. Cleavage, pressure, and change 
 
FRICTIONAL OR STATICAL ELECTRICITY. 71 
 
 of temperature, more especially in crystalline minerals, are 
 frequently attended with the development of electricity. 
 The electricity of cleavage is shewn by rapidly cleaving a 
 plate of mica, when one of the divided faces shews positive 
 electricity, the other negative electricity. A feeble lumi- 
 nosity also marks the separation when made in the dark. 
 If the laminae are pressed together and again separated, they 
 again shew the same electrification as before. Several other 
 minerals possess the same property. The light that is seen 
 to accompany the breaking of loaf-sugar and sugar-candy in 
 the dark is generally attributed to the electricity of cleavage. 
 Haiiy found that when a piece of calc-spar is pressed 
 between the fingers, it becomes positively electrified, and 
 remains so for days together. Fluor-spar, topaz, mica, 
 arragonite, quartz, and other minerals, assume one or other 
 electricity when pressed. When two discs, one of cork, 
 the other of caoutchouc, are pressed together by insulating 
 handles, and separated, the cork is found to be electrified 
 positively, the caoutchouc negatively. The same is also true 
 of cork and coal, shell-lac, zinc, and warm calcareous spar ; 
 but cork becomes negatively electrified when pressed against 
 dry fur, flannel, skin, fluor-spar, and cold calcareous spar. 
 A slice of cork and a slice of orange observe the same 
 relation in similar circumstances. When in the latter 
 case the separation is suddenly made, we obtain a greater 
 effect than when it is made slowly, from which we learn 
 that conducting surfaces when pressed together shew no 
 excitement, probably from the recombination of both elec- 
 tricities at the instant of their production. In fact it is 
 evident that unless one of the substances be a non-conductor 
 it will be very difficult to obtain a charge of electricity by 
 means of pressure. Tourmaline offers the most remarkable 
 illustration of the electricity got by change of temperature. 
 While a crystal of this mineral is being heated, it shews 
 positive electrification at one end of its principal axis, and 
 negative at the other. If it be divided when in this condition 
 it is found that each of the halves is electrified in the same 
 way as the whole. It thus manifests an electric polarity, 
 like the magnetic polarity of the magnet. When the rise in 
 
72 ELECt RICKY. 
 
 temperature ceases, for an instant it loses polarity, and then 
 as it cools it assumes the opposite polarity to that it had 
 before, being negative now where formerly it was positive. 
 Below 50 R, and above 302 R, tourmaline seldom shews 
 electric properties. Topaz, boracite, and several other 
 minerals resemble tourmaline in their action under heat. 
 The electricity thus developed by heat is sometimes called 
 pyro-electricity. There are other sources of electricity, of 
 which we shall afterwards treat, such as chemical action, 
 motion of magnets, heating of a circuit composed of different 
 metals, &c. 
 
 63. When water is evaporated, it is usually found that the 
 vessel from which it is evaporated is electrified, and that 
 the vapour has the opposite electrification. The electrifi- 
 cation apparently depends upon the nature of the other 
 substances present in the water. If it contains free oxides 
 of such metals as potassium, sodium, calcium, the water 
 becomes positively electrified : if there is a soluble acid or 
 a carbonate chloride, the water is negatively electrified. 
 When the water is perfectly pure, it does not become 
 electrified on evaporation. 
 
 64. Sir William Armstrong invented an engine by which 
 electricity can be generated by the friction of steam. It 
 consists of a boiler on insulating supports, which sup- 
 plies steam to tubes which pass through a condenser, D 
 (fig. 37), filled with cold water. This condenses the steam 
 partially, and it then escapes through nozzles, A, so formed 
 as to cause much friction between the escaping steam and 
 the sides of the nozzles. A comb, P, provided with a series 
 of points is placed in the jets of steam, and collects the 
 electricity and conveys it to the prime conductor, B. In 
 ordinary circumstances the prime conductor was charged 
 positively and the boiler negatively, and large sparks were 
 obtained. Faraday investigated the action of the Hydro- 
 electric Machine, and shewed that the small drops of water 
 produced by the partial condensation were essential to the 
 production of electricity: that electricity was due to the 
 friction between these drops and the sides of the nozzles, for 
 on changing the material with which they were lined, the 
 
FRICTIONAL OR STATICAL ELECTRICITY. 
 
 73 
 
 amount or the kind of electricity produced was changed : 
 when the water was made a conductor, by dissolving in it any 
 salts, acids, &c., no electricity was produced : when turpentine 
 or any fatty substance was added to the water, the boiler was 
 
 Fig. 37. 
 
 charged positively, the prime conductor negatively : the 
 production of electricity increased with the pressure of 
 the steam. A current of moist air driven through the 
 nozzles charged them negatively, but carried positive to 
 the points : there was no electricity produced when perfectly 
 dry air was used. 
 
74 
 
 CHAPTER V. 
 DYNAMICAL PRINCIPLES. 
 
 65. To understand the phenomena of electricity and 
 magnetism, a knowledge of the elementary terms and prin- 
 ciples of dynamics is necessary, and for the convenience of the 
 reader a short epitome of them is given here. 
 
 66. Units of Measurement. Every quantity is measured in 
 terms of a standard or unit, and its value is expressed as a 
 multiple of that unit. For example, the unit of length 
 usually adopted is either the foot or the metre, or some 
 multiple of one or other, and lengths are expressed as being 
 so many feet or metres. Thus a mountain is said to be 
 4567 feet high. In the measurement of time the second is 
 usually adopted for the standard ; an average day is so many 
 seconds. So a sovereign is a unit in the measurement of 
 money : a degree in the measurement of angles. 
 
 67. A body at any instant is in some definite position, but 
 if it change from one position to another it is said to 
 move or to be in motion. A body in motion has at any 
 
 instant a definite rate and a 
 definite direction of motion. A 
 ship, for example, is said to sail 
 at ten knots per hour in a north- 
 easterly direction. Velocity is 
 the rate of motion ; but it 
 
 A ~~*& involves the idea of direction 
 
 Fig. 38. as well as that of magnitude. 
 
 Hence a straight line may 
 
 represent the velocity of a body at any instant the length 
 being proportional to the magnitude, and the direction repre- 
 senting the direction of motion. Thus AB would repre- 
 sent a velocity twice as great as, and in a direction perpendi- 
 cular to, the velocity represented by CD. Velocity is uniform 
 when the rate of motion does not change, that is, when equal 
 spaces are traversed in equal portions of time. It is measured 
 by the number of units of length passed over in unit of time. 
 
DYNAMICAL PRINCIPLES. 75 
 
 The velocity of sound in air at the temperature of freezing 
 water is 1093 feet per second that is, sound travels 1093 feet 
 in one second. Unit velocity is the velocity of a body which 
 passes over unit of length in unit of time. Thus if a foot 
 and a second are the units of length and of time respectively, 
 unit velocity is that of a body moving over one foot in one 
 second. The velocity of a body may be changed either by 
 increasing or diminishing the rate of motion, or by altering 
 its direction. AB, A'B', A"B" represent the velocities of three 
 
 Fig. 39. 
 
 bodies at one instant of time, and AC, A'C', A"C" their 
 velocities at another. In the first case the velocity has 
 changed in magnitude only, in the second it has changed 
 in direction only, and in the third both in magnitude and 
 direction ; and the changes of velocity are represented by 
 BC, B'C', B"C". 
 
 68. Acceleration is the rate of change of velocity per unit of 
 time, and may take place either in the direction of motion 
 or not. ^ U^tJo^ 
 
 69. Mass is the quantity of matter in a body. The Unit of 
 mass generally adopted is either the quantity of matter in a 
 grain, a pound avoirdupois, or ^a gramme. (The weight of a 
 body is due to the gravitation attraction of the earth for it, 
 and is always proportional to the mass.) 
 
 70. The Momentum of a body, or its quantity of motion, is 
 measured by the product of the velocity of the body into the 
 mass. The momentum of a given mass is changed when the 
 velocity is changed. Unit momentum is the momentum of 
 unit mass moving with unit velocity. In British units, a 
 pound moving with a velocity of one foot per second, or half 
 mi ounce moving at thirty-two feet per second, or two pounds 
 
7(1 ELECTRICITY. 
 
 moving at half a foot per second, has unit momentum. So a 
 mass of one pound moving with a velocity of 32'2 feet per 
 second, has 32'2 units of momentum. In the centimetre 
 gramme second system (written C.G.S.) the unit momentum 
 adopted is that of one gramme moving with a velocity of one 
 centimetre per second. Change of momentum is measured by 
 the product of the mass and the change of velocity, and 
 may be due to a change either in the direction or in the 
 rate of its velocity. 
 
 71. Force is any cause which tends to alter a body's natural 
 state of rest or of uniform motion in a straight line. 
 
 A force is measured by the momentum it generates in 
 its own direction in unit of time. The force is then, said to 
 be measured in Kinetic or Absolute units. The absolute 
 measures are so called because they are independent of any 
 variable such as the intensity of gravity. They are all 
 expressible in terms of the fundamental units of mass, 
 space, and time. 
 
 72. Unit Force is that force which generates unit momentum 
 in unit of time. One very familiar instance of a force is the 
 weight of a body. If a pound be allowed to fall at Edinburgh 
 under the action of its own weight the attraction of the 
 earth for it it acquires in one second a velocity of 32 -2 feet 
 per second. Hence the weight of a pound at Edinburgh 
 acting for one second generates 32'2 units of momentum, and 
 is therefore equivalent to 32 '2 British units of force in 
 absolute measure. Again a gramme acquires, after falling 
 freely for one second at Paris, a velocity of 980*9 centimetres 
 per second, and therefore its weight is 980*9 C.G.S. units of 
 force. Hence if M be the number of pounds in a given mass, 
 and g the number which expresses the weight of unit of 
 mass in absolute measure at the place, Mg is the weight. 
 
 73. It is often very convenient to measure a force in terms 
 of the weight it can support. This is called the Statical or 
 Gravitation system of units. The objection to this method 
 is that the standard by which the forces are compared has not 
 the same value at different parts of the globe. "We could by 
 proper apparatus measure the attraction of one magnet for 
 another at a specified distance, by the weight necessary to 
 
\ 
 
 DYNAMICAL 
 
 E K S %f* 
 
 counteract the attraction. Let this be clone in Britain. 
 Repeat the experiment at the equator. There, supposing 
 the magnets to remain exactly the same, we would find that 
 the same counterpoise would no longer neutralise the attrac- 
 tion. It would be too little, because the weight of the 
 counterpoise is less at the equator than in Britain. In other 
 words, although the attraction between the two magnets 
 remains the same, its value as measured in gravitation 
 units is different in the two places ; for the weight of a mass 
 varies with the latitude and also with the height above the 
 sea-level. This variability in results renders the measurement 
 of forces in gravitation units useless for purposes of compari- 
 son, unless the latitude and the level be specified. To reduce 
 forces measured in gravitation units to absolute measure, it is 
 necessary to multiply the value of the force in gravitation 
 measure by the weight in absolute measure of unit of mass 
 at the place. Thus a force equal to the weight of six pounds 
 at Edinburgh is in absolute units equal to 6 x 32'2 = 193'2, 
 if 32 '2 be taken as the value of g at Edinburgh. 
 
 74. Forces, like velocities, may be represented by straight 
 lines the direction and length of the line representing 
 the direction and magnitude 
 of the force. Thus DA and 
 DB represent two forces act- 
 ing at the point D in the 
 directions indicated by the 
 lines, and with magnitudes 
 proportional to their lengths. 
 
 When two or more forces 
 act at a point simultaneously, 
 one force can always be found equivalent to them all. It 
 is called the Resultant Force. In the example above, it is 
 represented in magnitude and direction by the line DC, 
 found by drawing BC equal and parallel to DA and joining 
 DC. The resultant of any number of forces represented by 
 all the sides of a polygon but one taken in order, is repre- 
 sented by that one taken in the opposite direction. 
 
 A force may be resolved in any two directions at right 
 angles to one another and these are called the components 
 
78 ELECTRICITY. 
 
 of the force. Thus the components of AB in the directions 
 AC and AD are found geometrically by drawing through A 
 and B lines parallel to the two 
 directions the components being 
 represented by the parts intercepted 
 that is, by AC and AD. AC is 
 equal to AB multiplied by cosine 
 BAG, and AD is equal to AB 
 multiplied by sine BAG. 
 Fig. 41. 75. Work is done when resist- 
 
 ance is overcome, and the quantity 
 
 of work done is measured by the product of the resisting 
 force and the distance through which that force is overcome. 
 Unit of work is the work done when unit force is overcome 
 through unit space. 
 
 76. When work is done opposite to the direction in 
 which a force acts, it is said to be done against the force ; 
 when it is done in the direction in which the force acts, 
 the force is said to do work. As an example, take the 
 case in which the attraction of the earth for a body is 
 the resistance to be overcome. The amount of the resist- 
 ance is measured by the weight of the body, and the 
 direction in which it acts is vertical. Therefore, to 
 measure the work done against gravity when a body is 
 raised from one level to another, we must multiply its 
 weight by the height the weight being the force overcome, 
 and the height the distance through which it is overcome. 
 The ordinary gravitation unit of work is the work required 
 to raise a pound one foot, hence called a foot-pound. In 
 raising a hundredweight of coals 100 feet, the work done is 
 112 x 100 foot-pounds. The same amount of work is 
 required to raise half a hundredweight 200 feet, or a quarter 
 of a hundredweight 400 feet, or five hundredweight 20 feet. 
 But as the work done in raising a mass through any height 
 depends upon the intensity of gravity at the place, it is 
 necessary, in order to convert this into absolute units, to 
 multiply the gravitation measure by the value of g at the 
 place. Thus if M be the number of pounds, and h the height 
 through which they are raised, and g the value of gravity at 
 
DYNAMICAL PRINCIPLES. 79 
 
 the place, Nh is the gravitation measure of the work, 
 the same in absolute measure. In estimating in these 
 examples the work done against gravity, no account is taken 
 of the path by which the body was raised. It may have 
 been a load of stones dragged from a deep quarry up a long 
 series of inclined roads, or it may have been an equal load of 
 coals brought up the shaft of a pit by machinery. Or as in 
 the case of firing into a fort above the level of those attacking 
 it, it may have been necessary to project the shell to a height 
 above the fort, so that it may drop into the fort in its descent. 
 In one case we go over a long path before we attain the level 
 we wish to reach, in another case a comparatively short one, 
 and in a third case we go beyond the level and partially 
 return, but the work done is estimated solely by the product 
 of the weight lifted and the vertical space through which on 
 the whole it is lifted that being the direction in which we 
 have overcome the resistance. So long as the weight is the 
 same, the work done is proportional simply to the difference 
 of level between the original and the final positions. There 
 may be more tear and wear by one path than by the other ; 
 but that is not due to gravity, and at present we are con- 
 cerned only with the work done in overcoming gravity. 
 
 77. Similarly we do work in compressing air, into a 
 cylinder for instance. If we know the average resistance 
 which we had to overcome during the process or what is 
 the same thing, the average pressure it was necessary to 
 employ and the distance through which the piston has been 
 pushed, the work done is measured by the product of these 
 two quantities. 
 
 78. It has been shewn that two bodies repel each other 
 when charged with the same kind of electricity, and attract 
 each other when charged with opposite kinds. Suppose that 
 an insulated conductor A is charged with a known quantity 
 of positive electricity, and that another conductor B is charged 
 with a known quantity of negative, they will attract each 
 other. If we remove B a short space further from A, work 
 will be done against the electrical forces, which can be 
 measured by the product of the distance through which B 
 has been removed and the average value of the force exerted. 
 
80 ELECTRICITY. 
 
 Exactly the same amount of work would be done if, B being 
 removed altogether, a third body C, similar to B, charged 
 with a quantity of positive electricity equal to B's negative 
 charge, were brought from B's second position to its first. 
 
 As another example, take the case where a weight is 
 transported from one place at any height above the level of 
 the sea to another place at the same height. In such a case 
 there is on the whole no work done against gravity, even 
 though in transit it may have been necessary to take the 
 body over a very high pass, because the positions at the 
 beginning and the end of the operation are at the same 
 level. This may perhaps be better understood by considering 
 that however much work was required to be done against 
 gravity to raise the body to the highest point, an exactly 
 equal amount of work was done by gravity when the body 
 descended to the old level. In all cases where there is no 
 displacement in the direction in which the force acts, there 
 is no work done against or by the force. 
 
 79. Work is also done when the rate of a body's motion is 
 changed, and it is then measured by half the product of the 
 mass of the body and the difference of the squares of the 
 initial and final velocities. If a body of mass M increase its 
 velocity from v 1 to v 2 , the work done in overcoming the 
 
 inertia is M(v 2 2 v^}. Again in the case of a body of mass 
 M, falling freely from rest under the action of its own weight, 
 
 and acquiring a velocity v, the work done by gravity is Mv 2 . 
 
 2 
 
 This can be shewn to be equal to "high, where h is the height 
 fallen through, and g is the weight of unit mass at the place. 
 It was stated in sect. 76 that this is the work necessary to 
 raise the body to its former position against the earth's 
 attraction. 
 
 80. Energy is the power a body has of doing work. There are 
 very many forms of energy. Thus a raised stone can fall, and 
 in doing so may raise other stones, or do work in other ways ; 
 a wind can root up trees, drive a windmill, or bring ships 
 from one port to another ; gunpowder can propel bullets 
 or blast rocks ; a horse can draw wagons ; a stream can 
 
DYNAMICAL PRINCIPLES. 81 
 
 carry ships ; coal can generate heat itself a form of energy 
 which may be employed to do work in various ways ; a 
 current of electricity can generate heat, decompose liquids, 
 give light, noise. 
 
 81. Potential energy is energy in virtue of position. Any 
 raised mass is an example of a body possessing potential 
 energy. Because of its weight it can fall : in doing so it will 
 perform work of some kind. In the case of the monkey of a 
 pile-driving engine it will drive a beam into the earth. In 
 the case of the weight of a clock it will keep the works in 
 motion by overcoming the friction ; or in the case of a pond 
 of water it will turn an overshot mill-wheel by making one 
 side heavier than the other. Compressed gas is another 
 instance of a mass possessing potential energy. If confined 
 in a chamber provided with a movable piston, it can press out 
 the piston against external resistance, as in the case of any 
 steam, air, or gas engine. Gunpowder has potential energy, 
 for by giving play to the chemical affinity of its ingredients 
 we can make it explode, and so do work in a variety of 
 ways. Other instances, due to chemical affinity, are seen 
 in combustion, as of coal, and the oxyhydrogen blowpipe. 
 
 82. The mutual potential energy of two bodies in any 
 relative position is the amount of work obtainable from their 
 mutual repulsion or attraction by allowing them to separate 
 from that position to an infinite distance apart {in the case of 
 repulsion), or to come from an infinite distance to that posi- 
 tion (in the case of attraction). The potential energy always 
 diminishes in the direction of the resultant force. In cases 
 of repulsion, as of two similarly electrified bodies, the 
 potential energy increases as the bodies are brought nearer 
 each other : the opposite is the case in attraction. 
 
 The potential at any point due to any attracting or 
 repelling body or distribution of matter, is the mutual 
 potential energy between it and a unit of matter placed at 
 that point. 
 
 83. Kinetic energy is the energy a body has in virtue of its 
 motion, and is measured by half the product of its mass into 
 the square of its velocity. As examples of kinetic energy we 
 have a bullet propelled from a rifle, a running stream, winds, 
 
82 ELECTRICITY. 
 
 tides. When a body M is thrown vertically upwards it rises 
 to a height, and so does work = M#/i. It can be shewn that 
 
 h is equal to , where v is the velocity of projection. In 
 
 other words, the height the body rises or the work it does 
 is proportional to the square of its velocity. Hence, when 
 the velocity is trebled, the height the body will rise, and 
 consequently the kinetic energy it possesses, is multiplied 
 ninefold. 
 
 84. The law of the Conservation of Energy asserts that the 
 quantity of energy in the universe is a constant quantity. No 
 energy can be created, no energy can be destroyed. Energy 
 may be transformed from one form to another. Water or 
 any raised mass may fall and so lose potential energy ; but in 
 falling it will either gain kinetic energy or do work by 
 turning a wheel or in some other way. Gunpowder may 
 explode and so lose its potential energy ; but the bullet it 
 has propelled and the gun which has recoiled have kinetic 
 energy. Some of the energy of the powder has changed into 
 energy of sound, and some into energy of heat and light. 
 But if the energy of the bullet, and the gun, the energy 
 of the sound, the heat, and the light be all measured, it will 
 be found that their sum will equal the original energy 
 of the powder. In other words, to do work of any kind, 
 energy must be transformed from one form into another; and 
 if any energy is seen to come into existence at one place, that 
 must be due to an equivalent amount of energy having dis- 
 appeared in another. No energy can disappear in one form 
 without appearing in some other. Hence, wherever we see 
 energy of one form produced, we should always be able to 
 find that it is due to the transformation of energy of some 
 other form. 
 
 85. Consider now the case of the raised stones. Because 
 they have weight they will fall if unsupported, and will 
 then do work in some form or other. In other words, by 
 raising the stones against gravity we have given them 
 potential energy. If they are allowed to fall freely, gravity 
 will do work upon them, which will take the form of kinetic 
 energy equivalent to the energy originally spent in raising 
 
DYNAMICAL PRINCIPLES. 83 
 
 them. In the case of the compressed air, the energy spent in 
 compressing takes the form of potential energy, in virtue of 
 which the air can do work in pushing out the piston against 
 external pressure the work done may be measured as 
 described above. So in the case of the electrified bodies, if B 
 be allowed to pass from ft to , the electrical forces will do 
 work equal to what was done against them in the previous 
 case. Hence, as a slightly different form of expressing what 
 was said above (sects. 76 and 78), if B be removed from a to 
 by any path, no matter what, and then be allowed to return 
 to by any path, there is no work done on the whole, 
 for as much work is done against the electrical forces in the 
 first translation as is done by them in the second. 
 
 CHAPTER VI. 
 ELECTRICAL QUANTITY AND DENSITY. 
 
 86. We have seen that a conductor may have a charge 
 given to it in virtue of which it will exert a certain influence 
 on other bodies. If this body be placed in contact with 
 another exactly similar conductor, the charge of electricity 
 is shared between them, and the influence exerted by either 
 singly is different from that exerted by the first? in the same 
 circumstances. If the original charge is distributed in a 
 similar manner over a number of conductors, the effect due 
 to any one of the charged conductors is different from that 
 exerted by the original one. Hence we see that electricity 
 exerts an influence apparently depending upon its quantity ; 
 and from some of the effects of a charge we may obtain a 
 method of measuring its quantity. 
 
 87. For instance, bodies charged with electricity exert 
 either a repellent or an attractive force upon other bodies 
 charged or electrified by induction, and therefore the amount 
 of this attraction under given conditions may be made the 
 basis of measuring electric quantity. The force exerted may 
 be measured in several ways. The instrument originally 
 
 F 
 
84 
 
 ELECTRICITY. 
 
 used was the torsion balance, of which there is a description 
 in sect. 23. For electrical measurements a slight modification 
 is necessary. The air inside is kept dry by a vessel contain- 
 ing sulphuric acid or chloride of calcium. The torsion wire 
 supports at its lower extremity a horizontal rod of shell-lac 
 
 carrying at one end 
 a gilt pith ball, B, 
 and a counterpoise 
 at the other. In the 
 cover of the balance 
 there is an aperture 
 through which an- 
 other ball, A, sup- 
 ported by a rigid 
 insulating stem, can 
 be introduced. The 
 centres of the balls, 
 the rod of shell-lac, 
 and the graduated 
 strip of paper, ought 
 to be all in the 
 same horizontal 
 plane. When the two 
 balls are in contact, 
 the shell-lac rod 
 
 Fig. 42. 
 
 should point to zero on the scale, and the wire should be 
 without torsion, with the index also at zero. 
 
 88. The instrument being so set, a charge is given to A ; 
 it is introduced and touches B, and there is an immediate 
 repulsion. After some oscillations, B comes to rest at an 
 angle from A. The torsion on the wire is , and the force 
 of torsion brought into play equals the repulsion between 
 
 the two balls at a distance 2r sin. ~, where r is the length 
 
 of the arm carrying B. If the nut be turned through an 
 angle 6 tending to diminish the distance between A and B, 
 B will then take up a position $ degrees from A, the wire 
 will be twisted through an angle 6 -|- 0, and the force of 
 torsion will equal the repulsive force between the balls at the 
 
ELECTRICAL QUANTITY AND DENSITY. 85 
 
 distance 2r sin. ~ . In this way the force exerted by these 
 
 2i 
 
 spheres at different distances can be measured, and it is 
 found that for any given quantities the force exerted varies 
 inversely as the square of the distance between their centres 
 that is, if at a distance of a foot the force exerted is repre- 
 sented by the number 1 ; at six inches, that is, one half of the 
 original distance, it will be 4 times as great ; at four inches, 
 9 times ; at three inches, 16 ; and at two inches, 36. At 
 two feet, that is, twice the original distance, the force will 
 have only one-fourth of its original value. As the distance is 
 diminished or increased in any ratio, the force is increased or 
 diminished in the square of that ratio. 
 
 89. The next point to be ascertained is, how the force 
 varies with the quantities of electricity on the balls. A and 
 B are discharged, and the apparatus is set as previously 
 described. A is charged and inserted. It touches B, and 
 repulsion ensues. The wire is twisted so as to bring the 
 balls to a certain distance, D, from each other, and the 
 repulsion is measured by the torsion of the wire. By 
 removing A, and making it touch an exactly equal and 
 similar ball, A's remaining charge is halved ; and on A being 
 replaced, the force now necessary to keep the balls at the 
 same distance is again measured by the torsion. B's charge 
 is similarly halved, and the force again measured, and so on. 
 
 If E and E' be the original charges on A and B, and T' the 
 
 -ri 
 
 torsion, -^ and E' and T" the charges and torsion in the second 
 
 T? "R" 
 
 case, ^r and -~ and T 7// the charges and torsion in the third 
 z> A 
 
 case, &c., and D the fixed distance ; then it is found, as the 
 result of very careful experiments, that the force exerted at 
 a fixed distance is always proportional to the product of the 
 numbers representing the charges that is : 
 
 T' : T" : T" : : E x E' : | x E' : | x ^ : : 1 : \ : i 
 
 Hence if two balls removed beyond the influence of other 
 electrified bodies, and charged with E and E' units of 
 electricity respectively, are kept at a distance r from each 
 
86 ELECTRICITY. 
 
 other, they will exert a force represented by the expression 
 
 W / 
 
 . If the electricities are different, their signs will be, 
 
 the one -J-, the other ; their product will therefore be 
 , and signifies an attractive force ; when both are -|- or 
 , the product is positive, which indicates repulsion. 
 
 The force exerted between two small bodies charged respectively 
 with E and E' units of electricity, is proportional to the product 
 of the charges divided by the square of the distance. 
 
 90. The electrostatic unit of electricity is that quantity of 
 electricity which, when placed at unit distance from an 
 equal quantity, repels it with unit force (when air is the 
 medium between them). The units adopted are the centi- 
 metre, gramme, and second. The force exerted by these 
 quantities so placed would generate, if acting for a second on 
 a gramme of matter perfectly free to move, a velocity of one 
 centimetre per second. The equal quantities may be obtained 
 by charging one of two exactly similar conducting balls with 
 electricity, and then placing it in contact with the other ; 
 evidently the charge will be equally divided between the two. 
 
 91. Coulomb's experiments with the torsion balance to 
 prove the above laws were carried out with an extra- 
 ordinary degree of care and accuracy ; but there are several 
 circumstances which render a perfectly accurate result almost 
 impossible except in one or two cases. He pointed out 
 that these laws are rigorously true only when all extraneous 
 conductors have been removed beyond the influence of the 
 electrified bodies. These must be spheres, and separated by 
 distances, large compared with their diameters. When the 
 charges on the repelling spheres are unequal, repulsion ceases 
 at a certain distance, and at all smaller distances there is 
 attraction. His results, so far as they go, have been com- 
 pletely verified by later experimenters ; but the best proof 
 of the truth of his law is derived as a mathematical conse- 
 quence of the experiment described in sect. 103. 
 
 In all these experiments there was an unavoidable loss of 
 electricity by dissipation into the air. The method followed 
 by Coulomb to compensate for this was extremely ingenious, 
 but want of space allows us only to allude to it. 
 
ELECTRICAL QUANTITY AND DENSITY. 
 
 87 
 
 92. When two equal balls are insulated, and a charge is 
 given to one of them, and the second is charged by contact 
 with the first, it is found that the charge is divided equally 
 between the two. Hence if the charge be uniformly distri- 
 buted over the surface of each, the quantity of electricity per 
 unit of surface of either is half what it was on the first. The 
 electric density of a uniformly charged surface is the quantity 
 of electricity on a unit of area. Where the distribution is 
 not uniform, the electric density is the quotient obtained by 
 dividing the quantity of electricity distributed over a small 
 portion of the surface by the area of this portion. As we 
 increase the surface of a conductor, the charge remaining 
 constant, the density on any one portion diminishes. Thus, 
 when a chain is charged and laid on the plate of an electro- 
 scope by means of a glass rod, the gold leaves diverge 
 considerably when the chain lies in a heap on the plate. As 
 it is lifted up, the leaves approach each other, because the 
 surface of the conductor being increased, the electric density 
 on the gold leaves is less, and consequently their repulsion is 
 diminished. 
 
 93. Electricity found only on the outer surface. Experiment 
 teaches us that electricity is exhibited only on the surfaces of 
 conductors ; this is shewn by the apparatus represented in 
 fig. 43. A brass ball is suspended by a silk thread, and 
 
 Fig. 43. 
 
 covered with two hemispheres of brass, which are held by 
 insulating handles, and exactly fit it. A charge is com- 
 municated to the ball so compounded. The hemispheres 
 
ELECTRICITY. 
 
 are put on so as to inclose the ball entirely, and they are 
 found to be electrified. When they are carefully withdrawn, 
 not the slightest charge is found on the ball. No electricity 
 is found on the inner surfaces of two gold leaves diverging 
 under the same charge. 
 
 94. A proof plane is an instrument used in measuring the 
 density of electricity upon different parts of the surface of a 
 conductor. It consists of a small circular disc of gold leaf or 
 gilt paper fastened to the end of an insulating stem (A, fig. 
 
 44). The disc is small 
 compared with the con- 
 ductor under investiga- 
 tion, and its thickness is 
 small compared with its 
 radius. It is laid flat 
 upon the part of the 
 surface to be examined, 
 and being thus made to 
 form part of that surface, 
 it acquires a charge pro- 
 portional to the density 
 of electricity at that 
 part. This charge is 
 measured by means of 
 an electrometer. The 
 proof plane having been 
 discharged, is applied to 
 some other part of the 
 conductor, and the new 
 charge measured as before, and so on in succession to different 
 portions of the surface. The ratio of the measurements 
 with the electrometer is the ratio of the densities at the 
 parts touched. 
 
 95. That electricity is found only on the outer surface 
 may also be shewn by the following experiment. A hollow 
 spherical metallic conductor of ever so thin material on an 
 insulating stand, with a hole in the top, is charged. A proof 
 plane is made to touch different parts of the outer surface, 
 and when removed is always found to be electrified. But 
 
 Fig. 44. 
 
ELECTRICAL QUANTITY AND DENSITY. 89 
 
 when the proof plane is tested, after having been made to 
 touch the interior, it is found to possess not the very least 
 charge ; proving that none of the charge is in the interior of 
 a hollow conductor. Care must be taken, in removing the 
 proof plane from the interior, that it does not touch, or 
 receive a spark from the edge of the hole. 
 
 To Faraday's ingenuity we owe the following experiments 
 illustrating the same fact. A cylinder of wire network (fig. 
 44), whose meshes need not be fine, is placed upon an 
 insulating stand, and charged either positively or negatively 
 by communicating a charge either to the inside or the 
 outside. When the cylinder is examined by the proof 
 plane, the charge is found on the outer surface only. 
 
 Faraday attached a conical bag of cotton gauze to a ring, 
 which was supported on an insulating stand, and kept it dis- 
 tended by a silk thread attached to the apex. It was electri- 
 fied, and the proof plane shewed that the charge was wholly 
 on the outside ; none whatever on the inside. The bag was 
 turned inside out by means of another silk thread and 
 again tested. Considerable charges were again obtained from 
 the outer surface of the bag, but none from the inner 
 the electricity having changed from the one surface to 
 the other. 
 
 96. Faraday made experiments to ascertain what effects a 
 charge given to a conductor exerted throughout its interior. 
 In one of these he had a large cube whose sides were of thin 
 metal. This was carefully insulated, and then submitted 
 to violent discharges from a powerful electric machine. In 
 the interior of the cube, which was full of air, were several 
 very delicate electroscopes ; but at no time before, during, 
 or after a discharge, could he detect the slightest trace of 
 electrification on them. 
 
 One very useful application of this is when it is desirable 
 to keep any electrical apparatus free from the inductive 
 action of other electrified bodies. The apparatus only 
 requires to be surrounded by a screen of conducting mate- 
 rial. It may be continuous, or it may be simply coarse 
 wire-netting. Such a screen effectually prevents any 
 inductive action. 
 
.X 
 90 ELECTRICITY. 
 
 97. The next point to be noticed is how a charge given to 
 a conductor is distributed over its outer surface. We may 
 consider first the cases where the conductor is uninfluenced 
 by other conductors. Coulomb found, by the aid of a proof 
 plane and the torsion balance, that the density on different 
 parts of a conductor depends upon its shape. Investigations 
 based upon the mathematical theory of electricity have in 
 many cases shewn what the distribution should be ; and in 
 every case which has been solved, theoretical deductions have 
 entirely agreed with the experimental results. 
 
 In the case of a sphere, the density is the same at every 
 point of its surface. In an ellipsoid formed by the revolu- 
 tion of an ellipse about one of its axes, the densities at the 
 extremities of the two axes are proportional to the axes 
 consequently there is a greater accumulation at the extremity 
 of the major axis ; or more generally, the density at any point 
 is proportional to the perpendicular from the centre upon the 
 tangent plane at that point. Hence the difference in the 
 electric densities on the ends and sides of a conductor gets 
 greater and greater as the conductor is more and more drawn 
 out in shape. Theoretical investigations shew that on a cone 
 
 
 
 Fig. 45. 
 
 the electric density should be infinite at the apex, and in 
 practice it is found impossible to keep a permanent charge on 
 a pointed body ; the charge is gradually given off to the air 
 surrounding the point. The variations in electric density at 
 
ELECTRICAL QUANTITY AND DENSITY. 
 
 01 
 
 different parts of a conductor will be best understood by 
 reference to the figures. It is to be observed that the dis- 
 tance of the dotted line from the surface is intended to 
 represent the relative electric density at the different parts, 
 but it must not be supposed that there is actually a layer 
 of electricity on the body of the depth indicated. When 
 the dotted line is inside the body, a negative electrification 
 is indicated. 
 
 Fig. 46. 
 
 When other bodies, charged or not charged, are near, 
 the distribution of electricity on the conductor is greatly 
 affected. The phenomena will be best understood by refer- 
 ring to the figures. 
 
 In such cases the distribution is said to be affected by 
 Induction. 
 
-2 
 
 ELECTRICITY. 
 
 CHAPTER VIL 
 INDUCTION. 
 
 98. We have already shewn in sect. 54 that a body originally 
 non-electrified can be charged without being in contact with 
 another charged body, or by any of the other processes men- 
 tioned in sects. 61, 62. We shall now consider the pheno- 
 menon more fully. 
 
 99. When a body charged with electricity, as the insulated 
 brass ball A, is brought near a brass cylinder B, with rounded 
 ends, uncharged and mounted on an insulating stand, it is 
 found that the cylinder shews signs of being electrified the 
 end nearest the ball having the opposite kind of electricity, 
 
 Fig. 47. 
 
 while the end farthest away has the same kind as the ball. 
 It is then said to have a charge induced upon it by A. If 
 the cylinder has previously been provided with pairs of pith 
 balls hung by cotton threads at different parts of its length, 
 the balls of each pair will by conduction be charged in the 
 same way as the portion of the cylinder to which they are 
 attached, and will consequently repel one another, as shewn. 
 The amount of this divergence varies with the distance of A 
 
I 
 
 
 INDUCTION. 
 
 V 
 
 from B, being greatest when the distance is least, and dimin- 
 ishing as A is removed, until at last no sign of electrification 
 can be found the electrification is manifest only~chrrrng the 
 proximity of A. Moreover, for a given distance of A from B, 
 the angle between the balls differs with their position on the 
 cylinder ; being greatest when they hang at the extremities, 
 and zero near the middle. This agrees with what is estab- 
 lished by a proof plane and an electrometer, that the density 
 of the electricity is greatest at the ends, and diminishes as we 
 recede from them ; being zero at a line nearly coincident 
 with the middle. The position of this line varies with the 
 proximity of A to B ; but is always between the middle of 
 B and A, and shifts nearer to the end as A is brought nearer. 
 It can easily be demonstrated by a proof plane and an elec- 
 troscope that the end of B nearest A is always charged with 
 the opposite electricity to that of A, and the end farthest from 
 A is charged with the like electricity. Thus, if A be charged 
 positively, there will be negative electrification at C and posi- 
 tive at D (fig. 47). If A be negative, C will be positive and D 
 negative. That the induced electricities are equal in amount, is 
 
 Fig. 48. 
 
 proved by the fact that they neutralise each other when the 
 ball is withdrawn. If the cylinder were made up of two 
 parts, each supported by a glass stem, it would be found, on 
 separating the two in presence of the charged body, that the 
 one end was electrified positively and the other negatively. 
 The action of the electricity of the charged ball inducing in 
 the cylinder this peculiar electrical condition is called induc- 
 tion, and the cylinder in this state is said to be polarised- 
 that is, its ends have similar and opposite properties. 
 
94 ELECTRICITY. 
 
 100. The electricity induced on either end of the cylinder 
 behaves in many respects as if it were a free charge. This 
 can be shewn by its action on other bodies. If another 
 cylinder, C, is placed near the first, as in fig. 48, it is found, 
 on the approach of A to B, to be affected by B in the same 
 way as B was by A ; and to have the power of similarly 
 influencing another cylinder, D. The series may be continued 
 indefinitely with the same results. When the charged ball 
 is withdrawn, the whole series returns to its natural condi- 
 tion without being in any way permanently affected. The 
 moment A is again brought near, each cylinder becomes again 
 polarised, and there is manifested at the farther end of the 
 last, a charge of positive electricity, which exerts the same 
 influence on other bodies as if a portion of the electricity 
 of the ball had been actually communicated or transferred 
 to it. But the induction does not stop here. It is found that 
 there is a charge induced, on the furniture and walls of the 
 room, the clothes of the experimenter, &c., equal and opposite 
 to the original charge. 
 
 101. If while A is close to B (fig. 47), we touch any part of 
 B with the finger for an instant, the pith balls at D collapse, 
 and those at C diverge rather more. If A be then removed, 
 the pith balls will again be seen to diverge, and it will be 
 found on testing with a proof plane that B has a permanent 
 charge of negative electricity. The explanation is, that the 
 proximity of A charged, separates the neutral electricity on 
 B, drawing the unlike kind towards the extremity nearest it, 
 and repelling like electricity to the other extremity. On B 
 being put in connection with the earth, the repelled positive 
 electricity runs to the ground, the negative electricity is 
 retained, and on A being removed, spreads over the whole of 
 B. If an insulated conductor in the neighbourhood of a 
 charged body is put in connection with the earth for an 
 instant and then removed, it is found to have a charge of 
 the opposite kind of electricity. 
 
 102. We are now in a position to understand how a charged 
 conductor attracts light bodies and repels them after contact. 
 Let A (fig. 49) be a conductor charged positively. By induc- 
 tion it separates the neutral electricity of B, drawing negative 
 
INDUCTION. 
 
 95 
 
 electricity to the nearest side, and repelling positive to the 
 farther side. By the law of attraction (sect. 88), the negative 
 electricity being nearer A, is attracted with a greater force 
 than the positive is repelled, and consequently B as a whole 
 is attracted. Similarly with the gold leaves of the electro- 
 scope. When they are charged they induce an opposite 
 charge chiefly on the tinfoil pasted on the interior of the 
 glass cover. There is attraction between the oppositely 
 electrified surfaces until contact takes place ; when the elec- 
 tricities neutralise one another, and the leaves fall back. 
 
 Fig. 49. 
 
 Fig. 50. 
 
 103. The amount of the opposite kind of electricity induced 
 by an electrified body on surrounding conductors is equal to 
 that of the inducting body. It was Faraday who proved this 
 by the following experiment. He insulated an ice pail, A 
 (fig. 50), ten and a half inches high and seven inches in 
 diameter, and connected it by a wire with the knob of a 
 gold-leaf electroscope, E. A brass ball, C, suspended by a 
 long dry thread of white silk, was charged with positive 
 electricity, and introduced within the pail. By induction 
 the electricity on the pail was separated, negative electricity 
 being on the inner, and positive on the outer surface, the 
 wire, and the electroscope. When the ball was removed, the 
 
96 ELECTRICITY. 
 
 electrification of the inner and outer surfaces of the pail and 
 of the wire and electroscope disappeared. On C being again" 
 introduced, the same separation took place ; the divergence 
 of the leaves caused by the induced positive electricity 
 increasing as the ball was lowered, until it had sunk three 
 inches below the opening, below which they remained steadily 
 in the same position at whatever depth it was, and whether 
 it was near or far from the sides. This shews that at depths 
 of three inches and more the charge induced by C is at 
 the maximum, and that at such depths the ball is practi- 
 cally wholly inclosed by the pail. The ball was lowered till 
 it touched the bottom, and communicated its charge to 
 the pail, the leaves still remaining in the same state as 
 before. The ball when lifted out was found to be entirely 
 uncharged ; shewing that the positive electricity developed 
 by induction on the outer surface was exactly the same in 
 amount as that of the ball itself. The negative electricity 
 of the inside of the pail, being equal to the positive on the 
 outside, was therefore equal to the positive electricity of the 
 ball, but opposite in kind. Faraday varied the experiment 
 so as to have four insulated pails inside one another, and the 
 effect on the outmost pail was exactly the same as before. 
 Nor was any difference found on substituting a similar 
 vessel of any other substance for the inner pail. We may 
 conclude from this and similar experiments that, on the 
 walls of a room, or other conductors surrounding a charged 
 body, the total amount of the opposite electricity induced 
 is equal in amount to that of the body itself. 
 
 As this is very important, we give another illustration. If 
 we imagine a conductor charged positively, say, and which 
 we may for defmiteness suppose spherical, surrounded by any 
 number of other spherical conductors, all insulated from it 
 and from one another : we shall always find on the external 
 surface of the outer one a positive charge equal in amount to 
 the charge on the conductor, and the electrical effects at 
 external points will be the same as if the original conductor 
 had alone been present, independent of the radius of the 
 outer one or of the number of those inclosed within it. If 
 the outermost conductor be connected with the earth, then 
 
INDUCTION. 97 
 
 no effect due to it will be experienced at points external to it, 
 and no charge will be found upon its outer surface ; but a 
 charge equal and opposite to the original charge will remain 
 on its inner surface. 
 
 104. By similar experiments it can be established that, if 
 conductors charged with the same or opposite electricities be 
 placed as above in the interior of a hollow metal globe or pail, 
 their inductive action will develop on its outer surface a charge 
 equal to the algebraic sum of all their charges. By using such 
 a vessel and an electroscope, it can be shewn that when any 
 two substances are rubbed together, equal quantities of the 
 opposite electricities are produced. Let each of the two sub- 
 stances be insulated and then rubbed together. On introduc- 
 ing either into the pail the gold leaves will diverge in the 
 one case with positive electricity, in the other with negative. 
 But if we put both into the pail together, still insulated and 
 not touching, there will not be any divergence of the leaves ; 
 shewing that the quantity of electricity is the same on each. 
 
 It is mainly from induction that the difficulty arises of 
 measuring exactly the attraction which two known amounts 
 e and e 1 of electricity on two conductors A and B exert upon 
 each other at a given distance, as in the torsion balance. The 
 e on A induces a quantity e' of negative electricity on B the 
 amount of which is not easily ascertained except when the 
 bodies are spherical ; ^ also induces e^ on A ; these induced 
 charges tf and e{ respectively induce fresh amounts of electri- 
 city, and this is continued in an infinite series. The apparent 
 attraction therefore is not due to the original quantities by 
 themselves, but to them modified by the inductive action. 
 The amount of the induced charge, and the distribution of 
 the original and the induced charges, vary with the distance 
 between the bodies, the configuration of the bodies, their 
 shape, the presence of other bodies, and the dielectric. 
 
 105. By an exhaustive series of experiments, Faraday 
 investigated the phenomena of induction as depending upon 
 the insulating medium or dielectric between a charged body 
 and those affected by it. 
 
 A rod of shell-lac, A (fig. 51), is surmounted with a hemi- 
 spherical metal ball, B. A is charged negatively by rubbing 
 
98 ELECTRICITY. 
 
 it with flannel, and the neutral electricity on B is separated ; 
 
 on connecting B for an instant with the ground, a positive 
 charge is left on it. Faraday placed a proof 
 plane successively in the positions a b c d e f 
 g h i, touched it, and then removed it to an 
 electroscope, and found that in every case it 
 was charged positively ; charged, therefore, 
 by the inductive action of the wax. But the 
 amount of the induced charge varied ; the 
 amounts being in the order c d h i g e /, 
 c giving more than three times the charge 
 that / gave. This proves that the inductive 
 action must radiate from the inducing body, 
 ,.,7"' not merely in straight lines, as was formerly 
 
 supposed, but also in curves. The same 
 
 results were found when other gases were substituted for air. 
 
 106. By other experiments, in which Faraday interposed 
 various dielectrics, both liquid and solid, between the induc- 
 ing body and the proof plane, he established that in every 
 substance the lines of induction are curves. When, however, 
 a hollow metal cylinder, in connection with the ground, sur- 
 rounded A, so as to interpose between A and the proof plane, 
 the latter shewed no charge wherever it was placed, until the 
 cylinder was removed, when the usual charge was found on it. 
 
 107. Faraday next, by a variety of experiments, proved 
 that the quantity of electricity induced by a charged con- 
 ductor upon the surface of another conductor depends not 
 only upon their distance asunder, but also on the particular 
 medium. A, B, and C (fig. 52) are metal plates. C is 
 insulated, and A, B, at equal distances from C (I.), are each 
 in electric communication with one of the gold leaves, a, 6, 
 but also insulated. The distance of A or B from C can be 
 varied at pleasure. C is charged positively, and A and B are 
 touched simultaneously for an instant. They are then found 
 to have a negative charge, but the leaves remain vertical. 
 A is then placed nearer C (II.) without the insulation being 
 disturbed, and immediately the leaves attract ; the nearer 
 surface of A is found on examination to be negatively elec- 
 trified ; the outer surface of A, the wire, and a are positive ; 
 
INDUCTION. 
 
 99 
 
 while the outer surface of B, its wire, and b are found 
 negative. For on the nearer approach of A to C some of the 
 neutral electricity in A is separated, the negative portion 
 
 Fig. 52. 
 
 being drawn near C, the positive spreading over the outer 
 surface of A and a. At the same time part of the negative 
 electricity on B, previously kept there by the inductive 
 action of C, is set free, and reaches b. 
 
 108. A, B, and C being placed and charged as at first (III.), 
 the same result followed the introduction of a cake of 
 shell-lac between A and C, as was obtained when A was 
 moved nearer to C than B was. This shews that the 
 inductive action of C on A is greater when the interposed 
 medium is partly shell-lac and partly air than when it is 
 air alone that is, the induced charge is greater when the 
 medium is shell- lac than when it is air, other conditions 
 remaining the same. Similar results were obtained by substi- 
 tuting discs of glass, sulphur, &c. for the shell-lac. Faraday 
 used the term specific inductive capacity to denote the power 
 of a dielectric to transmit induction, as compared with 
 that of air. He found that all gases have the same specific 
 inductive capacity as air, whatever be their temperature or 
 pressure, and that every other substance he tried had a 
 greater specific inductive capacity than air. It has been 
 
 G 
 
100 ELECTRICITY. 
 
 recently shewn, however, that the specific inductive capaci- 
 ties of all gases are not the same. 
 
 109. The question Faraday next attempted to solve was of 
 this nature. In sect. 99 it is shewn that a body charged with 
 electricity exerts an influence on other bodies at some distance 
 from it. Faraday had discovered (sect. 108) that the amount 
 of electricity induced depends on the dielectric or insulating 
 medium interposed between the charged body and those acted 
 on. He surmised from this that the induction must be due 
 to some action in the medium, which will vary with the 
 particular medium employed. A similar phenomenon occurs 
 in acoustics. A sound was produced under the surface of the 
 Lake of Geneva, and was propagated both through the water 
 and the air. It took a shorter time to travel a given 
 distance through water than through air. This is easily 
 explained when we know that the propagation of sound 
 consists in the transmission of a particular kind of dis- 
 turbance through the medium, and the rate of transmission 
 varies with the properties of the medium in question. Or 
 as in the case of a bell rung at some distance off by the aid 
 of a wire : the action at a distance can be explained when 
 we know that there is a similar handing on of a pull, and 
 consequent motion of the successive parts of the wire, till 
 it reaches the mechanism which causes the bell to sound. 
 Previous to Faraday's researches, it was known that the one 
 body exerted an influence on the other, but it does not seem 
 to have occurred to any one to inquire whether it was due 
 to the action of the medium or not. What Faraday sought 
 to find was, what is the nature of the action in the medium, 
 and what properties of the medium will account for it ? 
 
 110. His theory is as follows : When any substance is in 
 presence of an electrified body, every one of its particles 
 becomes polarised that is, acquires equal and opposite pro- 
 perties on opposite sides which we may suppose due to the 
 separation of the neutral electricity in it, the opposite elec- 
 tricity to that of the body being on the side of the particle 
 next it, an equal amount of the like electricity on the farther 
 side. This state of polarisation is first produced in the layer 
 of particles nearest the charged body ; the first layer then 
 
INDUCTION. 101 
 
 induces a similar condition in the next one, and in this way 
 the polarisation is propagated throughout all space. Hence 
 two adjacent particles have oppositely charged ends next one 
 another. The particles when polarised resemble a number 
 of magnets or iron filings in the presence of a magnet, or the 
 cylinders of sect. 100. The amount of the displacement of 
 electricity, or the separation of the neutral electricity, in 
 the particles of any one medium is proportional to the 
 electro-motive force* to which it is exposed a greater 
 electro-motive force producing a greater displacement. In 
 different media subjected to equal electro-motive forces, with 
 other conditions the same, the displacement varies, depending 
 upon a property of the medium which Clerk Maxwell has 
 named electric elasticity. This property of electric elasticity 
 is analogous to the elasticity of an elastic substance, and to 
 the coercive force of steel. Just as with two elastic bands 
 perfectly similar as regards length, cross section, &c., or two 
 spiral springs, the same appended weight may produce twice 
 the extension in one that it does in the other, so the same 
 electro-motive force may produce in the particles of one 
 of two media double the electric displacement that under 
 exactly the same conditions it produces in the other. The 
 electric elasticity has also the property of causing the medium 
 to recover its original condition when the electro-motive 
 force is removed, just as the elasticity of the elastic band 
 enables it to recover its original length and form when the 
 appended weight is removed. The displacement under given 
 circumstances in air would be only half what it is in 
 shell-lac. Hence the coefficient of electric elasticity is twice 
 in air what it is in shell-lac. It is due to this electric elasticity 
 that the displacement disappears when the electro- motive 
 force is removed. In this theory all substances may be 
 considered as consisting of conducting particles immersed in 
 an insulating medium, and so insulated from one another 
 to a greater or less extent. The displacement is limited by 
 the insulating power of the medium. In a non-conducting 
 
 * Whenever there is a tendency to a passage of electricity from one point to 
 another, there is said to be an electro-motive force between them. (We shall see 
 later on to what this tendency is really due.) 
 
102 ELECTRICITY. 
 
 substance the particles may be polarised to a considerable 
 extent before two contiguous particles will discharge into one 
 another. In a conductor the insulating power is so small 
 that these discharges take place with great ease, and so the 
 polarisation disappears as quickly as it is produced. At any 
 point in the interior of a conductor the opposite electrifica- 
 tions of contiguous particles neutralise ; but at the surface 
 there will be an apparent superficial electrification, consti- 
 tuting what on the old theory is called the electrification of 
 the conductor. In other words, 'it is only at the surface 
 of the dielectric that the effects of the electrification become 
 apparent, although the polarisation exists throughout the 
 whole of the interior, but is there neutralised by the juxta- 
 position of neighbouring parts.' A somewhat analogous 
 phenomenon is seen in the surface tension of liquids. That 
 is mainly due to forces exerted between the particles of the 
 liquid, but the effects are apparent only at a surface, that is, 
 only where there is a break in the continuity. 
 
 111. By this theory the energy of an electric charge 
 consists in the polarised condition of the dielectric. In 
 a conductor the state of constraint is continually giving 
 way, the potential energy of the state of constraint being 
 transformed into heat. When a continual flow or current of 
 electricity takes place, it is due to the electro-motive force 
 continually re-establishing the state of constraint as soon as 
 it is destroyed. 
 
 The dynamical part of the theory requires that at every 
 point in the medium there must be a tension in the direction 
 of the resultant force R at that point, and a pressure equal to 
 the tension in every direction perpendicular to R. By sup- 
 posing these to exist, their mechanical effect on any portion 
 of the medium bounded by any surface is identical with the 
 mechanical effect of the electrical forces, according to the 
 ordinary theory of action at a distance ; besides agreeing 
 with the form taken by the lines of force. 
 
 The theory gives a satisfactory explanation of the fact that 
 equal quantities of electricity are always produced simul- 
 taneously that no absolute charge can be given to matter. 
 The difference between conductors and insulators as above 
 
INDUCTION. 103 
 
 noted, consists in the capability of sustaining the forced con- 
 dition of polarisation or of readily allowing this to decay. It 
 also follows as a consequence that the amount of electricity 
 induced is always equal to the charge. 
 
 It also follows as a consequence of this theory that no 
 induction can take place between two conductors at the same 
 potential, and that the amount of induced charge is propor- 
 tional to the difference of potential between the induced 
 body and the body inducing. 
 
 CHAPTER VIII. 
 POTENTIAL. 
 
 112. In sect. 76 one method is given by which the work 
 done in transferring a portion of attracted or repelled matter 
 from one position to another may be estimated : there is 
 another which is of great importance, especially in gravita- 
 tion, magnetic, and electric problems namely, in terms of 
 the difference of potentials at the original and final positions. 
 
 113. The potential at a point due to electrical or magnetic 
 attraction is the work required to carry away a unit of 
 negative electricity, or of south magnetism, from the point 
 to an infinite distance against the electric or magnetic attrac- 
 tion. Suppose that at a certain point a. 
 
 (fig. 53) we have a particle charged with 
 a quantity of negative electricity, and 
 
 that there are other electrified bodies, 
 A, B, C, &c. in the neighbourhood. 
 They will exert an attraction on the 9gc 
 
 particle. To remove it from them will ||^ 
 
 require work to be done against the 
 electric attraction, and also perhaps 
 against magnetic and gravitation attrac- 
 tion, and friction ; these latter we are 
 not at present concerned with. As the particle is removed 
 farther and farther, the attraction at any position will 
 in all likelihood diminish, and the work to remove it 
 
104 ELECTRICITY. 
 
 a given space farther will also diminish ; and both will 
 vanish when the particle is very far removed from the 
 attracting bodies. Let the charge on the ball be a unit of 
 negative electricity, and let the whole work spent in over- 
 coming the attraction of A, B, C, &c. from a to an indefinitely 
 great distance be V. V, is called the potential at . To 
 take the same particle from /3 to the earth would probably 
 require a different amount of work V/3, and the potential at 
 /S is then said to be V/3. In bringing a particle charged with 
 a unit from an indefinitely great distance to , an amount 
 of work would be done by the electrical forces equal to what 
 was spent against them in going from to a great distance. 
 
 114. It is found as an immediate consequence of the fact 
 that a body is completely discharged when made to touch the 
 interior of a hollow and virtually closed conductor (sect. 103), 
 and also as an experimental fact (sect. 88), that if E be the 
 number of units of electricity on one body, e the quantity on 
 another, and r be the distance between them, the force 
 
 exerted by the one on the other is represented by the formula 
 pi 
 
 ~2. The same law also holds for gravitation and magnetic 
 
 attraction, and therefore all theorems derived from this law 
 
 for gravitating matter hold also for similarly electrified or 
 
 magnetised bodies. 
 
 In considering the application of these theorems and 
 
 definitions to elec- 
 trical phenomena, 
 we must observe 
 that because of the 
 dual nature of elec- 
 tricity the same 
 amount of work may 
 be done either by 
 
 Fig 54, removing a given 
 quantity of negative 
 
 electricity from to $, or by bringing up an equal quantity 
 
 of positive electricity from /3 to a. 
 
 115. The following theorems are among the most import- 
 ant. Geometrical proofs of them will be found in Thomson 
 
POTENTIAL. 
 
 105 
 
 and Tait's Elements of Natural Philosophy, sects. 479 and 488 ; 
 to which book we would strongly recommend every one to 
 apply who wishes clear statements upon this and almost 
 every other dynamical question. 
 
 116. (I.) If the different points of a spherical surface attract 
 equally, with forces varying inversely as the squares of the 
 distances, a particle placed within the surface is not attracted 
 in any direction. 
 
 (II.) The attraction of a spherical shell on an external 
 particle is the same as if the whole mass were collected 
 at the centre. 
 
 Thus, if there be a spherical conductor A (fig. 55) charged 
 with a quantity E of posi- 
 tive electricity, a nega- 
 tively charged particle 
 placed anywhere in the in- 
 terior, say, at , will expe- 
 rience no attraction what- 
 ever that is, there will be 
 no tendency for it to move 
 in any one direction in 
 the sphere. A negatively 
 charged particle outside, 
 at /3 or at y, say, will be Fig. 55. 
 
 attracted with a force , 
 
 directly proportional to the charge, and inversely as the 
 square of the distance from the centre. The attraction of A 
 on the particle at ft, if charged with a unit of negative electri- 
 "F 1 
 
 city, would be 2 ; of A on the same quantity at y would be 
 
 E 
 
 2 ; on the same quantity at = 0. Hence, the same charge 
 
 . 
 given in succession to spheres of different radii will always 
 
 exert the same attraction on the same charge at external 
 points, so long as it keeps the same distance from the centre 
 of the charged sphere. 
 
 Thus, if we remove the shell A, and replace it by either 
 of the shells B or C their centres lying where A's was, and 
 charged with the same quantity E although the density 
 
106 ELECTRICITY. 
 
 (sect. 92) is different from what it was on A, the attraction 
 
 TT V 
 
 on one unit at and at y will still be --$ and 3 respec- 
 
 "l ~2 
 
 tively. The attraction of the charged shell B on a unit at 
 will still be ; in G's case, as a is external to C, the attrac- 
 tion is %. 
 
 117. It can be shewn by a mathematical investigation too 
 advanced for this work, that if there is a quantity Q of 
 electricity concentrated at a point, the potential due to it at 
 
 a distance r is , which is + or , according as Q is posi- 
 tive or negative. It can also be shewn that if there are 
 several quantities Qj_ Q 2 Q 3 &c., condensed in points at 
 distances r r z r 3 &c., from a given point a, the potential 
 
 due to them at a is^ i +^ + ^+ &c., or 2 %, where 2 
 
 r l T 2 T 3 
 
 is used to signify that all these quotients are added together : 
 effect being given to any of the charges being negative. 
 
 The potential due to a given distribution of electricity has 
 in general different values at different points. It may be 
 positive at some points, negative at others. 
 
 118. Suppose that the value of the potential for one point 
 a is V a , and for another 6 is V&, then the work required to 
 carry unit of negative electricity from a to & is V Vj. 
 Because, as the path pursued in going from the one position 
 to the other does not affect the amount of work done (sects. 
 76, 78, 85) against the electric forces, we may suppose the 
 change of position to be effected by going from a to infinity, 
 and then from infinity to 6. 
 
 119. If F be the average value of the attraction between a 
 and 6, then F x ab V Vj, since each expresses the 
 work done in transferring a unit from a to 6: therefore 
 
 Va Vft 
 F = ^g ; that is, the average value of the attraction 
 
 upon a unit, or the average value of the force tending to 
 move a unit in any direction, is the rate at which the poten- 
 tial falls off per unit of length in that direction. When a 
 and b are very near, the average coincides with the actual. 
 
POTENTIAL. 107 
 
 Hence the force exerted on unit mass or quantity of electri- 
 city in any direction is the rate at which the potential falls 
 off in that direction. In the case of gravitation, the potential 
 has different values at different heights above the earth's sur- 
 face ; and what we call the acceleration due to gravity, is 
 equal to the rate at which the potential falls off in the ver- 
 tical direction. If the potential is the same at a and 6, two 
 points near one another, there will be no work done in 
 moving a unit from one to the other ; hence the resultant 
 force will be zero there. Conversely, where the resultant 
 force is zero, the potential is constant. 
 
 120. An equipotential surface is one at all points of which 
 the potential has the same value. In the case of an 
 equipotential surface, the attraction or the resultant force is 
 everywhere perpendicular to the sur- 
 face. Because (fig. 56) if the attrac- 
 tion, F, were inclined at an angle a 
 to the normal, it would have a com- 
 ponent parallel to the surface equal to 
 F sin. (sect. 75) ; that is, the result- 
 ant force along the surface would not 
 be zero ; in other words, the potential 
 would not be constant. 
 
 Hence equipotential surfaces are surfaces of equilibrium 
 that is, a particle on such a surface is in equilibrium, so far as 
 the forces under investigation are concerned, since there is 
 no force tending to make it move along the surface. Hori- 
 zontal or level surfaces are familiar instances of equipotential 
 surfaces with gravitation as the attracting force. What is 
 true of equipotential surfaces in general, is true of level 
 surfaces. The value of gravity is the same at all points at the 
 same level. For instance, no work is done against gravity 
 in passing from one point to another of the same level sur- 
 face, and the direction in which gravity changes most rapidly 
 is perpendicular to the horizontal. An attracting mass is 
 virtually inclosed in a series of equipotential surfaces which 
 may be imagined existing at such distances from one another 
 that the difference of potential between any two successive ones 
 is always the same. In the case of the earth, such a series 
 
108 ELECTRICITY. 
 
 would be very nearly concentric spheres at rapidly increasing 
 distances from each other. A particle could be moved from 
 any one part of any one of them to any other part without 
 work being done, and the work in moving it from one position 
 to another would depend solely on the number of such 
 surfaces cut, supposing no surface cut oftener than once. 
 
 121. A line of force is a line drawn so that the tangent, at 
 every point of its length, is the direction of the attraction at 
 that point. The force at every point falls off most rapidly in 
 the direction of the line of force passing through it. They 
 cut equipotential surfaces at right angles. A particle free 
 to move will always move along a line of force. 
 
 Faraday's idea was that from every electrified body lines of 
 force or induction, as they are also named, may be supposed 
 to proceed in all directions to all space, and that the number 
 issuing from any body depends upon and is a measure of the 
 quantity of electricity in it. Wherever any of these lines 
 terminate, on the earth, the sun, the walls or floor or roof of 
 a room, or other bodies, there is an equal and opposite 
 quantity of electricity to that on the part from which they 
 proceeded. Lines of force can be found by one method or 
 another, and from them we can ascertain what are the forms 
 of the surfaces of equilibrium round a conductor, what is the 
 surface density of electricity at different points on variously 
 shaped bodies, where on a given conductor the density would 
 be greatest, where least ; or the surfaces of equilibrium may 
 be found, and from them we can deduce the lines of force. 
 
 122. To illustrate the properties of potential further, we 
 introduce some analogies. By comparing the value of the 
 potential at a point with the values in the neighbourhood, we 
 ascertain whether and in what direction an electrified particle 
 placed at the point will move. A particle of attracted matter 
 free to move always moves from places of higher to places of 
 lower potential ; that is, in the direction in which its potential 
 energy diminishes. In the case of gravitating matter, height 
 above the sea-level corresponds to rise of potential, and hence 
 a stone falls water invariably flows from places of higher to 
 places of lower level. In thermal questions, temperature is 
 closely analogous in many respects to potential in electricity : 
 
POTENTIAL. 109 
 
 and we find that heat invariably flows from the body of higher 
 to the one of lower temperature. In fluids, again, the flow 
 is always in that direction in which the pressure falls off most 
 rapidly. Consequently, if it is known where the barometer is 
 high, and in what direction it is falling off, we expect a strong 
 wind from the places where the barometer is high to those 
 where it is less. So when the pole of a magnet is brought 
 into the neighbourhood of iron filings, the filings move 
 towards it, because in so doing they are moving so as to 
 diminish their potential. Just as in all these cases the direc- 
 tion of motion is from places of higher to places of lower 
 level temperature or pressure, so in electricity the flow is 
 always from points of higher potential to those of lower, and 
 always in the direction in which the potential falls off most 
 rapidly, which is not in general a straight line. 
 
 123. Just as one point is said to be at a higher level than 
 another, although no stone or water may be there, so in 
 electricity, two points may be at different potentials, although 
 there is no charge at the points. 
 
 As has been stated, the flow of water is in many respects 
 closely analogous to the assumed flow of electricity, and by 
 studying the phenomena of the one we may learn something 
 about the other. If there be two cisterns of water at different 
 levels, there will always be a tendency for water to flow from 
 the one at the higher level to the other. So long as the dif- 
 ference of level is the same, it is immaterial to the amount of 
 flow whether the two cisterns are both above the level of high 
 water, or one above and one below, or both below. So again 
 in heat conduction, the rate at which the heat passes from 
 one point to another at a different temperature is simply 
 proportional to the difference of temperature, whatever be 
 the temperatures, if we suppose other properties involved to 
 remain constant. Similarly with electrical phenomena. A 
 conductor, A, charged with + E, is said to be electrified 
 positively. By that is meant that -f- E would flow from it 
 to the earth, if they were electrically connected. It may have 
 negative potential relatively to some other conductor, B, 
 which is charged positively, but to a higher potential than A. 
 So a conductor, C, with negative electrification, has negative 
 
1 10 ELECTRICITY. 
 
 potential relative to the earth and to all other conductors 
 charged positively, and to a conductor charged to a smaller 
 negative potential, but it has a positive potential to conductors 
 at a higher negative potential. 
 
 124. The earth is so large and so good a conductor that its 
 electrification remains practically constant. No electricity 
 that we can take from it or give to it alters its electrification 
 or its potential to any appreciable extent. Hence it is used 
 as the body with which all others are electrically compared, 
 and its potential is taken as zero potential. The work re- 
 quired to carry an electrified particle to the earth is the 
 same as to an indefinitely great distance or to infinity, and 
 the phrase ' put to earth ' is used to signify that the conductor 
 spoken of is discharged or reduced to zero potential. All 
 points at which the potential is greater than that of the earth 
 have positive potential: all points at which the potential is 
 less have negative potential. A positively charged particle 
 placed at the point of higher potential, would tend to 
 move to the other, and if there were charges at the points 
 and electrical connection was made, positive electricity would 
 flow in the same direction till equality of potential was 
 established. (This is the conventional way of describing the 
 phenomenon ; but at present it is not known whether the 
 equilibrium is produced by a flow of positive electricity in 
 one direction, or by a flow of negative electricity in the 
 other j or by a simultaneous flow of both electricities in 
 the two directions.) Of two points at both of which the 
 potential is positive but of different values, the less has 
 negative potential relative to the greater ; and similarly, for 
 
 two negative points, the one for which S =D has the smaller 
 
 numerical value, has positive potential relatively to the other. 
 
 125. The Electromotive Force is the name given to the 
 tendency of electricity to flow from one conductor or one 
 point to another conductor or another point, and depends 
 upon the difference of potential between them. 
 
 126. A flow of electricity between two points is due to 
 their being at different potentials. An absence of flow 
 between places electrically connected, or an absence of 
 
POTENTIAL. Ill 
 
 disposition of a charged particle to move from one to the 
 other, indicates that they are at the same potential. One inva- 
 riable effect of a flow or current of electricity is to generate 
 heat. The potential is constant over a charged conductor, 
 otherwise there would be a constant current between points 
 at different potentials. This means a creation of energy 
 without an equivalent supply ; by the conservation of energy 
 this is impossible. No work is necessary to move a charged 
 particle from one part of a conductor to another. The 
 potential is constant over an insulated conductor, even when 
 the electrification varies from point to point, as when 
 some parts of the conductor are -f-> others , and one part 
 has no electrification at all. This happens when an un- 
 charged insulated conductor is in the field of a charged 
 conductor. That it must have the same potential throughout 
 is manifest when we consider that, were it not so, there 
 would of necessity be a flow of electricity which would pro- 
 duce equality of potential. But we know that the distribution 
 of electricity on its surface does not change. The potential of 
 the conductor is that of its neutral zone. 
 
 Clerk-Maxwell proves this proposition in the following 
 instructive way : Starting with a conductor, charged positively 
 at one end, and negatively at the other, he shews that it can 
 be at constant potential if another electrified body is in the 
 neighbourhood. Allow a + particle from a -f- part of the 
 surface to move from it always along a line of force. It will 
 ultimately either come to a negatively electrified body or go 
 off to infinity. This latter event can happen only in the case 
 of the conductor having a positive potential. Similarly, a 
 - point from the portion of the conductor passing along a 
 line of force must come either to a positively electrified body 
 or go off to infinity, and the latter case can only happen when 
 the potential of the conductor is negative. Hence, as the 
 potential is supposed constant, the two second events cannot 
 both happen. Hence there must be another electrified body 
 in the neighbourhood. 
 
 127. The potential has the same value throughout the sub- 
 stance of a conductor as on the conductor itself. This may 
 also be proved by an appeal to the Conservation of Energy. 
 
112 ELECTRICITY. 
 
 128. When a charge of electricity, however small, has been 
 given to a conductor, the communication of more of the like 
 kind is opposed by the charge already given, and work has 
 to be expended to overcome this resistance. The work needed 
 to put in an additional unit of electricity to the conductor is 
 the potential of the conductor. The potential evidently 
 increases with the charge. 
 
 129. A conductor or a point is at unit potential when, to 
 put in or bring up an additional unit of electricity, unit of 
 work has to be done. 
 
 130. We have seen that electricity distributed uniformly 
 over a sphere acts upon all external bodies as if condensed at 
 the centre, and that the potential at a point at a distance R 
 
 from a given quantity Q of electricity is ^ . Hence this is' 
 
 the potential of a point on the surface of a sphere of radius 
 R charged with a quantity Q. By sect. 127 this is the value 
 of the potential throughout the interior of the sphere. From 
 this it follows that the capacity of a spherical conductor, or 
 the quantity of electricity necessary to change its potential by 
 unity, is measured by its radius. In simple conductors of 
 similar form, the capacity is proportional to the linear 
 dimensions. If charges of electricity in the ratio of 1, 2, 3, 
 &c. be given to spheres whose radii, or to similar conductors 
 whose linear dimensions, are in the ratio 1, 2, 3, &c., the 
 potential of each would be the same. This might be tested 
 by placing the conductors at such a distance from each 
 other that they exerted no sensible inductive action, and 
 then connecting them by fine wires. If they were all at 
 the same potential, there would be no flow of electricity 
 along the wires. 
 
 131. We have pointed out that the potential of the con- 
 ductor, or the work required to bring up an additional unit to 
 it, is proportional to the charge already in that is, the poten- 
 tial grows uniformly with the charge. We may suppose the 
 charge to be given by successive instalments of a unit each. 
 The total work in charging will therefore be equal to the 
 number of units put in, multiplied by the average work to 
 put in one, that is, the average potential. As the potential 
 
POTENTIAL. 113 
 
 grows uniformly, the average potential will be the potential 
 when half full. Let C be the capacity of the conductor, Q the 
 
 number of units of charge. The average potential = Q 
 The energy = ^ x Q = ^. 
 
 132. The same charge given to different conductors will 
 produce different potentials. Thus n units given to spheres 
 of radii in the ratio of 1, 2, 3, will have potentials in the ratio 
 of 3, 2, 1. And the energy of the charge will be in the ratio 
 of 3, 2, 1 that is, the same charge given to a small sphere 
 will produce a greater effect than when on a large one. The 
 explanation is, that it requires a greater expenditure of energy 
 to charge a small sphere than a large one, with equal amounts 
 of electricity. 
 
 This is again seen if we divide a charge between two equal 
 spheres. Thus n units given to a sphere of capacity C, has 
 
 energy = |^, But if the charge be shared with another 
 u 
 
 sphere of exactly the same size, each will have units, and 
 
 * v 4.1. -n v 
 
 the energy of both will be 
 
 that is, only one half of what it was before. The loss of 
 energy is accounted for by the energy of the spark which 
 occurred when the two were brought into contact. This is 
 one way of explaining how the energy of a charge on a con- 
 ductor disappears when it is put in connection with the 
 ground. Because the charge being spread over an infinitely 
 large surface, has its potential thereby reduced to zero. 
 
 133. If we have a machine which can produce a differ- 
 ence of potential V, then the amounts of electricity which 
 it can pump into different conductors will depend solely on 
 their capacities, and the energy to be obtained from a con- 
 ductor charged to this potential will be proportional also to 
 the capacity. 
 
 Suppose now that we charge a given conductor of capacity 
 C, with different machines, which can produce potentials V x 
 
114 ELECTRICITY. 
 
 V 2 V 3 &c. Since C = - , n will be proportional to V. The 
 
 energy will consequently be proportional to the square of the 
 
 nV V 2 
 potential the machine can give, that is, E = -g- = ~%~' 
 
 134. Again, on a conductor of non-spherical form the 
 electricity accumulates at prominent parts, although the 
 potential is the same all over. Hence the potential energy, 
 which is proportional to i^V, will be greater and greater 
 according as the accumulation is greater ; on a pointed con- 
 ductor, although the potential is the same on every part of 
 its surface, the electric density is enormous at the point 
 that is, the quantity of electricity is much greater there, 
 and hence the resultant force is much greater there than at 
 other parts of the same conductor. 
 
 135. There are many ways in which a difference of poten- 
 tial may be produced. One is the contact of dissimilar bodies. 
 Thus, when the glass rod and the silk are put in contact and 
 separated, the glass is found charged with + E, the silk with 
 . Moreover, with any two substances, the difference of 
 potential produced by contact is constant. Thus in an elec- 
 trical machine all that is done is to produce a certain differ- 
 ence of potential between the prime and secondary conductors 
 (sects. 138, 139). If the secondary conductor be connected 
 with the earth, and therefore at zero potential, the potential 
 of the prime conductor is the difference of potential which the 
 machine can produce. If the prime conductor be connected 
 with the ground, then the negative or secondary conductor 
 will have a negative potential equal numerically to the differ- 
 ence of potentials the machine can give. In this way an elec- 
 tric machine strongly resembles a pump. All that a pump 
 can do is to raise water say from one level to another. It can 
 change the level of the water by a certain maximum amount. 
 If this be 30 feet, then the pump can raise water from a depth 
 of 30 feet to the surface of the ground, or from 10 feet below 
 the ground to 20 feet above it, or from 50 feet above it to 80 
 feet above it. The absolute level makes no difference in 
 regard to its lifting power. In the case of an electrical 
 machine, all that the machine does is to produce a given 
 
POTENTIAL. 115 
 
 difference of potential. If the one conductor be kept at a 
 constant potential B, the machine will always tend to keep 
 the other at another constant potential A, so that A - B is 
 constant. Although the difference of potential between the 
 conductors of a machine remains always the same, what may 
 be termed its productiveness is very materially affected by 
 the absolute values of the potential of the negative and prime 
 conductors. For instance, suppose that the machine is driven 
 at the same rate (1) when the negative conductor is not con- 
 nected with the ground ; (2) when it is. The machine will 
 tend to maintain in each case the same constant difference 
 of potential. Suppose while the machine is kept steadily 
 working, a conductor D, uncharged and therefore at zero 
 potential, is held to the prime conductor. In (1) the potential 
 of the prime conductor will be V, and of the negative con- 
 ductor V 1 , where V 1 will be as far below the potential 
 of the earth as V is above it. Electricity will pass from 
 the prime conductor to D, till D is charged to the potential 
 V, and then no more electricity will pass. In the second 
 case D will also be at zero potential, but the potential of the 
 prime conductor will be V + V 1 . Hence the difference of 
 potential between prime conductor and D will be greater, 
 and a greater flow will take place. It will be found later on 
 that the spark we can get depends on the difference of 
 potential. We should therefore expect much longer and 
 more powerful sparks in the second 
 case than in the first, and such is 
 the fact. 
 
 136. Measures of potential all 
 depend upon the fact that a body 
 always tends to move in the direc- 
 tion in which the potential falls off 
 most rapidly. Let ABCD (fig. 57) 
 be a ring composed of two metals, 
 copper and zinc, soldered together, FJ 57 
 
 lying in a horizontal plane, and e a 
 
 wire capable of motion about a vertical axis, and charged 
 positively. Its potential is positive. It is found that the 
 needle rotates from the zinc to the copper ; shewing that 
 
116 
 
 ELECTRICITY. 
 
 the difference between the potentials of the copper and 
 needle is greater than between zinc and needle. Again, 
 when the needle is in connection with a negatively electri- 
 fied body it turns towards zinc ; proving that the potential 
 of zinc is positive to that of copper when the two are in 
 contact. It is by an arrangement somewhat similar to this 
 that Sir "William Thomson's quadrant electrometer acts. It 
 will be more fully described later on, but the following is a 
 description of the part of special interest at present. It con- 
 sists of a cylindrical box divided into four quadrants, ABCD 
 (fig. 58), completely separated from one another and insulated, 
 but connected by wires diagonally, A with C and B with D. 
 A flat plate, E, is suspended so as to be capable of turning 
 about a vertical axis, in a plane parallel to the surface of 
 ABCD, and in equilibrium takes up the position indicated 
 by the figure. It is kept charged to a constant potential by 
 
 an arrangement to be 
 more fully described 
 hereafter. The quad- 
 rants A and C are con- 
 nected with the earth, 
 B and D with the 
 conductor F, whose 
 potential is to be 
 measured, and they 
 
 C F J ^>v _^*/ at once acquire the 
 
 potentials of the 
 earth and conductor F 
 respectively. If the potential of F be +, E will move so as 
 to have more of its surface covered by A and C than by B 
 and D, and will take up a position of equilibrium when the 
 torsion of the wire just equals the force tending to make E 
 move. When the potential of E is large compared with that 
 of the conductors whose difference of potential is being 
 ascertained, the torsion can be shewn to be proportional to 
 this difference. If the potential of F be -, the deflection is 
 the other way. 
 
 137. Again, both experiment and the mathematical inves- 
 tigation of electricity go to shew that the phenomenon of 
 
 Fig. 58. 
 
POTENTIAL. 117 
 
 induction depends entirely on a difference of potential 
 between the conductor inducing and the conductor on which 
 a charge is induced. That is, where two conductors are at 
 the same potential, whatever it be, no induction takes place 
 by the one on the other. 
 
 CHAPTER IX. 
 FRICTION ELECTRIC MACHINES. 
 
 138. The requisites in a machine of this nature are a large 
 surface, to give a great amount of electricity, and some 
 arrangement to collect it and render it available. This 
 portion of the machine is denominated the prime conductor. 
 The rubbed surface of the electric machines is either a 
 
 Fig. 59. 
 
 cylinder or a plate of glass ; hence we distinguish them into 
 cylinder machines and plate machines. The former, from 
 their more compact form, are the more manageable ; and 
 the latter, from both sides of the glass plate being rubbed, 
 are the more powerful forms of the instrument. 
 
118 ELECTRICITY. 
 
 139. Plate Machine. The description of Winter's plate 
 machine (fig. 59) will be sufficient to shew the general require- 
 ments and construction of electric machines. It was designed 
 by Carl Winter of Vienna. The first machine on this prin- 
 ciple in this country was made under the superintendence of 
 Dr Ferguson of Edinburgh in 1858. It is one of the best exist- 
 ing forms of the machine. The glass plate is turned on the axis 
 a&, by means of the handle c. The longer end of this axis, 
 consisting of a glass rod, moves in the wooden pillar d, and 
 the other rests in the wooden head of the glass pillar e. The 
 plate is thus completely insulated, and little loss of its elec- 
 tricity can take place through its supports. The two rubbers 
 
 (fig. 60) are triangular pieces of 
 wood, covered with a padding 
 of one or two layers of flannel, 
 inclosed in leather, and they 
 present a flat hard surface to the 
 glass, so that friction between 
 it and them takes place in every 
 part. They are placed in a 
 wooden frame on each side of 
 the plate, and the pressure is 
 Fig. eo. regulated by metal springs. 
 
 Before use, they are covered, 
 
 with the aid of a little grease, with an amalgam of mercury, 
 zinc, and tin, which increases immensely the production of 
 electricity. The surfaces of the rubbers are conducting, and 
 communicate by strips of tinfoil with the negative conductor, f 
 (fig. 59). To prevent the electricity of the glass from dis- 
 charging into the air, before reaching the prime conductor, each 
 rubber has a non-conducting wing ; this consists of several 
 sheets of oiled silk, kept together by shell-lac varnish, beginning 
 at the rubber with several, and ending with one or two sheets. 
 When the machine is in action, these become negatively 
 electrified, and are attracted by and adhere to the glass, and 
 so diminish the attraction between the charges on the glass 
 and the rubber ; but when it is out of action, they may be 
 kept up by a split pin, g. As the plate turns, the rubbers 
 are kept in the frame by their ledges, h. The whole frame- 
 
FRICTION ELECTRIC MACHINES. 
 
 119 
 
 work of the rubbers and negative conductor can be insulated 
 when required. The prime conductor, k, is a brass ball 
 insulated on the long glass pillar I ; and to prevent the edges 
 of the ball at the junction dissipating the electricity, the 
 pillar enters the ball by a trumpet-shaped opening. The 
 electricity is collected from the glass by a row of points 
 placed in grooves, inside of two wooden rings, m, m, which 
 are attached on each side of the plate to a piece of brass pro- 
 jecting horizontally from the ball of the conductor. The 
 grooves are covered with tinfoil, which conveys the collected 
 electricity to the ball, and the points are kept out of the way 
 of injury by not projecting beyond the grooves. 
 
 A section of the ball of the prime conductor is shewn in 
 fig. 61. There are four openings into it : the lower one for 
 
 Fig. 61. Fig. 62. 
 
 the head of the supporting pillar ; the one at the right for the 
 attachment of the collecting apparatus ; the one at the left 
 for the stalk of a small brass ball ; and the upper one for 
 admitting the lower end of a large wooden ring, removable 
 at pleasure. The last forms the peculiar feature of Winter's 
 machine. It consists of an iron wire bent into the shape 
 shewn in the figure, carefully covered all round with polished 
 wood, and communicating with the prime conductor by a 
 pin at the loot of the biulk on which it stands. The 
 
120 ELECTRICITY. 
 
 value of this addition depends upon its great capacity, 
 because it acts like a Leyden jar (sect. 157). To receive the 
 sparks from the machine, the spark-drawer (fig. 62) is provided. 
 This consists of a wooden pillar of the same height as the 
 prime conductor, in the head of which a brass rod slides, 
 with a large flat ball at the one end and a small ball at the 
 other. All the fittings of the machine are of wood, metal 
 being used only for the prime and negative conductors, arid 
 thereby much loss is prevented. The insulating pillars 
 should be, if possible, of green glass, which, from the absence 
 of lead, is less conducting than flint glass. It is desirable, 
 likewise, to cover them with shell-lac varnish, which prevents 
 the formation of a conducting layer of moisture on them from 
 the atmosphere. As the plate is turned, E is developed 
 on the rubbers, and led to the negative conductor, and thence 
 to the ground ; and + E is formed on the glass, which, as it 
 recedes from the rubber, acquires a high potential. Negative 
 electricity is induced on the points, so that when the electrified 
 glass comes close to them, the mutual attraction of the oppo- 
 site electricities is sufficient to overcome the insulation of the 
 air ; a discharge takes place ; the prime conductor is charged 
 positively, and the greater portion of the charge on the glass 
 is neutralised. If the negative conductor were insulated, 
 the mutual attraction of the electricities of both conductors 
 would act inductively on each other, so that the + E of the 
 prime conductor would be to a considerable extent bound by 
 the E of the other conductor. It is explained in sect. 135 
 why electricity is obtained more readily when one of the 
 conductors is connected with the ground. If E is wanted, 
 the negative conductor is insulated, and the prime conductor 
 connected with the ground, when sparks of E are given off 
 by the negative conductor. 
 
 140. The source of the electricity in the case of friction 
 electric machines is the extra work required to turn it when 
 it is producing electricity, due to the attraction between the 
 separated electricities. Any portion of the glass, as it passes 
 from the rubber to the spikes and round again to the rubber, 
 has a greater quantity of electricity on it between the rubber 
 and the spikes than in the rest of its course, and conse- 
 
FRICTION ELECTRIC MACHINES. 
 
 121 
 
 quently it will be seen that there is more work done in over- 
 coming the electric attraction than is done by them in the 
 reverse journey. 
 
 141. The influence of the large flat ball of the spark-drawer 
 is of importance. Long sparks do not necessarily imply a 
 very powerful machine, but they guarantee good production 
 of electricity. For the generality of electric experiments, 
 sparks of one or two inches are amply sufficient. These, 
 Winter's machine gives readily without the ring ; and when 
 occasionally long sparks are wanted, the extension of the 
 prime conductor can be added without inconvenience. It 
 might be supposed that while the long sparks pass, the 
 machine works more powerfully than at other times ; but 
 such is not the case, for if the machine be working at 
 the same rate, the long spark occurs at much longer 
 intervals than the short ones. All the forms of disrup- 
 tive discharge are accompanied with the peculiar odour 
 which arises from the production of ozone, a modification 
 of oxygen. 
 
 142. Cylinder Machines. Fig. 63 represents a cylinder 
 machine. A is the glass 
 
 cylinder ; E, the negative 
 
 conductor, insulated on a 
 
 glass pillar, D, which can 
 
 be adjusted by the screw, in 
 
 the sole of the instrument. 
 
 The rubber is attached to 
 
 the negative conductor, and 
 
 the flap of oiled silk, KK, 
 
 to the rubber ; G is the 
 
 prime conductor, insulated 
 
 on the glass pillar, H, and 
 
 provided with a comb of 
 
 pointed teeth to collect the 
 
 electricity ; B, B, are the 
 
 wooden standards in which the axis of the cylinder works. 
 
 The rest of the machine is sufliciently explained by the 
 
 figure. 
 
 143. Electrophorus. This generally consists of a tin mould, 
 
122 
 
 ELECTRICITY. 
 
 Fig. 64. 
 
 A, which in practice is kept in connection with the ground, 
 
 filled with shell-lac or 
 resin, B, and a movable 
 nietal cover, C, with a 
 glass handle, D, as shewn 
 in fig. 64. The shell- 
 lac is poured in when 
 melted, and it is mixed 
 with some other sub- 
 stance, to make it less 
 brittle. Five parts of 
 shell-lac, one of wax, 
 and one of Venice 
 turpentine, are given as 
 a good mixture. The 
 surface of the resin 
 or shell-lac is smartly 
 beaten with cats' fur. 
 This electrifies the resin 
 negatively. When C is brought near B, it is charged posi- 
 tively on its under surface, negatively on its upper. If then 
 it is touched, the negative escapes, and C is charged with + E ; 
 and if removed and applied to any conductor, it will give a 
 positive charge to it. The process may be repeated for a great 
 number of times with only a small diminution of B's charge, 
 except by connection or dampness. It is usual to have the 
 earth connection made by a metallic pin passing through 
 B to A, or by a piece of tinfoil pasted extending slightly over 
 
 B, and connected with A. In removing C charged from the 
 neighbourhood of B, extra work is done against the mutual 
 attraction of the charges. This is the equivalent of the 
 energy of electrification obtained. 
 
 144. Electrical Discharge Glow Brush Spark As the 
 charge upon any conductor is increased, the electromotive 
 force tending to overcome the resistance of the dielectric 
 becomes greater and greater, until at length the dielectric 
 gives way, and a discharge takes place in the form of a more 
 or less luminous, noisy, and hot spark. The electro-motive 
 force necessary to produce a discharge depends among 
 
f/ 
 
 FRICTION ELECTRIC MACHINES: 123 
 
 other things upon the nature of the diele^na^ Jn7l$ie case; v 
 of air, it diminishes with the density until a certain rarity is 
 reached, and afterwards increases enormously as the rarefac- 
 tion is continued. The term disruptive discharge is applied 
 to all cases where discharge is attended by a permanent or 
 temporary rupture of the dielectric, accompanied with light, 
 sound, and heat. The concomitant phenomena of sound, light, 
 and heat also vary with the capacity of the conductor. All 
 the forms of discharge may be well shewn with the aid of a 
 good electrical machine. When the conductor, which we 
 shall suppose connected with a machine in working order, 
 terminates in a point, there is always a great accumulation of 
 electricity at the point, giving rise thereby to a great resultant 
 force tending to infinity. Before this limit can be reached, 
 the dielectric gives way, and allows the electricity to be dis- 
 charged into the neighbouring parts of the dielectric. In the 
 case of air, the particles in the immediate neighbourhood of 
 the point are electrified by this discharge with the same 
 electrification as the point, and are then immediately repelled : 
 their place is occupied by non-electrified particles, which are 
 also immediately electrified and repelled, and thus a constant 
 electric discharge takes place between the point and the 
 surrounding atmosphere. The repelled particles fly off in 
 almost continuous streams, and discharge themselves on 
 oppositely or non-electrified bodies. The pointed conductor 
 may therefore be said to discharge itself by convection. The 
 currents of air produced are often strong enough to blow out 
 the flame of a candle. 
 
 When the room in which the experiments are made is 
 darkened, there is seen about the point a constant glow, due 
 to the intense heat produced in the air by these discharges. 
 The energy of the discharge takes the form partly of heat, 
 partly of light, sound, &c. The glow may be increased or 
 diminished by aiding or preventing the currents of the 
 repelled particles. This passage of electricity from one place 
 to another is called electrical convection or convective dis- 
 charge. The glow may be seen on the tops of masts and 
 lightning conductors ; also upon the surface of the Holtz 
 machine (sect. 149) in the neighbourhood of the points. 
 
124 ELECTRICITY. 
 
 145. The electric brush is the name given to the luminous 
 appearance of the discharge of electricity when the conductor 
 is not pointed, but of small capacity, usually a small ball. 
 Here, as in every case, the discharge takes place when the 
 electromotive force of the charge is sufficient to overcome the 
 resistance of the dielectric. Even with the best machines, a 
 finite amount of time is required to charge a small conductor 
 sufficiently to produce this effect. Hence the discharges take 
 place at small intervals of time and in small quantities thus 
 producing a greater luminous appearance and little noise, but 
 no current of air. The brush presents the appearance of a 
 bush, which is formed by the successive discharges breaking 
 off into ramifications, as it passes from the one conductor to 
 the other. 
 
 146. When the capacity of the conductor is greater, longer 
 intervals of time are necessary to charge it to the necessary 
 potential than in the case last considered ; and accordingly, 
 when the discharge takes place, a larger quantity of electricity 
 passes in the form of a spark, and a much greater effect is 
 produced. The light is often very intense, and the noise 
 loud and sharp. 
 
 147. Sir W. Thomson measured with an electrometer the 
 electromotive force necessary to produce a spark across strata 
 of air of different thicknesses, between two surfaces, one 
 slightly convex, the other plane. He found that for distances 
 of about a millimetre and under, the electromotive force 
 increased with the distance, but in a less rapid ratio. 
 
 148. The appearance of the spark varies with the distance 
 between the plates, and also with the medium. When the 
 distance is small, the spark is comparatively straight, but gets 
 more forked and crooked or zigzag in form as the distance 
 increases, and beyond a certain distance, varying with the 
 capacity of the conductors, it takes the form of the brush dis- 
 charge. Professor Tait and Mr A. Mathieson of Edinburgh 
 University have recently photographed sparks from a power- 
 ful Holtz machine. From these photographs it is seen 
 that the sparks in many instances are not merely deflected 
 from their course, but double back upon it as in fig. 65. 
 Again, they often bifurcate, and after travelling some die- 
 
FRICTION ELECTRIC MACHINES. 125 
 
 tance separate and again unite. They have also shewn that 
 the cause of the abrupt change of direction of the spark is 
 probably due to germs, &c. floating in the atmosphere, 
 because when the discharge was made to take place in air 
 
 Fig. 65. 
 
 heated by being previously passed through a considerable 
 length of red-hot tube, for the purpose of destroying these 
 germs, the path was almost free from these jagged points and 
 other peculiarities. 
 
 Holtz and other Electro-Static Induction Machines. 
 149. One great objection to an ordinary friction machine 
 like that described in sect. 139, is that there is a great waste 
 of energy in overcoming the friction. In recent years, several 
 instruments have been invented which work rather on the 
 principle of the electro- 
 phorus, and in them the 
 
 energy spent in driving /* "X 
 the machine is almost / \ 
 
 all transformed into |[J] o jjj] 
 A 
 
 tially of one or more 
 
 electricity. 
 
 They all consist essen- Ny^ \f 
 
 insulated conductors, 
 movable and fixed : the c 
 former are usually called 
 carriers ; the latter, in- 
 ductors, &c. We shall 
 give a detailed descrip- 
 tion of one, and mention 
 
 some others. In the Holtz machine the inductor, I (fig. 66), 
 is a circular glass plate with two apertures cut near the 
 
 iniim 
 
 j 
 
126 
 
 ELECTRICITY. 
 
 circumference, to the edge of which a pointed piece of paper, A 
 and B, is fixed. The carrier, C, is another plate of same dimen- 
 sions, turning on an axle. Near the side of the carrier, remote 
 from the inductor, are two combs, E and F, for collecting the 
 electricity. The paper A is charged negatively, say, by a piece 
 of excited vulcanite, and induces ,E on the outer surface of 
 C in its immediate neighbourhood, + on the inner side. We 
 may suppose the carrier to be composed of a number of sectors, 
 one of which we shall examine as C is turned round. When 
 it is opposite A, it has -\- E on its inner surface, E on the 
 
 Fig. 67. 
 
 outer. On coming to E, the negative E is carried off by E ; 
 and a little farther on, B is charged + by drawing the + from 
 the inner side of C. Then a new separation takes place by 
 inductive action of B, -j- being now on the outside of C, on 
 the inside. At F the comb draws off the negative again, 
 and A gets a fresh charge of and a further separation 
 ensues. But what is true of the small region is true of 
 the whole surface of that is, the separation, &c. goes 
 on continuously. 
 
FRICTION ELECTRIC MACHINES. 127 
 
 The distance between the balls can be varied at pleasure, 
 and by attaching Ley den jars to K and L, their capacity can 
 be made very great, and large sparks of several inches in 
 length can be obtained. 
 
 In fig. 67 is shewn a complete Holtz machine with a single 
 revolving plate. D is the inductor, and A the revolving 
 plate mounted on the axis L L', which runs in sockets fixed 
 in the cross-pieces of vulcanite, L and I/. P and P' are two 
 pieces of paper glued to the glass, the one on the upper and 
 the other on the lower side of the window-holes. C C' are the 
 collecting combs connected with the spark-drawing balls B 
 and B' by the brass rods R and R'. 
 
 150. Discharge by Points and Flames. When the machine 
 is in action, and sparks of several inches in length are passing, 
 they instantly cease when a sharp metal point held in the 
 hand is presented to the machine at some distance from 
 the prime conductor. The reason is that the electricity on 
 the prime conductor induces an opposite charge on the rod, 
 which accumulates at the point so as to produce an enormous 
 electric density there. The mutual attraction which ensues 
 is sufficient to overcome the insulation of the dielectric, 
 and the charge of the prime conductor is drawn away 
 continuously, instead of by successive discharges of much 
 larger quantities. It is on the same principle that a lightning 
 rod discharges a thunder-cloud of its electricity, silently and 
 without a flash. If a pointed rod be placed on, or connected 
 with, the prime conductor, no spark can be got from it ; 
 powerful currents of air proceed from the point, sufficiently 
 powerful to turn a small wheel furnished with paper vanes, 
 or to blow away the flame of a candle, as in the electric glow 
 discharge, due to the repulsion between the charged point 
 and the air in its neighbourhood charged by contact. This is 
 generally shewn by taking a wire pointed at both ends, and 
 bending it so that its points are at right angles to it and on 
 opposite sides of it, and poising the whole on a point on the 
 machine. When the machine is in action, the points are 
 driven backwards, and the wire revolves on the principle of a 
 reaction wheel. In the dark, the points describe a luminous 
 ring from the glow at them. 
 
128 ELECTRICITY. 
 
 151. When the flame of a candle is held near the machine, 
 it acts like a point ; if uninsulated, it acts more decidedly 
 than when insulated. In the latter case, it appears to point 
 towards the machine and out from it, acting like a double 
 point one discharging the machine, the other discharging 
 the flame into the air. Professor Guthrie describes experi- 
 ments which throw light upon the nature of the influence 
 exercised by flames as dischargers. He shews that, whether 
 the flame be a luminous or non-luminous one that is, whether 
 it be charged with solid matter or not it discharges an 
 electroscope with equal rapidity when held above it. That 
 this is not due to the currents of air produced by the flame, 
 is shewn by the fact that currents of air, either cold or hot, 
 blown from a bellows on an electroscope, do not discharge it. 
 He thinks the heat relieves the strain of induction by the 
 thermal agitation of the molecules, which allow the charge of 
 the electroscope to dissipate ; and this again gives rise to 
 heat, which further aids the discharge. It is also due to the 
 vibration of the molecules by heat that he attributes the non- 
 reception or non-retention of a charge, even for an instant, by 
 an insulated and white-hot iron ball. As it cools, it acquires 
 at a red-heat the power of receiving and retaining a negative 
 charge, and at a lower temperature charges of either kind. 
 These variations are partly due to the apparent preference of 
 air for + over E. He finds too that an earth-connected 
 iron ball discharges equally, when white-hot, an electroscope 
 charged positively or negatively; but as it cools to dark- 
 heat, it is found to discharge one negatively electrified, but 
 not positively. 
 
 152. The heat of the sparJc is shewn by holding a spoonful 
 of ether below the small projecting ball so as to receive a 
 spark from it. The spark instantly kindles the ether. 
 
 153. A person standing on an insulating stool (that is, a 
 stool with glass legs), with one hand on the machine, can 
 with the other send sparks to everything and everybody 
 about him. In this position he can kindle ether, or light 
 with his finger a jet of gas. The most extraordinary experi- 
 ment that can be performed with Winter's machine is the 
 lighting of a gas-jet by a person wholly unconnected with 
 
FRICTION ELECTRIC MACHINES. 129 
 
 the machine, and standing some eight or ten feet from it. If 
 the person so situated holds the blade of a knife or other 
 point over the gas-burner, at a distance only short of touching, 
 at each long spark from the machine, a small spark passes 
 between the blade and the burner, and thus ignites the gas. 
 The reason is as follows : The body of the person in question 
 is electrified negatively by the extensive prime conductor of 
 the machine acting inductively. When the spark passes, the 
 ring is discharged, and its inductive power for the moment 
 ceases ; and the negative electricity of his body, now no 
 longer attracted by it, returns to the ground, and taking the 
 easiest route, causes the spark in question. This is quite 
 similar to what is known in thunder-storms as the back-stroke. 
 A person in a prominent position, under a highly charged 
 cloud, experiences a violent, sometimes fatal shock at the 
 same time as a flash of lightning, although the flash was 
 not at all near him. 
 
 The physiological effect of the spark may be felt by any one 
 holding the back of his hand near the machine so as to get 
 a spark from it. A ten-inch spark from Winter's machine 
 produces a stinging sensation accompanied by a nervous 
 twitching, and this may be felt by a dozen persons at 
 once, joined hand in hand, the first presenting his free 
 hand to the machine, and the last having his free hand 
 connected with the ground or negative conductor. 
 
 CHAPTER X. 
 ACCUMULATORS. 
 
 154. An accumulator is the name given to an apparatus 
 for receiving and retaining large quantities of elec- 
 tricity. It consists essentially of two conducting plates, 
 separated by a layer of non-conducting material which is 
 called the dielectric. Thus two parallel sheets of metal 
 separated by air form an accumulator. Also any insulated 
 conductor may be regarded as an accumulator, the other 
 plate being represented by the walls of the room in which 
 
1 30 ELE CTRICITT. 
 
 it is placed, and the intervening air being the dielectric. 
 A common form of accumulator, first adopted by Franklin, 
 is made by coating a pane of glass on both sides with tinfoil, 
 with the exception of a margin about two inches wide all 
 round. Another form employed by Faraday in his researches 
 on specific inductive capacity consists of a metallic sphere 
 surrounded by a concentric spherical shell, also of metal, 
 and of slightly larger radius, the space between being filled 
 with air or other dielectric substance. 
 
 An accumulator is charged by putting one of its plates, 
 usually called the receiving plate, in connection with the 
 prime conductor of an electric machine, while the other is 
 connected with the earth. Let A and B be the two con- 
 ducting plates, parallel to each other, and separated by a 
 layer of air ; and let A be insulated, and B in connection with, 
 the ground. Suppose a positive charge of electricity to be 
 given to A. This, acting on B through the air as dielectric, 
 will induce a negative charge on the side of B next to A ; 
 and, if the charge of A be continually increased, a cor- 
 responding increase in the negative charge of B will take 
 place. This will go on till a certain limit is reached, when 
 the electricity of A begins to escape through the air and by 
 its insulating support. The accumulator is then said to be 
 fully charged. The quantity of electricity accumulated in 
 this way will depend upon the area of the plates, their 
 difference of potential, and the thickness of the dielectric. 
 
 By the capacity of an accumulator is meant the quantity 
 of electricity which must be communicated to the receiving 
 plate to produce unit difference of potential between the two 
 plates. Other things being the same, the capacity will vary 
 with the specific inductive capacity of the dielectric employed. 
 If the specific inductive capacity of air be taken as unity, 
 and C represent the capacity of an accumulator with air for 
 the dielectric, then, if K denote the specific inductive 
 capacity of another substance, the capacity of the same 
 accumulator with that substance substituted for air will be 
 represented by KG. 
 
 155. The capacity of an accumulator formed of two 
 parallel plates is calculated as follows : 
 
ACCUMULATORS. 
 
 131 
 
 Let A and B, fig. 68, be the two plates whose potentials 
 are V and V respectively, and whose areas A R 
 are each equal to S. Also let the distance 
 between them, or the thickness of the di- 
 electric, be t. Except near the edges, which 
 may be neglected if the plates are large in 
 comparison with their distance apart, the 
 lines of force, for this case, will be perpen- 
 dicular to both plates, and hence the tubes of 
 force will be cylinders. Now it is known 
 that if R be the resultant force at any point, 
 and to the area of the section, perpendicular 
 to the direction of R, of the tube of force at 
 that point, the product Ro> is constant. Fig. 68. 
 Hence, as w is constant for a cylinder, so 
 must R be constant. The value of R vanishes for points 
 within the plate A, and since its value changes by the 
 quantity 4?ro- (where o~ is the surface density) on passing 
 through an electrified surface, its value just outside the 
 surface must be 47ror. Therefore, 
 
 R = 47ro-. 
 
 But R is also equal to the rate of change of potential per 
 
 unit of length between A and B that is, to ^ . 
 
 V-V 
 
 Therefore 
 
 Therefore 
 
 R = 47r<r 
 
 V-V 
 
 4-rrt 
 
 But Q, the quantity of electricity on A, is So-. 
 
 Therefore 
 
 = Scr 
 
 But the capacity, C, is the quantity of electricity necessary 
 to produce unit difference of potential. 
 
 Q 
 
 Therefore C = . 
 
 If the plate B be connected to the earth, V = O and 
 
132 ELECTRICITY. 
 
 If a plate of shell-lac or vulcanite whose specific inductive 
 capacity is K be inserted between A and B, then Q = KCV. 
 
 156. As it is an important case, we shall also find the 
 capacity of a sphere, A, surrounded by a concentric spherical 
 shell, B (fig. 69), both being insulated. 
 
 Let r be the radius of A, R the 
 radius of the inside surface of B, 
 and x the thickness of B. Let a 
 quantity, Q, of electricity be 
 distributed over the surface of 
 A. This will induce a quantity 
 Q, on the inner surface of B, 
 the complementary -f- Q going to 
 the outer surface of B. The 
 potential at every point within 
 Fig. 69. the sphere A is the same as at 
 
 its centre. Let it be V ; then, 
 
 The potential just outside B is the same as if Q were 
 collected at the centre. Therefore, calling it V, 
 
 V = _ . Therefore subtracting, 
 
 Therefore Q = -^ (V - V). But when V - V'=l, Q = C. 
 Therefore C = -^-. 
 
 x\i T 
 
 157. By far the most useful form of accumulator is the 
 Leyden jar, so named from the place of its discovery. The 
 discovery was accidentally made in 1746, by Cuneus, a pupil 
 of Muschenbroek, while endeavouring to give an electrical 
 charge to water. He took a wide-mouthed glass flask 
 partially filled with water, and, holding it in his hand, 
 allowed a chain, hanging from the prime conductor of an 
 electrical machine, to dip into the water. The machine was 
 then worked for some time, and on taking hold of the chain 
 to remove it from the water, Cuneus was surprised to feel 
 
ACCUMULATORS. 133 
 
 a smart shock pass through his arms. He describes the 
 shock as very severe ; but no doubt its extreme novelty led 
 him greatly to exaggerate its severity. In this experiment 
 Cuneus had unconsciously made an accumulator whose 
 dielectric was the glass, and whose conducting plates were 
 respectively his hand and the surface of the water next the 
 glass. 
 
 The Leyden jar, as usually constructed, consists of a glass 
 jar (fig. 70) with a coating of tinfoil carefully 
 pasted inside and out, extending to within a 
 few inches of the mouth. The mouth is 
 generally closed by a wooden stopper, through 
 which passes a brass rod surmounted by a 
 brass ball or knob. The connection between 
 the inside coating and the ball is made by a 
 chain extending from the lower end of the 
 brass rod to the bottom of the jar. If this jar 
 be put upon an insulating stool, and sparks 
 drawn to the knob from the prime conductor 
 of the machine, it will be observed that, after a few sparks 
 have passed, no more will follow although the machine be 
 worked ; or, if they do, they are immediately dissipated from 
 the knob in a brush discharge. If then, however, the knuckle 
 of the experimenter be brought near the outer coating, sparks 
 begin again to pass freely, and for every spark wnich passes 
 between the machine and the knob a similar spark passes 
 between the knuckle and outer coating. This continues for 
 some time, and then the jar is fully charged. The action 
 of the jar is as follows : The + E communicated to the 
 inner coating by the machine acts inductively through the 
 glass on the outside coating. It produces a charge E on 
 the inside of that coating, the complementary positive charge 
 going to the outside. It is this complementary -j- E which 
 is observed to pass to the earth when the knuckle is applied 
 to it. As the inside coating of the jar forms nearly a closed 
 surface, the charge on its outer surface is very small, con- 
 sisting only of the electricity on the knob and brass rod and 
 chain. 
 
 If the glass of the Leyden jar be thin, the curvature of the 
 
134 ELECTRICITY. 
 
 jar may be neglected, and hence, it may be regarded as an 
 accumulator consisting of two parallel plates. We can, in 
 consequence, apply the result of section 155 in order to find 
 its capacity. Let Q be the quantity of electricity given to 
 the inside coating, whose area is S, V and zero the potentials 
 of the inside and outside coatings respectively, t the thickness 
 of the glass, and K its specific inductive capacity ; then 
 
 VKS 
 Q = ~4~J~- Hence, if C be the capacity of the jar, 
 
 KS 
 
 C = -: .. This can be put into the form t , which shews 
 4-n-t 4-rr ^ ' 
 
 j\. 
 
 that the capacity of the jar is the same as that of a similar 
 jar with air of the thickness ~- instead of glass for the 
 
 dielectric. 
 
 158. The Leyden jar is discharged by establishing a con- 
 ducting connection between its inner and outer coatings. 
 This is usually done by an instrument called discharging 
 tongs (fig. 71), which consists of two 
 brass arms ending in balls, and mov- 
 able on a hinge by glass handles. One 
 of the balls is placed on the outer coat- 
 ing, and the other brought round to the 
 knob. When this is done, a brilliant 
 p. 71 ** flash, accompanied by a sharp snap, is 
 seen to pass between the knob and the 
 approaching ball. If the discharge is made through the 
 body by laying the hands simultaneously on the knob and 
 outside coating, a violent shock is felt. A charged Leyden 
 jar obviously represents a store of potential energy ; and the 
 amount of this energy which is transformed into heat, light, 
 sound, &c. by the discharge of the jar is, by section 131, equal 
 to 4QV = |CV 2 , and is thus proportional to the square of 
 the potential of the inner coating. When a Leyden jar is 
 charged, it is a question whether the opposite electricities 
 reside on the surfaces of the tinfoil coatings next the glass, 
 or on the surface of the glass itself. To test this, Franklin 
 devised the experiment of the jar with movable coatings. 
 
ACCUMULATORS. 135 
 
 This jar, which in shape resembles a common tumbler, is so 
 constructed that its coatings, although fitting closely to the 
 glass, can be easily removed and replaced. In making the 
 experiment, the jar is charged in the ordinary way. The 
 inside coating is first removed and' discharged by touching 
 it with the finger ; the glass is then lifted out of the outside 
 coating and placed on an insulating stand ; the outside coat- 
 ing is now discharged, and the whole is put together again. 
 When the discharging tongs are applied, a bright spark and 
 snap is produced. This shews clearly that at least, during 
 the time when the glass jar was separate from its coatings 
 the electrical charges must have been on its inside and out- 
 side surfaces. 
 
 159. Residual Charge. If a large Leyden jar be fully 
 charged, allowed to stand for some time, and then discharged, 
 it will be found to re-charge itself to a small extent in the 
 same way as before. This is observed on connecting its two 
 coatings by the discharging tongs, when a considerable spark 
 takes place, followed sometimes by as many as four similar 
 discharges, each less than the preceding, and all from the 
 same initial charge. These, called secondary discharges, are 
 attributed to what is known as the residual charge of the 
 Leyden jar, and this again is referred to the phenomenon of 
 electric absorption observed in glass and other solid dielectrics. 
 When the jar is strongly charged, the glass seems to have 
 soaked up to a small depth below its surface a certain quan- 
 tity of the opposite electricities, which it again allows to 
 ooze out after discharge has taken place. It is the quantity 
 thus oozing out which re-charges the jar, and produces the 
 secondary discharge. Although dielectrics behave as if they 
 absorbed electricity when under strong polarisation, it does 
 not follow that they actually do so. If they did, as has been 
 observed by Clerk- Max well, the fact could not fail to be de- 
 tected by the following experiment : Let the dielectric sub- 
 stance be surrounded by a metallic vessel well insulated. Let 
 it then receive a charge of electricity, and immediately let 
 the outside vessel be discharged and again insulated. Now, 
 if any electricity had been absorbed by the substance of the 
 dielectric, uud were now being given out, it would certainly 
 
136 ELECTBICIT?. 
 
 charge the outside of the metallic vessel in such a way as to 
 be manifest to the ordinary delicate tests. No such charge 
 has ever been observed, and hence no real electric absorption 
 can have taken place. A different explanation of electric 
 absorption has been given by Clerk-Maxwell. By a mathe- 
 matical investigation, he shews that no such phenomenon 
 can take place in a strictly homogeneous dielectric ; and by 
 a similar investigation he shews that it must take place, pro- 
 vided the dielectric be heterogeneous ; and that it will not 
 matter whether the heterogeneous dielectric be disposed in 
 layers, each in itself homogeneous, or consist merely of a 
 conglomeration of particles. It will readily be seen that 
 this explanation amply accounts for the phenomenon in 
 glass and solid dielectrics generally. 
 
 160. Discharge by Alternate Contacts. If a Leyden jar be 
 charged and insulated, it can be gradually discharged by 
 alternately touching the knob and outer coating with the 
 finger. At each contact a feeble spark takes place. Suppose 
 Q to be the entire charge on the inner coating. Part of this 
 will be on the outside of that coating, including the knob, 
 brass rod, and chain ; and part on the side next the glass. 
 Let x be the fraction of Q, which is next the glass ; then 
 xQ will be the charge on the outer coating, which was in 
 connection with the ground. Hence, a; is the coefficient 
 by which we must multiply the charge on the inner coating 
 at any time, in order to get the charge on the outer coating 
 at the same time, that coating being at zero potential. Simi- 
 larly, let x be the coefficient by which we must multiply 
 the charge on the outer coating, insulated, to get the charge 
 on the inner coating when it is at zero potential. Now let 
 the knob be touched ; the charge on the inner coating imme- 
 diately after will be got by multiplying the charge on the 
 outer coating by x' ; that is, it will be -}- xx'Q. Next let 
 the outer coating be touched, and similarly the charge on it 
 immediately after will be got by multiplying the charge on 
 the inner coating by x ; that is, it will be x-x'Q. 
 Hence, we see that the charge on either coating after any 
 contact is got by multiplying the charge on the same coating 
 after the previous contact by xx' ; that is to say, the charges 
 
ACCUMULATORS. 
 
 137 
 
 left form a geometric series, whose common ratio is xx f . 
 The quantity removed from the inner coating after n contacts 
 will be : 
 
 Q (1 - a?*-) ; 
 
 and from the outer, xQ (1 x n x' n \ 
 Since x and x r are fractions very nearly equal to unity, the 
 quantity removed at each contact is very small, and, theo- 
 retically speaking, it would require an infinite time to 
 remove the whole. 
 
 This method of discharge is prettily illustrated by a toy 
 called the electric spider. A ball connected with the outer 
 coating is placed at the distance of one or two inches from 
 the knob, and a piece of pith made up so as to resemble a 
 spider is hung by a silk thread between them. The spider 
 keeps moving between the two balls under the influence of 
 the opposite electricities alternately on the knob and out- 
 side coating. 
 
 161. In order to find the specific inductive capacity of 
 different substances, Faraday made use 
 of two precisely equal and similar 
 accumulators, in one of which the 
 dielectric was air, and in the other 
 the substance, whose specific inductive 
 capacity he wished to determine. One 
 of his accumulators is represented in fig. 
 72. It consists of a metallic sphere A, 
 attached to the knob M by means of a 
 rod passing through a plug of shell-lac. 
 A is surrounded by a concentric spheri- 
 cal shell B, made in two halves, which 
 can be separated so as to allow different 
 solid dielectrics to be included between 
 A and B. The diameter of A is 2'33 
 inches, and the distance between the 
 
 surfaces A and B '62 of an inch. By 
 
 means of a stopcock R, the space be- Fig. 72. 
 
 tween A and B can be exhausted of air, 
 and filled with different gases. The two accumulators are 
 used as follows : 
 
138 ELECTRICITY. 
 
 Denote them by X and O respectively. X is first 
 filled with air and O with the substance, such as shell-lac, 
 whose specific inductive capacity it is required to determine. 
 Let K denote this ; then, if C be the capacity of X, the capa- 
 city of O will be KG. A charge of electricity is given to X 
 by the knob M, the outside of B being in connection with 
 the earth. If V be the potential of A, the quantity of elec- 
 tricity communicated to it will be CV. Now, let the knob, 
 M, of X be joined to the corresponding knob of O, which is 
 uncharged. The charge of X will be divided between X and 
 O ; and if V' be the common potential, we have, since the 
 quantity of electricity is the same as before, the equation 
 V'(C + KC) = CV. 
 
 From this, V = 
 
 1 + K, 
 
 V V 7 
 
 whence K = ^ , which determines K. 
 
 As an example, take one of Faraday's experiments on shell- 
 lac. The initial potential of X, as ascertained by Coulomb's 
 torsion balance, was 290. When X and O were joined the 
 common potential was 114. Hence, 
 
 K 290 - 114 = 176 = 
 114 ~ 114 ~~ 
 
 When different gases were put into 0, X containing air as 
 before, Faraday found that in all cases the common potential 
 V' was equal to ^V, from which it follows that the value 
 of K for all gases is unity (sect. 108). 
 
 162. Electric Battery. In order to get a great accumulation 
 of electricity, large surfaces are necessary. This can be 
 obtained either by constructing a large jar, or by uniting 
 several small jars together so as to act as one. The latter 
 method is preferable, as we can vary the surface according 
 to the number of jars employed. A number of small jars 
 united together as one is called an electric battery. A very 
 convenient form of electric battery is shewn in fig. 73. The 
 knobs of each jar communicate with a large central one by 
 means of arms of brass moving on hinges, and the outer 
 coatings are put in conducting connection by being placed 
 on an insulated stool covered with tinfoil. The interior 
 
ACCUMULATORS. 
 
 coatings are conveniently charged by a long projecting arm 
 from the central knob, and the exterior ones by connecting 
 
 Fig. 73. 
 
 the stool with the ground. Any jar can be thrown out of 
 action by throwing back its arm. 
 
 If there be n equal jars in the battery, each of capacity C, 
 it is clear that the capacity of the battery will be nC, since 
 the total amount of coated surface is n times the surface of 
 a single jar. If the battery be charged to potential V, the 
 quantity, Q, of electricity accumulated will be nCV, and the 
 energy which is equal to -?QV will be nCV 2 . 
 
 Let the n jars be insulated and so arranged that the knob 
 of the first jar is connected with the machine, and its outer 
 coating with the knob of the second, and the knob of the 
 third with the outer coating of the second, and so on, the 
 outside of the last being in connection with the earth. This 
 is called charging by cascade; and the whole is discharged 
 by bringing the knob of the first in connection with the 
 outer coating of the last. Let C be the capacity of each jar, 
 and V the potential of the knob of the first. The difference 
 of potential between the knob and outer coating of each jar 
 
 y 
 will be -, and the quantity of electricity accumulated in it, 
 
140 ELECTEICETT. 
 
 cv 
 
 i Hence, the whole charge in the n jars is CV, the same 
 
 as if one alone had been charged in the ordinary way. The 
 
 V CV 2 
 
 potential energy will be CV . -, that is \ . 
 
 Again let the n jars be each charged separately in the 
 ordinary way. Then let the knob of the first be put into 
 connection with the outside coating of the second, the knob 
 of the second with the outside of the third, and so on. This 
 is called charging in series. Let C be the capacity of each jar, 
 and V the potential to which it is raised before contact with 
 the others. When the connections are made, the potential of 
 the second will be 2V, of the third 3V, and so on, the potential 
 of the nth being nV. If we compare this arrangement with 
 the ordinary electrical battery, we find that, since the electro- 
 motive force that is, the difference of potential is nV 
 instead of V, the striking distance is much greater in the 
 former than the latter. The quantity of electricity, however, 
 is less, being CV instead of nCV. The potential energy for 
 
 this case is JCV . riV, that is ^CV 2 , and so is the same as for 
 
 the battery. This was to be expected, since it requires the 
 same amount of work to charge n jars separately as n jars 
 together to the same potential, their outside coatings being 
 in connection with the earth. 
 
 Experiments with the Leyden Jar or Battery. By discharg- 
 ing the Leyden jar or electric battery through particular 
 channels, we obtain some beautiful illustrations of the 
 power of electricity. When the discharge is effected through 
 thin wires of gold or platinum, the heat accompanying 
 its passage is so great as to dissipate them in vapour. The 
 expansion of the air caused by the spark is shewn by the 
 electric mortar. This is a wooden mortar with two wires 
 entering air-tight at the opposite sides of the breach, with a 
 small wooden ball fitting closely in the muzzle. The spark 
 passing between these wires in discharge causes a sufficient 
 expansion of the air within the mortar to drive the ball to 
 some distance off. When the discharge is made through 
 gunpowder, it tosses the grains violently about, but causes no 
 
ACCUMULATORS. 141 
 
 ignition ; when, however, it is retarded by introducing an 
 imperfect conductor, such as a wet string, into the circuit, the 
 gunpowder is fired. When the discharge is made through 
 glass by two points pressing against its opposite surfaces, a 
 small hole is drilled into the glass. To assist in such experi- 
 ments, the universal discharger (fig. 74) is used. This consists 
 
 Fig. 74. 
 
 of two arms of brass mounted on glass pillars, so that their 
 position and distance can be easily adjusted, and of a small 
 movable table placed between them, the whole resting on a 
 wooden foot. When the discharge of a Ley den jar is made 
 through a number of individuals, each receives an equally 
 powerful shock. The want of insulation here does not cause 
 a loss as when they receive a spark from the machine, for the 
 electricities of the two coatings have each other, not the 
 ground, for their final termination. 
 
 163. Velocity of Electric Discharge. The rapidity with 
 which electric discharge takes place is so great, that we 
 might well despair of reaching any definite information about 
 it. Wheatstone, by means of a revolving mirror, determined 
 its rate of propagation in certain circumstances. A small 
 mirror was made to revolve fifty times a second, and the 
 reflection of the electric spark was observed in it. Any one 
 who takes a mirror in his hand and makes it revolve, sees 
 that objects are apparently displaced by it, and it admits of 
 an easy geometrical demonstration, that the reflected image 
 describes an angle the double of that of the mirror. If, while 
 the small mirror rotates at this rate, the image of a spark 
 
142 ELECTRICITY. 
 
 should shew a displacement of 90, we know that the mirror 
 has moved through 45, and the time during which this takes 
 place is -fifo of T V = iw of a second. If the duration of the 
 spark, then, had been ?bv of a second, we should have seen 
 its image move through 90. The eye, however, during this 
 time would not have been able to discern any difference 
 between the beginning and the end of the spark, so that the 
 90 would have appeared as one arc of light. Examined in 
 this way, however, the spark of a machine and that of a 
 Leyden jar were seen as if the mirror had been at rest. Thus 
 analysed with an apparatus where a duration of -g^inr part of 
 a second would have shewn an arc of 1, the electric spark 
 appears instantaneous. The discharge 
 of a Leyden jar through a long wire 
 is not so instantaneous. Wheat- 
 stone's method of finding this was 
 as follows : Six balls (fig. 75) were 
 arranged in pairs, each pair being 
 quite near the other. The ball 2 was 
 Fig. 76. connected with 3 by a copper wire a 
 
 quarter of a mile in length, so were 
 
 also 4 and 5 the dotted lines in the figure marking simply 
 the connection. When discharge took place, the electricity 
 of the inner coating was communicated to 1, and of the outer 
 coating to 6. Supposing charge to travel from the inner 
 to the outer coating, it would proceed from 1 to 2 by spark, 
 then by the long copper wire to 3, by spark to 4, by the 
 other long wire to 5, and by spark to 6. To 
 the eye, the three sparks seemed simultaneous. 
 In the mirror, however, they presented the 
 appearance of three arcs of equal length, the 
 middle one rather behind the others (fig. 76). 
 In this instance, the mirror revolved 800 
 times a second, and the retardation of the middle line 
 was about . The time, therefore, taken by the discharge 
 to travel from 2 to 3, or 5 to 4, a quarter of a mile, was 
 
 360 X 8T)6 = 1,152,000 f a SeC nd > wMch corres P OIids to 
 286,000 miles per second ; greater than the velocity of light, 
 
ACCUMULATORS. 
 
 143 
 
 which is only 194,000 miles per second. In the same manner, 
 it was calculated from the lengths of the arcs, which were 24, 
 that the duration of each spark was irdjTnr of a second. It 
 thus appeared that the discharge was a successive one, not, 
 at least, as instantaneous as through a short conductor. 
 
 CHAPTER XL 
 ELECTROSCOPES AND ELECTROMETERS. 
 
 164. Strictly speaking, an electroscope is an instrument 
 which merely indicates the difference of electric potential 
 between two conductors, whereas an electrometer is one 
 which not only indicates but also measures the amount 
 of that difference in terms of the proper unit, although the 
 one is often used for the other. They both depend for their 
 action upon the effects produced by electrostatic force acting 
 between two conductors, one of which is usually fixed and 
 the other movable. The move- 
 ments of the latter are, in 
 electrometers, registered on a 
 suitable scale, and the cor- 
 responding differences of poten- 
 tial can be compared with each 
 other, or, if desired, expressed 
 in absolute measure by multi- 
 plying by the proper constant. 
 
 The most simple example of 
 a rough electroscope is the 
 electric pendulum already de- 
 scribed (sect. 51). A more deli- 
 cate instrument is the double 
 pendulum electroscope of Ca- 
 
 vallo (fig. 77.) It consists of two pith balls suspended side by 
 side by fine silver wires, and inclosed in a glass case, which 
 is surmounted by a bell-shaped cover in metallic contact with 
 the wires. When an electrified body is brought near the bell- 
 
 Fig. 77. 
 
144 
 
 ELECTRICITY. 
 
 Fig. 78. 
 
 shaped covering, the balls become similarly electrified and 
 repel each other. 
 
 The most delicate and useful instrument on the double 
 pendulum principle is the gold leaf 
 electroscope of Bennet. It is repre- 
 sented in fig. 78. A is a glass vessel 
 closed by the metal support, B. At 
 C are seen two strips of gold leaf 
 gummed to the parallel faces of a flat 
 piece of brass. This piece is attached 
 to a stout brass rod, which passes up 
 through an insulating plug in the 
 neck of the vessel, and carries the 
 brass disc, D. Close to the glass, on 
 the inside, is a cylinder of wire gauze, 
 H, which is tall enough to surround 
 the gold leaves. This essential addi- 
 tion was first made by Faraday, and 
 it is strange that since that time the 
 instrument has been often used with- 
 out it, and the defect not realised. It is obvious that the 
 motion of the gold leaves, C, will depend upon the difference 
 of potential between them and the inclosure, H ; and hence 
 the importance of keeping H at a definite potential, as by 
 connecting it with the ground through the sole-plate. If H 
 be removed, and the surface of the glass only be exposed to 
 the gold leaves, the indications of the instrument become 
 unreliable, as the potential of the glass surface may be incon- 
 stant. In these circumstances it is not even an electroscope, 
 as the leaves might diverge when the difference of potential 
 to be tested was nil Besides giving a definite potential, the 
 wire gauze H serves the important purpose of screening the 
 gold leaves from the action of all external electrified bodies. 
 
 165. Sir William Thomson has divided electroscopes and 
 electrometers into two great classes the idiostatic and the 
 heterostatic. In the former, only one electrification is made 
 use of namely, that which is being tested or measured ; in 
 the latter, besides this, an auxiliary electrification is employed, 
 supplied from some independent source, such as a charged 
 
ELECTROSCOPES AND ELECTROMETERS. 
 
 145 
 
 Leyden jar. The electroscopes already mentioned are ex- 
 amples of the idiostatic class. Of the heterostatic class, the 
 simplest example is the Bohnenberger electroscope repre- 
 sented in fig. 79. It consists of a single strip of gold leaf, /, 
 suspended symmetrically 
 between the opposite poles, 
 P and P', of a dry pile (sect. 
 192), the whole being in- 
 closed in a glass jar, C. A 
 permanent difference of 
 potential is maintained be- 
 tween P and P' ; P, let us sup- 
 pose, being the positive and 
 P' the negative pole. When 
 /is neutral, it will remain 
 stationary between P and 
 P ; but if it be electrified, 
 let us say, positively,^ 
 through the knob, D, it 
 will be simultaneously re- 
 pelled by P and attracted 
 by P'. The opposite will 
 
 be the case if / be negatively electrified. It is this double 
 action which gives great sensitiveness to instruments of this 
 class. 
 
 166. Absolute Electrometer. This is an instrument for deter- 
 mining differences of potential in absolute measure that is, 
 in terms of the fundamental units of length, mass, and time. 
 To understand theoretically how this is done, suppose A 
 and B to be two horizontal circular discs of metal placed face 
 to face, one above the other, and separated by a narrow 
 space. Let A be undermost, insulated, and kept at a 
 constant potential V by being in contact with a Leyden jar. 
 Let B be suspended by a wire from one arm of a delicate 
 balance in connection with the ground, and consequently at 
 zero potential. In the other scale of the balance let a weight, 
 w, be placed such that it will just balance the attraction of 
 A for B, and keep them at the distance d apart. Now, 
 neglecting the influence of the electrification on the un- 
 
 Fig. 79. 
 
146 ELECTRICITY. 
 
 opposed faces of A and B, and the want of uniformity in 
 the electrical distribution near their edges, we have the 
 equation 
 
 y 
 
 47TXT = R = -p 
 
 where R is the resultant force at a point between A and B, 
 and <r the surface density. Also the attraction between the 
 discs per unit of area is 27ro* 2 . Therefore if S be the area 
 of the lower disc, A, we have, since the attraction is equal 
 to the weight w, 
 
 wg = 
 
 where g is the acceleration produced by gravity. 
 
 Therefore V = d - (1), 
 
 which expresses V in absolute measure. 
 
 Now, suppose the disc, A, to be detached from the Leyclen 
 jar and put in contact with a body at potential V 7 . Keeping 
 everything else the same, let A be moved parallel to itself up 
 or down till the attraction between A and B at distance, d', 
 is again just balanced by w, then 
 
 v'.<r^22 (2). 
 
 Subtracting (2) from (1), we have 
 
 From this we see how the difference of potential between two 
 bodies can be determined by getting the difference of two 
 distances on a scale, and multiplying by a constant. 
 
 The above principle of the attracted disc was first employed 
 by Sir W. Snow Harris, and has been adopted by Sir 
 William Thomson in the construction of his absolute electro- 
 meter. 
 
 167. Thomson's Absolute Electrometer. This is a heterostatic 
 instrument, and can be viewed as consisting of two distinct 
 
ELECTROSCOPES AND ELECTROMETERS. 147 
 
148 ELECTRICITY. 
 
 parts. One of these is for testing and maintaining a certain 
 constant auxiliary potential V, and the other for determining, 
 in absolute measure, the difference between the potentials of 
 any two given conductors. The first of these parts embraces 
 a Leyden jar, forming the case of the instrument, an idiostatic 
 gauge, and a replenisher, E (fig. 80). The Leyden jar is a 
 cylinder of white flint-glass, closed at top and bottom by 
 metal plates. It is coated inside and out to within a short 
 distance of the top with tinfoil, openings being left where 
 necessary for viewing the internal parts. The idiostatic gauge 
 
 will be understood 
 from fig. 81. P is a 
 small square plate of 
 aluminium, which just 
 fills, like a trap-door, 
 without touching the 
 edges, a square hole 
 in the metal plate, G. 
 One side of the alu- 
 Fig. 81. minium plate is drawn 
 
 out and bent so as to 
 
 form a handle to it, h, exactly like a spade. Through the 
 bend at the part of the handle next the spade passes a 
 platinum wire, /, which is stretched between two supports 
 attached to G. The torsion of this platinum wire, which is 
 bent out of the straight line over a slight projection at the 
 point where it passes through the handle, regulates the 
 motions of the aluminium plate. The fork, F, at the end of 
 the handle passes over a white enamelled projecting piece 
 of metal, which has two black dots upon it near together, 
 and in the same vertical line. Across the end of the fork is 
 stretched a black hair, whose motion up and down in front 
 of the enamelled projection is watched through the lens, I. 
 It is so arranged that, when the plate P has its surface in the 
 same plane with that of G, the hair is seen straight, and 
 exactly between the two black dots. This is called the 
 sighted position. At F (fig. 80) is seen a circular disc, sup- 
 ported on a metal rod rising from the disc A, which is in 
 contact with the inner coating of the Leyden jar. F is thus 
 
ELECTROSCOPES AND ELECTROMETERS. 
 
 nnrrv 
 
 always at the same potential as this cfldatingr that is, at the 
 value V. The disc F is fixed opposite to", .and below G, when 
 the gauge is in its proper position ; and the distance between 
 F and G is so regulated that, when the potential of F is V, 
 its attraction for the aluminium plate, P, is such that it just 
 overcomes the torsion of the platinum wire, and keeps P in the 
 sighted position. In this way the constancy of the potential 
 V is tested. To keep V constant is the object of the replen- 
 isher seen at E. 
 
 This is, in reality, a small electrical machine worked on the 
 Holtz principle (sect. 149). It is represented with the revolv- 
 ing axis detached in fig. 
 82. A and B are two 
 bent pieces of metal 
 called inductors. They 
 are placed so as to de- 
 viate a little from being 
 parts of the same cylin- 
 drical surface. Attached 
 to them are two springs, 
 a and 6, called the re- 
 ceiver springs. C and 
 D are other two springs, 
 called contact springs, in 
 metallic communication 
 with each other, but 
 
 insulated from the rest of the machine. P and Q are two 
 curved pieces of metal called carriers, fixed to a cross-piece 
 of vulcanite, which is attached to the axis, T, also of vul- 
 canite. This axis, when in position, can be twirled round by 
 the milled head, E, so that the carriers, P and Q, revolve 
 inside the inductors, and successively touch the springs, a, D, 
 6, C. When the replenisher is in its place in the electro- 
 meter, the inductor, A, is put in metallic connection with the 
 plate, A (fig. 80), and in consequence with the inner coating 
 of the Leyden jar ; while B is similarly connected with the 
 outer coating by being in contact with the cover of the jar. 
 A has therefore the auxiliary potential, which it is desired to 
 keep constant. To see how this is done, let us suppose the 
 
 Fig. 82. 
 
150 ELECTRICITY. 
 
 axis, T, to be turned round in the direction opposite to the 
 hands of a watch held with its face upwards, from the posi- 
 tion where P is in contact with the spring D. At that point, 
 A being + electrified, P will receive a charge by induction 
 through the air-space separating A and P ; while Q will re- 
 ceive the corresponding + charge. When P comes in contact 
 with &, it is practically within a closed conductor, and so will 
 give up its charge to B. At the same time Q gives up its 
 -f- charge to a, and hence, by each turn of the axis, the differ- 
 ence of potential between A and B is increased by a certain 
 quantity. The reverse will be the case if T is turned in the 
 opposite direction. In this way, by simply turning the 
 replenisher in one direction or the other, the potential of the 
 jar can be raised or lowered at will, and so kept at the value 
 V, as indicated by the idiostatic gauge. 
 
 The second distinct part of the electrometer consists of the 
 attracted disc arrangement, whereby differences of potential 
 are expressed in absolute measure. A (fig. 80) is a circular plate 
 of metal called the guard-plate, in metallic contact with the 
 inner coating of the jar. At its centre is a circular opening 
 which is just filled, without touching, by the movable disc, 
 C. This is about 46 millimetres in diameter, and is made 
 of thin aluminium, flat and smooth on the lower side, but 
 stiffened by a projection round the rim and radial arms on 
 the upper side. C is supported by three symmetrically 
 placed steel springs, one of which is seen in the figure at S. 
 These springs resemble in shape very much the merry- 
 thought of a fowl. One prong of each is attached to the 
 centre of C, and the others to a brass piece cemented to the 
 end of a glass rod seen at I. This glass rod is attached to a 
 metal piece which is moved up and down in properly con- 
 structed guides by the micrometer screw, M. The move- 
 ments of the screw are registered by the scale G, and the 
 graduated disc, D. 
 
 Attached to the centre of the attracted disc, C, is a fine 
 hair, in front of which a lens, H, is so placed that it forms an 
 image of the hair at its conjugate focus near the surface of the 
 glass jar. This image is viewed through an eye-piece seen at 
 L. Two screws, K, are so placed that the image of the hair 
 
ELECTROSCOPES AND ELECTROMETERS. 151 
 
 is seen exactly between their points when the disc, C, is in 
 its sighted position that is, when its lower surface is in the 
 same plane with the lower surface of the guard-plate, A. B 
 is a metal disc, called the attracting disc, insulated from the 
 rest of the jar, and movable up and down by the micrometer 
 screw, M'. B is put into connection with the body whose 
 potential is to be tested by the electrode, N. The move- 
 ments of B are registered by the scale, R, and the graduated 
 disc, T. 
 
 The electrometer is used as follows : First, all electric 
 influence is removed by putting for an instant the electrode, 
 N, and A into metallic connection by a wire passing through 
 the cover. The attracted disc is then brought to its sighted 
 position by M, and the screw reading noted. A known 
 weight, iv, is then placed symmetrically upon the disc, so as 
 to depress it a little below the level of the guard-plate. By 
 the micrometer, M, the disc is again raised to its sighted 
 position, the reading noted, and then the weight, w, removed. 
 In one instrument, Sir William Thomson mentions that T^ths 
 of a gramme depresses the disc through a distance represented 
 by two turns and a very small fraction of the screw. The 
 Leyden jar is now charged to potential V as determined by 
 the idiostatic gauge. During each experiment this is kept 
 constant by the replenisher. B is next put into connection 
 with the outside coating by the electrode, N, and the micro- 
 meter, M', is moved till the attraction of B on the balance disc 
 brings it to its sighted position. The attraction of B is then 
 known to be equal to the weight, w. This reading being 
 noted, B is now insulated, and the bodies, the difference of 
 whose potentials, V x and V 2 , is required, are successively put 
 into contact with B through N. The distances, d 1 and d 2t 
 through which B has to be moved to bring the attracted disc 
 in each case to its sighted position, are determined, and the 
 difference of potential is given by the equation, 
 
 where S is the area of the attracted disc, or more correctly, 
 the mean of the areas of the disc and the circular hole in 
 which it moves. 
 
152 
 
 ELECTRICITY. 
 
 168. Quadrant Electrometer. This instrument, also due to 
 Sir William Thomson, is by far the most delicate electro- 
 meter hitherto invented. It is heterostatic, and consists essen- 
 tially of the following parts : A Leyden jar, a movable needle, 
 four quadrant inductors, a replenisher, and an idiostatic gauge. 
 The last two are exactly similar to those already described. 
 The Leyden jar is an inverted glass shade (of white flint-glass), 
 
 Fig. 83. 
 
 supported on three legs from a brass mounting cemented 
 round its rim. A cupful of strong sulphuric acid is put 
 into the glass shade, which serves the double purpose of inner 
 coating to the jar and of keeping the internal parts free from 
 moisture. The outside coating is formed of strips of tinfoil 
 in connection with the brass mounting and metallic supports. 
 
ELECTROSCOPES AND ELECTROMETERS. 
 
 153 
 
 The mouth of the jar is closed by a cover of stout sheet brass, 
 which carries all the internal parts of the electrometer. The 
 instrument is represented in fig. 83, with the lower part 
 removed. Rising from the cover, and over a hole in its 
 centre, is a lantern-shaped erection which carries the 
 electrodes, one of which is seen at 0, the charging rod, P, 
 and the idiostatic gauge, parts of which are indicated at 
 A, D, E, L. 
 
 The movable needle, seen edgewise at U, consists of a thin 
 strip of aluminium shaped like a figure 8, and attached rigidly 
 by its narrow part to the stiff platinum wire, X, the wire 
 being at right angles to the plane of the needle. The wire, 
 X, projects upwards and downwards from the needle. From 
 its lower end hangs a fine platinum wire, stretched by a 
 platinum weight, which dips in the sulphuric acid, and thus 
 puts the needle in conducting connection with the inner 
 coating of the jar. To its upper part 'is attached the light 
 silvered mirror, M, with its plane vertical ; and just above 
 this the wire, X, ends in a small T~ sna P e d piece of metal, to 
 which the two fibres are attached, by which the whole is bifi- 
 larly suspended from the projecting brass piece, E, which is 
 cemented to the glass support, Q. At S and W are seen fixed 
 guard tubes, which screen the suspended wire from external 
 electrification, and also serve, 
 by being put into contact with 
 P, to give the original charge 
 to the jar. The four quadrant 
 inductors are represented in 
 fig. 84. They are in reality 
 parts of a flat circular box, 
 cut into four by saw cuts at 
 right angles to each other 
 through its centre. The alter- 
 nate ones, A and A', B and B', 
 are connected by wires. The 
 four are supported all at the 
 same level by glass rods from the brass cover of the instru- 
 ment. Three of them are fixed by nuts, while the fourth can be 
 moved out and in horizontally by a spring and counteracting 
 
 Fig. 84. 
 
154 
 
 ELECTRICITY. 
 
 screw, and is guided by three rounded projections, two of 
 which move in a V groove, while the third simply slides on the 
 flat surface of the brass support. By this simple kinematic 
 arrangement, the quadrant has only one degree of freedom, 
 
 and moves with 
 great steadiness. 
 The four quad- 
 rants, it will be 
 observed, sur- 
 round the needle 
 on all sides, 
 as is seen in 
 fig. 84. The 
 motions of the 
 needle, U (fig. 83), 
 which is rigidly 
 connected with 
 the mirror, M, are 
 indicated by the 
 deflections of a 
 
 Fig. 85. 
 
 spot of light on a distant scale. This spot of light is the 
 reflection from the mirror of the rays of light which fall upon 
 it through a vertical slit from a lamp placed behind the scale. 
 The usual lamp and scale are represented in fig. 85. 
 
 The action of the instrument is as follows : The Leyden 
 jar is first charged to the auxiliary potential V, as indicated 
 by the gauge. During each experiment, this is kept constant 
 by the replenisher, not seen in the figure. The needle, U, is 
 thus permanently at potential V. If the quadrants, A and A', 
 B and B' (fig. 84), be at the same potential, there will be no 
 force tending to turn the needle ; but if the potentials of 
 these differ by a quantity ever so little, the needle, U, will 
 turn in a certain direction. This direction will be determined 
 by the following consideration : Let V be the potential of U, 
 A the potential of A and A', and B that of B and B' ; then if 
 the difference between V and B be greater than the difference 
 between V and A, the needle will move so as to oppose a 
 greater part of its area to B than to A that is, in the direc- 
 tion from A towards B. By a mathematical analysis, it is 
 
ELECTROSCOPES AND ELECTROMETERS. 155 
 
 found that the moment of the couple tending to turn the 
 needle from A to B is 
 
 a(A B) {V |(A -f- B)}, when a is a constant. 
 
 If, as is usual, V is very much greater than i(A + B), the 
 latter may be neglected, and the expression for the couple 
 becomes 
 
 aV(A-B). 
 
 From this it will be seen that the sensitiveness of the 
 instrument is increased by making V large. 
 
 The instrument is used by putting the bodies, the differ- 
 ence of whose potentials is required, in connection with the 
 quadrants, A and B, through the chief electrodes, one of which 
 is O, in fig. 83. The scale readings are then noted, and, within 
 certain limits, these are taken as proportional to the deflecting 
 couple, and in consequence proportional to the difference of 
 potential. To convert the scale readings into absolute 
 measure, they must be multiplied by a certain constant, which 
 is determined experimentally, once for all, for each individual 
 instrument. The quadrant electrometer is extremely sensitive, 
 as is shewn by the fact that it can give a deflection of a 
 hundred divisions on the scale for the difference of potential 
 between zinc and copper. 
 
 CHAPTER XII. 
 TERRESTRIAL AND ATMOSPHERIC ELECTRICITY. 
 
 169. Terrestrial Electricity. If the earth were merely a 
 smooth electrified sphere, its surf ace- density would be uni- 
 form all over ; if it were, as it is, an oblate spheroid, but smooth 
 and undiversified by hill and dale, the surface-density at 
 any point would be simply proportional to the perpendicular 
 let fall from the centre on the tangent plane at that point. 
 In this case the electric distribution could be easily deter- 
 mined. In the actual case, however, the surface is so 
 extremely irregular, embracing as it does, electrically speak- 
 
156 ELECTRICITY. 
 
 ing, the surface of all bodies in conducting connection with 
 the ground, that it would be utterly impossible to determine 
 mathematically the distribution, even supposing it to be 
 constant and uninfluenced by external electrified masses. 
 Speaking generally, however, it may be said that the electric 
 density would be greatest on the hill-tops and on all sharp 
 points and corners ; less on extensive plains ; and least of all, 
 approaching to zero, on the inside surfaces of all nearly 
 inclosed spaces, such as caves, rooms, and on the ground 
 below trees. 
 
 170. The electrification of the earth's surface varies con- 
 siderably from place to place. In some parts it is negative, 
 in others positive, with neutral lines of equilibrium between 
 them. The negative areas, however, always greatly exceed 
 the positive ones in extent. In calm serene weather the 
 electrification is almost always negative ; and if such weather 
 were to prevail for a short time all over the earth, it is con- 
 jectured that, for that time, the entire surface would be 
 negatively electrified. The surface electrification also varies 
 very much from hour to hour. This is caused by the induc- 
 tive action of large electrified masses of air moving not very 
 far above the earth's surface. Such masses moving, for 
 instance, over a level open country, would disturb the uni- 
 form distribution of electricity which would naturally be 
 there ; and this disturbance could be detected by simultane- 
 ous observations of electrometers at stations not very far 
 apart. Such observations have been made by Sir William 
 Thomson in the island of Arran ; and he gives a mile or two 
 as the probable height of the influencing masses of air at that 
 particular time and place. In many cases the height must 
 greatly exceed this, and cannot be ascertained, even approxi- 
 mately, without a very special set of simultaneous observa- 
 tions. 
 
 Although its surface is usually electrified negatively, the 
 earth is by no means to be regarded simply as a huge con- 
 ductor, insulated in free space, and having a negative charge. 
 In fact, in the higher regions of the atmosphere the air 
 becomes so rarefied as to be a conductor, and there must be 
 somewhere in those regions a complementary electric dis- 
 
TERRESTRIAL AND ATMOSPHERIC ELECTRICITY. 157 
 
 tribution to balance the distribution on the surface. Hence, 
 as suggested by Sir William, Thomson, we shall not be far 
 from the truth if we regard the earth's surface, the air, and 
 this high aerial stratum, respectively, as the inner coating, 
 the dielectric, and the outer coating of a huge spherical 
 Leyden jar electrified negatively. 
 
 171. Atmospheric Electricity. Several methods may be 
 employed to ascertain the potential at any point in the air. 
 One is to place a sphere of small radius at the given point, 
 connect it with the earth by a fine wire ; then insulate it 
 and carry it indoors to an electrometer. The potential 
 indicated will be equal, but of opposite sign, to that of the 
 air at the point. Two other methods have been adopted by 
 Sir William Thomson. In one he uses a burning match 
 supported on the end of a long conductor. The products 
 of combustion continually going off carry with them electri- 
 city so long as any difference of potential exists between the 
 conductor and the air surrounding the flame. In this way 
 the potential of the conductor is brought in a very few 
 seconds to be the same as that of the air at the point of the 
 flame. By connecting the conductor with the electrometer, 
 its potential can be found. The other method depends upon 
 exactly the same principle. It consists in insulating on a 
 suitable stand a can of water which has a long nozzle pro- 
 jecting at right angles from its lower part. The can is 
 usually placed in a room near a window, which is drawn up 
 a few inches to let the nozzle project to the outside. Water 
 is allowed to trickle slowly from the nozzle, and each drop 
 as it falls carries with it electricity till the potential of the 
 can is reduced to be the same as that of the air at the point 
 where the water from the nozzle just breaks into drops. 
 
 It is to be carefully observed that none of the above 
 methods gives us any information directly about the electri- 
 fication of the air itself. They merely indicate to us the 
 quantity and kind of the electrification of the earth's surface 
 at the time and place of observation. If we suppose the 
 water-dropping apparatus to be placed in an open plain at 
 the height d above the ground, and if cr be the surface- 
 density at the point, and V the potential as indicated by 
 
158 ELECTEICITY. 
 
 the electrometer, expressed in absolute measure, we have 
 
 V V 
 
 47TO- = -,, which gives o- = ^~> ^ * 8 usua l in such observa- 
 
 tions to express V in terms of the potential of so many 
 Darnell's elements (sect. 197). Thus, by using a lighted 
 match, Sir William Thomson found the value of V for a 
 point nine feet above the ground on a level sea-beach in the 
 island of Arran to be from 200 to 400 Daniell's cells. This 
 gives a resultant force perpendicular to the earth of from 
 about 22 to 44 Daniell's cells per foot of air. The same 
 observer also found that the electrometer invariably shewed a 
 high positive potential in clear weather before and during east 
 wind ; and in some cases he was able to predict the approach 
 of east wind from the electrometer indications. There can 
 hardly be a doubt that by-and-by observations on atmospheric 
 electricity will give important aid to the meteorologist in 
 weather prognostication. As yet only one set of continuous 
 observations has been made on atmospheric electricity. This 
 was done at Kew for two consecutive years by means of a 
 self-recording electrometer attached to a water-dropping 
 apparatus. The movements of the index were recorded by 
 photography. These observations amply confirm what was 
 previously known regarding the annual and diurnal varia- 
 tions of atmospheric electricity. They shew that the average 
 potential is greater in winter than in summer ; and they 
 clearly point out two daily maxima for each month. In 
 January these occur about ten A.M. and seven P.M. ; in July 
 at eight A.M. and ten P.M. 
 
 It is only by balloon experiments that we can get any 
 direct information respecting the electrification of the air 
 itself, and of these we have not yet a sufficient number to 
 warrant any reliable conclusions. We can, however, get 
 very important indirect information regarding the air's elec- 
 trification by observing the variations produced by it in the 
 electric density on the earth's surface. 
 
 172. Lightning. The resemblance of lightning to the 
 electric spark was noticed almost as soon as the first spark 
 was seen. Franklin saw that they agreed in light, colour, 
 smell, shortness of duration, and in the property of being 
 
TERRESTRIAL AND ATMOSPHERIC ELECTRICITY. 159 
 
 transmitted by metals, which they sometimes fused ; and he 
 conjectured that they must also have the property in common 
 of being attracted by sharp points. In 1752, Dallibard in 
 France, acting on this conjecture, erected a long pointed rod, 
 insulated at the lower end, and succeeded in getting sparks 
 from it during a thunder-storm. In the same year, Franklin 
 made his famous kite experiment, which completely proved 
 the identity of lightning and the electric spark. His kite 
 was made of a silk handkerchief stretched on a wooden 
 frame, with a fine metal point in connection with the string. 
 A key was tied to the lower end of the string, and when the 
 kite was elevated during a thunder-storm, sparks were drawn 
 in rapid succession from the key as soon as the conduction 
 of the string was improved through its being wetted by the 
 falling rain. 
 
 173. Three kinds of lightning are usually spoken of 
 namely, forked-lightning, sheet-lightning, and ball-lightning. 
 Forked-lightning is nothing more than a long electric spark 
 passing from cloud to cloud, or from a cloud to the earth. 
 The length has been ascertained to be often over a mile ; 
 frequently it is between four and five miles ; and in one 
 recorded case it was ten miles. The duration of the flash is 
 excessively short. This is shewn by the familiar fact that a 
 rapidly revolving wheel always appears stationary when 
 illuminated by a flash of lightning. Wheatstone, by means 
 of his revolving mirror, has estimated its duration, and finds 
 that it cannot exceed a millionth of a second. Viewed in 
 such a mirror, the reflection of the flash ought to appear 
 elongated if it lasted longer than that time. The form of 
 the flash is zigzag, and it often appears broken up into two 
 or three forks whence its name. The bifurcation is easily 
 explained by the spark always taking the path of least 
 resistance. The zigzag is not so easily accounted for. It is 
 destroyed in the case of short sparks by heating the air, 
 which not only removes motes and combustible materials 
 from the air, but also does away with all traces of electrifi- 
 cation in it. Hence, as is suggested by Professor Tait, 
 ' the zigzag form of the lightning flash may, in certain cases 
 at least, be due to local electrification, which would have 
 
160 ELECTRICITY. 
 
 the same sort of effect as heat in rarefying the air, and 
 making it a better conductor.' Sheet-lightning is in all pro- 
 bability merely the illumination of the clouds by a forked 
 flash, which is not directly visible to the eye. It often 
 lightens up only the edges of a cloud, and sometimes the 
 same cloud mass several times in succession. The species of 
 sheet-lightning called summer-lightning is always unaccom- 
 panied by thunder. It is most likely the illumination pro- 
 duced by a discharge so distant that the sound does not 
 reach us. Almost nothing is known about ball-lightning, 
 although its existence is proved by several well-authenticated 
 instances. It has not as yet been imitated by any laboratory 
 experiment. It is said to occur in this way : After a violent 
 explosion of lightning, a ball is seen to proceed from the 
 region of the explosion, and to make its way to the earth in 
 a curved line like a bomb. When it reaches the ground, it 
 either splits up at once, and disappears, or it rebounds like 
 an elastic ball several times before doing so. It is described 
 as being very dangerous, readily setting fire to the building 
 on which it alights ; and a lightning-conductor is no protec- 
 tion against it. Ball-lightning lasts for several seconds, and 
 in this respect differs very widely from forked and sheet 
 lightning, which are in the strictest sense momentary. 
 
 174. Sometimes highly charged clouds are discharged by 
 heavy falls of rain or sleet, with very little or no accompany- 
 ing thunder and lightning. In this case, the rain-drops are 
 often so highly charged as to emit sparks just before they 
 reach the ground. When this occurs in the dark, the ground 
 is lit up, and we have the phenomenon of luminous rain. 
 An interesting illustration of this mode of discharge was 
 recorded by a French observer in 1879 ; his umbrella became 
 so electrified by a slight fall of snow, that he was able to draw 
 sparks from it. 
 
 When lightning strikes a building, curious effects are often 
 observed. The bell wires are found fused, and marks along 
 their course produced on the walls. When it strikes trees, 
 they are commonly shattered and rent. This is caused, no 
 cloubt, by the sudden conversion of their sap into steam. 
 The danger of taking refuge under a tree in a thunder-storm 
 
TERRESTRIAL AND ATMOSPHERIC ELECTRICITY. 161 
 
 arises from the fact that the body is a much better conductor 
 than a tree, and will in consequence be preferred by the 
 flash to the height to which it reaches. The best protection 
 from lightning would be a complete coat of mail of thin 
 Bheet-copper. 
 
 175. Lightning-Conductors. The use of lightning-con- 
 ductors was first clearly pointed out by Franklin. They 
 are rods of metal attached to buildings, and overtopping 
 them to a certain extent, for the purpose of protecting them 
 from being struck by lightning. To be really effective, they 
 must terminate at the top in a fine point, be themselves 
 good conductors of electricity, and be in perfect connection 
 with the earth at the lower end. They should also be in 
 conducting connection with all masses of metal in the build- 
 ing. Rods of iron or copper are commonly employed, 
 terminating in a platinum or gilded point, to prevent oxida- 
 tion, and attached at the lower end to a mass of metal, 
 imbedded, if possible, in moist earth. In towns, the water 
 mains form a good and convenient ' earth.' For vessels at 
 sea, the lightning-rod should be connected to the copper 
 sheathing, or to some mass of metal which is constantly 
 immersed. The object of the lightning-rod is not so much 
 to conduct the lightning harmlessly to the ground as to 
 continuall} 7 drain, by the inductive action of its point, the 
 electricity from the thunder-cloud, and so prevent a dangerous 
 accumulation of electricity in it. This action is easily illus- 
 trated by the experiment of holding a sharp-pointed rod near 
 the prime conductor of an electrical machine, when it will 
 be found impossible to draw a long spark from the conductor, 
 as is the case when the pointed rod is away. The continual 
 drawing which goes on in the actual case is well seen when 
 there happens to be a gap in the lightning-rod. Across this 
 gap a perfect torrent of sparks is seen to pass whenever a 
 thunder-cloud is in the neighbourhood. This is a dangerous 
 experiment even to witness ; and more than one incautious 
 experimenter has lost his life by it. 
 
 176. When a lightning-rod is acting imperfectly or when 
 there is any very rapid production of electricity, a luminous 
 glow is seen at the point. This is called St Elmo's fire, and 
 
162 ELECTRICITY. 
 
 was long ago observed on the masts of ships, and on the points 
 of their spears when soldiers were marching during a thunder- 
 storm. Quite recently a remarkable instance of the same 
 kind occurred in Switzerland, when the tops of a whole 
 forest of trees glowed just before a flash of lightning passed, 
 and immediately after were dark. 
 
 177. Back-stroke. Besides the accidents to which men and 
 animals are exposed from the direct stroke of lightning, they 
 often suffer severely, even when entirely out of the path of 
 the flash, and at a considerable distance from the point 
 where it reaches the ground. This fact has been known for 
 a long time, and arises from what is called the back or return 
 stroke. It will be readily understood from the following 
 explanation : Suppose an elongated mass of highly charged 
 cloud to be hovering near the earth, with one end over a man 
 and the other over some exposed point such as a hill-top. 
 The cloud acting inductively on the man will cause, uncon- 
 sciously to himself, a separation of the electricities in his 
 person ; the one kind being attracted to his head, and the 
 other repelled to the earth through his feet. Suppose now 
 the cloud to be discharged by a flash passing from its other 
 end to the hill-top. All inductive action on the man will 
 instantly cease, and the electricities will suddenly recombine, 
 causing the sensation of a shock more or less severe. The 
 shock from this cause is seldom fatal. 
 
 178. Thunder. The noise of thunder is just the snap of 
 the ordinary electric spark on an enormously large scale. 
 When a flash of lightning pierces through the air, its heat 
 causes a sudden dilatation of the air in its track. This is 
 succeeded immediately by a sudden compression of the air 
 round the path, which again is followed by a rapid in-rush 
 of the air-particles to fill the vacuum. This explains the 
 origin of the sound. ' , When the sound is reflected repeatedly 
 from clouds, and from masses of air of different densities, 
 echoes are produced which account for the characteristic 
 rolling and reverberation often heard during thunder-storms. 
 If the flash be short, or such that the sounds from all parts 
 of its path reach the ear simultaneously, a thunderclap will 
 be heard. If the flash be long and very much zigzag, the 
 
TERRESTRIAL AND ATMOSPHERIC ELECTRICITY. 163 
 
 sounds from, the various points of its path, having different 
 distances to travel, will reach the ear in succession, and a 
 peal of thunder will be heard. 
 
 The extreme distance at which thunder is heard is not 
 very great as compared with other loud sounds. Cannon, 
 for instance, have often been heard at a distance of fifty 
 and a hundred miles, but the maximum distance at which 
 thunder is heard does not exceed nine or ten miles. This 
 is accounted for partly by the extreme variations in the 
 atmospheric density produced during a thunder-storm. It is 
 usual to allow five seconds to the mile in estimating the 
 distance of a thunder-cloud by the interval of time which 
 elapses between the flash and the sound ; but instances have 
 occurred where the sound of thunder has been propagated 
 far faster than ordinary sounds. Probably the true explana- 
 tion of this has been given by Sir William Thomson, who 
 has shewn that very likely sound is produced simul- 
 taneously at all parts of the air between the discharging 
 cloud and the ground. 
 
 179. Origin of Atmospheric Electricity. The source or 
 sources of atmospheric electricity are still involved in com- 
 plete uncertainty. One source usually named is the elec- 
 tricity produced by the evaporation of water, and another 
 the chemical actions going on in all vegetable growth. 
 Both of these may have some effect ; but the true cause is 
 only to be got by a carefully arranged set of experiments on 
 a large scale. In connection with this subject, certain facts 
 are of great importance ; such as the fact that cloud-capped 
 mountains have been seen luminous in the dark, and that 
 active volcanoes throw out vapour and smoke which emit 
 lightning flashes. An analogous fact of extreme importance 
 has lately been reported by an observer in Galway. He 
 states thas he has often seen in the spring-time small clouds, 
 evidently highly charged with electricity, start from the 
 hill-tops of Connemara, and discharge shortly after, sometimes 
 into a neighbouring church spire, and sometimes into the 
 sea. 
 
164 
 
 Part III-CURRENT ELECTRICITY. 
 
 CHAPTER XIII. 
 
 ELECTRO-MOTIVE FORCE, CURRENT, RESISTANCE, AND 
 ELECTRICAL UNITS. 
 
 180. Hitherto we have had to deal with Electricity either 
 as fixed on the surface of non-conductors, or as rigidly in 
 equilibrium on the surface of conductors, so that it had no 
 tendency to pass from one part of the conductor to another. 
 We now come to the consideration of the various phenomena 
 which accompany the transference of electricity from one 
 body to another. This forms a different branch of the 
 science, and is variously called Galvanism, Voltaic Electricity, 
 Dynamic Electricity, Electro-ldnetics, or simply Current Elec- 
 tricity. It took its origin in 1780 from an observation made 
 by Galvani, professor of anatomy in Bologna. While making 
 investigations on the nervous irritability of cold-blooded 
 animals, Galvani discovered by accident that the limbs of a 
 recently killed frog, when hung by the crural nerve on a metal 
 support near an electric machine, contracted convulsively at 
 the recurrence of each spark. This he properly accounted 
 for on the principle of the lack-stroll (sect. 177). Six years 
 afterwards, in experimenting on atmospheric electricity with 
 frog limbs as delicate electroscopes, he obtained also acci- 
 dentally the same convulsions by bringing the copper hook 
 on which the nerve hung and the limb itself simultaneously 
 in contact with an iron railing. Galvani attributed these 
 effects to electricity in the limb itself. Volta, on the other 
 hand, in 1792, after carefully repeating these experiments, 
 and making many additional ones on the same subject, came 
 to the conclusion that the convulsions were due to electricity 
 produced at the surface of contact of the heterogeneous 
 metals. In beginning this part of the subject, we must first 
 
CURRENT ELECTRICITY. 165 
 
 get clear ideas about the terms electro-motive force, current, 
 and resistance. 
 
 181. Electro-Motive Force, Current, Resistance. If two insu- 
 lated bodies, A and B, at the same potential, be joined by a 
 conducting wire, no electricity will pass between them ; but 
 if the potential of A be greater than that of B, part of the 
 electrification of A will pass to B, and their potentials will 
 become immediately equalised. This is analogous to the 
 case of two reservoirs of water connected by a pipe. If the 
 two be at the same level, no water will run through the 
 pipe ; but if one be higher than the other, a current will flow 
 through the pipe till the level of the water in both be the 
 same. It will make the matter clear if we calculate for a 
 particular case the fall of A's potential, and the quantity of 
 electricity transferred from A to B. Let then A and B be 
 two insulated spheres of radii a and b respectively. Also let 
 A denote the potential of A, and B that of B. Then, since 
 the capacity of a sphere is equal to its radius (sect. 130), the 
 quantity of electricity on A will be Aa, and on B, B&. Let 
 them now be joined by a fine wire, so as to equalise the 
 potential, and let the common potential be V. Since elec- 
 tricity obeys the law of continuity, or, in other words, 
 behaves like an incompressible fluid, the joint charge on 
 both balls will be the same as before. This give? 
 
 Therefore V = (1). 
 
 Therefore the fall of A's potential being A V, is equal to 
 
 Also the quantity of electricity transferred from A to B being 
 equal to 
 
 Aa Va = (A V) a = al) (A B) (3). 
 
 From this we see that, other things being the same, the 
 quantity of electricity transferred depends upon the differ- 
 ence of potential A B. This difference is called the electro- 
 
166 ELECTRICITY. 
 
 motive force acting between A and B, and is clearly equal to 
 the amount of work which would be required to carry a unit 
 of negative electricity from A to B against the electrical 
 attraction. 
 
 In the case supposed, the transference of electricity would 
 take place in a time so short as to be altogether inappreci- 
 able, and we would have a transient current. It would also 
 evidently be an ever-weakening current, inasmuch as the 
 difference of potential is continually getting less ; and to 
 render the current steady, it would be requisite to have some 
 means of keeping the difference of potential between A and 
 B constant. This is the function of the voltaic battery, 
 different forms of which will be described later. 
 
 Supposing a steady current to be maintained by some 
 means between A and B, we have next to inquire as to the 
 direction and strength of such a current. The direction is 
 denned by saying that the current always flows from places 
 of high to places of low potential ; but it must be kept in 
 mind that this is a mere convention, and that there is no 
 reason, experimental or other, for saying, in the case sup- 
 posed above, that positive electricity flows from A to B, any 
 more than that negative electricity flows from B to A. 
 According to Weber's hypothesis, a current consists of equal 
 quantities of positive and negative electricity passing in 
 opposite directions through the same conductor. 
 
 By the strength of the current between A and B is meant 
 the quantity of electricity which flows through any section of 
 the connecting-wire in a unit of time. If we denote the 
 strength by C, and employ the electro-static system of 
 measurement, then C is measured by the number of electro- 
 static units of electricity which passes any section of the wire 
 in a second. The value of C is found to depend not only 
 upon the electro-motive force A B, but also upon the 
 material of which the wire is composed, being greater for 
 good and less for bad conductors of electricity. This is 
 shewn as follows : Let two points, A and B, be kept at a 
 constant difference of potential, so that a steady current, C, 
 flows from A to B along a wire joining the two. Also let 
 this wire be homogeneous, and at the same temperature 
 
CUBRENT ELECTRICITY. 167 
 
 throughout. At any two points of this connecting- wire join 
 on two other wires of the same material, and lead them to 
 an electrometer. The electrometer will indicate a certain 
 difference of potential, denoted, let us suppose, by E. Now, 
 if we take the ratio of E to C for all pairs of points on the 
 wire, and also for wires of different thicknesses, we find that 
 it varies directly as the length of wire between the two 
 points and inversely as its cross section. ' If we put this in 
 the form of an equation, calling I the length and to the 
 
 E kl 
 section of the wire, we get -~ = , where Jc is a constant 
 
 Cy (l) 
 
 depending on the material of the wire. This quantity 
 , which depends only upon the length, section, and mate- 
 rial of the connecting wire, is called its resistance, and is 
 
 pi 
 usually denoted by E. This gives ^r = E, an expression of 
 
 great importance in electrical science, and which is called, 
 after its discoverer, Ohm's Law. 
 
 182. Absolute Electrical Units. In any absolute system of 
 measurement, all quantities must be expressed in terms of 
 the fundamental units of length, mass, and time. In elec- 
 trical measurements, the fundamental units usually adopted 
 by scientific men, as being the most convenient, are the 
 centimetre, gramme, and second ; and quantities expressed in 
 terms of these are said to be expressed in terms of the 
 C. G. S. system of units. From the fundamental units two 
 other systems of electrical units are derived. These are the 
 electro-static and the electro-magnetic systems ; the former 
 being founded upon the electro-static definition of the unit 
 quantity of electricity, and the latter upon the definition of 
 the unit magnetic pole. 
 
 The C. G. S. system of units has already been alluded to 
 in Chapter V., and the definitions of the units of velocity, 
 acceleration, momentum, force, work, &c. are there given. 
 
 183. Electro- static System of Units. According to this 
 system, we have the following definitions of units : 
 
 (1) Unit quantity of electricity is that which repels a 
 similar unit quantity at unit distance with unit force. 
 
168 ELECTRICITY. 
 
 (2) Unit current is that which conveys a unit quantity of 
 electricity through a conductor in a second. 
 
 (3) Unit electro-motive force, or unit difference of potential 
 between two points is the work done on or by a unit of 
 positive electricity, in moving from the one to the other 
 against the electrical resistances. 
 
 (4) Unit resistance is that of a conductor through which 
 unit electro-motive force between its ends can send a unit 
 current. 
 
 (5) Unit capacity is that of a condenser which contains 
 unit quantity when charged to unit difference of potential. 
 
 184. Effect of an Electric Current upon a Magnet. Before 
 giving the electro-magnetic system of units, it will be neces- 
 sary to explain an important magnetic effect produced by an 
 electric current in the space surrounding the wire through 
 which it flows. This was discovered by Oersted, and is the 
 effect upon which depends the construction of the instru- 
 ments commonly used for measuring electric currents. It is 
 this. If a magnetic pole be in the neighbourhood of a con- 
 ductor carrying a current, it will be acted upon by a force 
 whose magnitude depends upon the strength, and whose 
 direction depends upon the direction of the current. To 
 explain more fully, let AB (fig. 86) be a portion of a 
 
 Fig. 86. 
 
 straight wire conveying a current in the direction of the 
 arrow, and let m be the north pole of a magnetic needle ; 
 then the effect of the current on m is such that m will move 
 round the wire in the circumference of a circle whose centre 
 
CURRENT ELECTRICITY. 169 
 
 is at the wire, and whose plane is perpendicular to the wire. 
 The direction in which m moves is shewn by the arrow, and 
 can in all cases be determined by the following simple rule. 
 Suppose a cork-screw being screwed into a cork in the direc- 
 tion in which the current flows, then a north pole will move 
 round the wire in the direction in which the hand is turned 
 to put in the screw. A south pole will move in the opposite 
 direction ; and hence it is easy to see that if a magnetised 
 needle be freely suspended near the wire, it will always set 
 itself so as to be at right angles to the wire when in a posi- 
 tion of equilibrium. 
 
 The force of the current upon the magnetic pole is found 
 experimentally to be independent of the material of the 
 conductor, and to be strictly proportional to the current 
 strength ; and hence the reason why this effect is made use 
 of in the construction of galvanometers or measurers of 
 current strength. In what follows, we shall suppose our- 
 selves in possession of a galvanometer whereby currents may 
 be detected and measured. The theory and construction of 
 the instrument will be given in Part IV., after the pheno- 
 mena of electro- magnetism have been explained. 
 
 185. Electro-magnetic System of Units. Keeping in mind 
 the effect just explained, we can understand the following 
 definitions of units in the electro-magnetic system : 
 
 (1) Unit magnetic pole is that which repels a' similar unit 
 pole at unit distance with unit force. 
 
 (2) Unit current is one which in a wire of unit length, bent 
 so as to form an arc of a circle of unit radius, would act upon 
 a unit pole at the centre of the circle with unit force. 
 
 (3) Unit quantity of electricity is the quantity which a 
 unit current conveys in a unit of time. 
 
 (4) Unit electro-motive force is that which must be main- 
 tained between the ends of a conductor in order that unit 
 current may do unit of work in a second. 
 
 (5) Unit resistance is that of a conductor in which unit 
 current is produced by unit electro-motive force between its 
 ends. 
 
 (6) Unit capacity is that of a condenser which will be at 
 unit difference of potential when charged with unit quantity. 
 
170 ELECTRICITY. 
 
 It is of great importance that the student should have 
 clear ideas regarding the various units in terms of which the 
 quantities he is considering are measured. We give here, for 
 the sake of reference, in a collected form, the dimensions of 
 the various units, shewing, at the same time, how the 
 dimensions of the one are derived from those of the other 
 by simple algebraic changes. 
 
 186. Dimensions of Units. The meaning of the term dimen- 
 sions will be best understood from a few examples. Thus : 
 
 A line is said to be of one dimension. 
 
 An area being equal to a length X a breadth, that is, the 
 product of two lines, is said to be of two dimensions. 
 
 A volume being equal to a length x a breadth x a thick- 
 ness, is said to be of three dimensions. 
 
 A velocity being equal to -^^ - == = == LT' 1 , is said to be 
 
 of one dimension in length and 1 dimension in time. 
 
 According to Clerk-Maxwell's notation, the concrete unit 
 in terms of which any quantity, whose numerical value is X, 
 is measured, is represented by being inclosed in a square 
 bracket, thus [X] ; and the whole quantity is represented 
 by X [X], where X represents the number which specifies 
 how many times over the unit is taken. 
 
 FUNDAMENTAL UNITS. 
 
 These are the units of length, mass, and time, and are 
 represented respectively by [L], [M], [T]. 
 
 DERIVED MECHANICAL UNITS. 
 
 Velocity is equal to the length gone over in a unit of time. 
 Hence, denoting it by V, we have 
 
 V =4 = LT-'. 
 
 Hence V [V] = LT' 1 [LIT 1 ] 
 
 /. [V] = [LT->] (1). 
 
 Acceleration is equal to the velocity acquired in a unit of 
 time. Hence, denoting it by A, we have 
 
 A = =VT- 1 
 
CURRENT ELECTRICITY. 171 
 
 Hence A [A] = VT' 1 [VT~ 1 ]. 
 
 Substituting for [V] its value from (1), 
 
 we have [A] = [UT 2 ]* (2). 
 
 Hence acceleration is of 1 dimension in length and 2 
 dimensions in time. Similarly all the following equations 
 are to be interpreted. 
 
 Momentum is equal to mass multiplied by velocity. 
 Hence 
 
 [Momentum] = [MV] = [MLT' 1 ] from equation (1) (3). 
 
 Force is equal to momentum generated in a unit of time. 
 Hence, denoting it by F, we have 
 
 [F] = = [MVT->] = [MLT 2 ] (4). 
 
 Work is equal to force multiplied by the length through 
 which it is overcome. Hence, denoting it by W, we have 
 [W] = [FL] = (equation 4), [ML 2 T- 2 ] (5). 
 
 DEBIVED ELECTKO-STATIO UNITS. 
 
 If Q and Q' be two quantities of positive electricity 
 separated by a distance L, the force of repulsion between 
 
 Q(Y 
 
 them is, by Coulomb's law, -y^- Denoting this force by F, 
 we have 
 
 _QQ' 
 
 Hence 
 
 ... [F] = [Q 2 L- 2 ] 
 
 ... [Q] = [FL 2 ] = (equation 4) [MLT- 2 ]. 
 
 By extracting the square root, that is, dividing each index 
 by 2, we get 
 
 [Q] = [M4LIT- 1 ] (6). 
 
 * For shortness in what follows, we shall sometimes omit writing the letters 
 which precede the square brackets, and which stand for numbers. It must 
 be evident, from the examples already given, how they are to be inserted if 
 required. 
 
172 ELECTRICITY. 
 
 Current of electricity is equal to the quantity which flows 
 through any section of the conductor in a unit of time. 
 Denoting it by C, we get 
 
 = (equation 6) [MLT-] (7). 
 
 Electro-motive force is the work done on a unit of electricity 
 in urging it from one point to another. Hence, denoting it 
 by E, and if Q be the quantity moved, we have 
 W = EQ 
 
 pi 
 
 E = . Hence 
 
 m rE-i 
 
 [R] = Lc J = 
 
 = [L->T] (9). 
 
 The capacity of a condenser is the quantity of electricity 
 required to charge it to unit difference of potential Denoting 
 it by K, we have 
 
 Q = KE 
 
 c 
 
 = [L] (10). 
 
 This shews that capacity is of the dimensions of a line, and 
 this agrees with a result formerly found, viz., that the 
 capacity of a sphere is equal to its radius (sect. 130). 
 
 DERIVED ELECTRO-MAGNETIC UNITS. 
 
 | 
 
 If two similar magnetic poles, of strength m and m', be 
 separated by a distance L, the repulsive force between them 
 
 is - . Denoting it by F, we have 
 
CURRENT ELECTRICITY. 173 
 
 Hence [F] 
 
 .-. [m 2 ] = [L 2 F] = [L 3 MT- 2 ]. 
 
 .-. [m] = [LtMiT' 1 ] (11). 
 
 If a current of strength C, flow in a wire of length L, every 
 part of which is at distance d from a magnetic pole of 
 strength m, the force exerted by the current on m is 
 
 CLm 
 
 Hence 
 
 (12). 
 
 If Q be the quantity of electricity conveyed by a current 
 C, in time T, 
 
 Q = CT 
 .-. [Q] = [CTJ = [LTO] (13). 
 
 If E be the electro-motive force between .the ends of a 
 conductor, and Q the quantity sent through it, the work done 
 is EQ. Hence, 
 
 [W] 
 
 [LIM4T- 2 ] (14). 
 
 Tjl 
 
 Resistance, E = ^ . 
 
 = [LT-]= (15). 
 
 From the last equation, we see that the dimensions of 
 resistance are the same as those of a velocity. It will be 
 shewn later how a resistance can be expressed as a velocity. 
 
174 ELECTRICITY. 
 
 If we take the two expressions for [Q] given according to 
 the electro-static and the electro-magnetic systems of units, 
 and divide the one by the other, we shall obtain the dimen- 
 sions of the ratio of the electro-static to the electro-magnetic 
 unit of quantity. Doing this, we obtain 
 
 [E.S. unit of Q] _ rMlMT-'-i _ ^.^ , 6) 
 
 [E.M. unit of Q] 
 
 This shews that the ratio of the electro-static to the electro- 
 magnetic unit of quantity is a velocity. This velocity is a 
 very important physical quantity, and is usually denoted 
 by v. Different experimental methods of obtaining it will 
 be described later, and it will also be shewn that, according 
 to Clerk-Maxwell's Electro-magnetic Theory of Light, v is 
 very probably the actual velocity of light. 
 
 PKACTICAL ELECTKICAL UNITS. 
 
 187. The absolute units of electro-motive force and re- 
 sistance are so small, and those of quantity and capacity so 
 large, that the quantities with which the practical electrician 
 has to deal, would, if expressed in them, be represented either 
 by inconveniently large numbers or inconveniently small 
 fractions ; and hence a practical system of units has been 
 adopted which are certain multiples or submultiples of the 
 absolute units. These are derived from the absolute electro- 
 magnetic units by assuming a larger unit of length and a 
 smaller unit of mass. The large unit of length assumed 
 is 10,000,000 metres, or approximately the length of the 
 
 earth's quadrant, and the small unit of mass is the 
 
 part of a milligramme. The practical units have been name^d 
 after several eminent electricians. They are as follows : 
 
 The Weber, the practical unit of quantity = T V C. G. S. 
 unit. 
 
 The Volt, the practical unit of electro-motive force = 10 8 
 C. G. S. units. 
 
 The Oh/m, the practical unit of resistance = 10 9 C. G. S. 
 
 It will be shewn later that the Ohm is equal to a velocity 
 of 10,000,000 metres per second. 
 
CURRENT ELECTRICITY. 175 
 
 The Farad, the practical unity of capacity = 10~ 9 C. G. S. 
 unit. 
 
 The Microfarad = one-millionth of a Farad, is very 
 commonly used as the practical unit of capacity. 
 
 The practical unit current is that of one weber per second. 
 The weber is equal to the quantity of electricity transmitted 
 through one ohm by one volt, and is also equal to the 
 charge produced in a condenser of one farad capacity by the 
 electro-motive force of one volt. The following multiples 
 and submultiples of the practical units are also in use in 
 telegraph working. 
 
 The megavolt = one million volts, 
 it megafarad = \\ n farads. 
 ii megohm = M n ohms, 
 ii microvolt = one millionth of a volt, 
 it microfarad = n n farad, 
 
 it microhm = n n of an ohm. 
 
 CHAPTEE XIV. 
 VOLTAIC BATTERIES. 
 
 188. Having explained the terms electro-motive force, current, 
 and resistance, we come next to consider some of the methods 
 in common use of maintaining a constant electro-motive force 
 between two bodies, and so producing a steady current in the 
 connecting wire which joins them. In static electricity we 
 have already had an example of one such method, in the 
 continued flow of sparks which are drawn from the prime 
 conductor of an ordinary friction-machine, or, better still, in 
 the continuous discharge which takes place between the balls 
 of the Holtz machine. By far the most convenient method, 
 however, of producing a steady current is got from the voltaic 
 pair or cell. 
 
 189. Voltaic Cell. When two plates of copper and amalga- 
 mated zinc (zinc whose surface has been rubbed over with 
 mercury) are placed in a vessel (fig. 87) containing water to 
 which a small quantity of sulphuric acid has been added, they 
 
176 ELECTRICITY. 
 
 remain apparently unaffected, so long as they are kept from 
 touching each other, either within or without the liquid. If, 
 however, they be made to touch, bubbles of hydrogen gas are 
 formed in abundance at the copper plate, and their formation 
 continues until the plates are again separated. If the contact 
 be maintained for some time, and the plates and liquid be 
 afterwards examined, it is found that the copper plate weighs 
 
 Fig. 87. 
 
 exactly the same as before, that the zinc plate has lost in 
 weight, and that the liquid contains the lost zinc in solution 
 in the form of the sulphate of that metal. The chemical 
 action which goes on is represented by the equation H 2 S0 4 -{- 
 Zn = ZnS0 4 + H 2 . The contact need not be affected by the 
 plates themselves. If wires of copper, or any other conductor 
 of electricity, be soldered to the plates, or fixed to them by 
 binding screws, and be made to touch, the changes just 
 mentioned take place as if the plates were in contact. When 
 the wires are thus joined, and, so to speak, form one con- 
 necting wire between the plates, a steady current flows 
 in them, and they exhibit very peculiar properties, which 
 
VOLTAIC BATTERIES. 177 
 
 will be described in their order later on. One such property 
 has already been alluded to (sect. 184). 
 
 190. When a number of copper and zinc pairs, similar to 
 the one just referred to, are put together, so that the copper 
 plate of one cell is placed in conducting connection with the 
 zinc plate of the next, in the manner shewn in fig. 88, they 
 constitute a voltaic battery. The term battery is sometimes 
 also applied to a number of cells acting as one combination, 
 in whatever way they may be connected, and sometimes even 
 to one cell. When the terminal copper and zinc plates 
 (fig. 88) are connected, the current runs from each copper to 
 each zinc plate without the liquids, and from each zinc to 
 
 Fig. 88. 
 
 each copper plate within the liquids ; and when the contact 
 is broken, the zinc pole shews +> and the copper pole E. 
 The voltaic battery thus put up acts in all respects as a 
 compound voltaic pair, and constitutes a compound voltaic 
 circuit. If two cells be taken, the difference of potential is 
 doubled ; if three, tripled ; and so on. The electro-motive 
 force of a, battery is therefore proportional to the number of cells, 
 supposing, of course, that they are arranged consecutively, as 
 in the figure. 
 
 The four cells in fig. 88, as stated, form a compound voltaic 
 circuit. They may be made to form also a simple circuit. 
 If all the zincs were connected with one wire, and all the 
 coppers with another, and the circuit completed by one wire, 
 
178 
 
 ELECTRICITY. 
 
 then the four cells would act in every respect as one cell, 
 whose plates had four times the surface. A battery, such as 
 in the figure, would be said to have a tension arrangement ; 
 a battery like the one named, a quantity arrangement. 
 
 191. Volta's Pile is shewn in fig. 89. It consists of a number 
 
 of circular plates, each made up of a plate 
 of copper and a plate of zinc soldered 
 together, built up, so that the copper 
 plates face one way and the zinc the other ; 
 each compound plate being separated by 
 a circular piece of woollen cloth, moistened 
 with a solution of common salt or dilute 
 sulphuric acid. In consequence of the 
 great number of pairs, the difference of 
 potential of the poles of Volta's pile is 
 considerable. One furnished with from 
 60 to 100 plates can charge an electroscope 
 without the condensing plates. It is from 
 this battery that the term ' pile ' is applied 
 to the voltaic battery. Volta used 
 another form of battery, which he called 
 a crown of cups. This consisted of a 
 Fig. 89. number of cells like those in fig. 88, 
 
 arranged in a circle, so that the first and last were 
 
 contiguous. 
 
 192. Zamboni's Dry Pile consists of several hundreds, and 
 sometimes thousands, of discs of paper tinned on one side, 
 and covered with binoxide of manganese on the other, put 
 together consecutively, as in Volta's pile, and placed under 
 pressure in an insulating glass tube closed with brass ends, 
 which serve as the poles. The difference of potential of the 
 poles of this arrangement is considerable, but the strength of 
 the current which passes when the poles are joined is next to 
 nothing. The most important application of the dry pile is 
 in the construction of a very delicate electrometer or electro- 
 scope, which is named after its inventor, Bohnenberger's electro- 
 meter (sect. 165). In this instrument the dry pile is insu- 
 lated, and its ends are placed in conducting connection with 
 insulated wires, which are bent round so as to face each other. 
 
VOLTAIC BATTERIES. 179 
 
 The wires end in small faces, which thus constitute the poles 
 of the pile. A gold leaf is hung between the poles, and 
 turns to the one or the other according as it is charged. 
 As we know the names of the poles, we know at once the 
 name of the electricity with which the leaf is charged, as 
 it must incline toward the opposite electricity. 
 
 193. The Galvanic Trough, introduced by Cruikshank, is a 
 
 Fig. 90. 
 
 trough (fig. 90) into which rectangular plates of copper and 
 zinc, like those of Volta's pile, are fixed, the cells included 
 between each pair being filled with dilute sulphuric acid. 
 The inner surface of the trough is coated with an insulating 
 substance. 
 
 194. Wollastoris Battery. Each couple of this battery (fig. 
 91) is made up of a plate of copper, doubled up so as to 
 include a plate of zinc, from which it is kept apart by 
 strips of wood. Both faces of the zinc are thus equally 
 exposed to chemical action, a device by which the quantity 
 of electricity is increased. Fig. 92 shews a battery of five of 
 these. The connecting strips of metal are fixed to a wooden 
 rod, by which they can be lifted or lowered together. When 
 the battery is put in action, the whole is lowered, and the 
 five couples are immersed in five troughs filled with dilute 
 sulphuric acid (1 of the acid to 12 of water). When out of 
 action, the whole is lifted and fixed by binding screws to the 
 two supporting pillars. When the number of pairs is small, 
 as in the figure, it is of little consequence whether one large 
 trough or five small ones be used. 
 
 195. Smee's Battery. In Sniee's couple, the position of the 
 
 L 
 
180 
 
 ELECTRICITY. 
 
 plates of Wollaston's couple is reversed. It consists of a 
 silver plate, with, a zinc plate on either side, kept separated 
 from it by slips of wood, the two zinc plates being fastened 
 by a coupling. There are thus two + plates to one , in- 
 stead of two to one +, as in Wollaston's couple. The 
 zinc plates have not thus to be so often renewed as in 
 Wollaston's battery. The silver plate is platinised that is, 
 covered over with finely-divided platinum and this is 
 found to lessen the adhesion of the hydrogen bubbles to 
 
 Fig. 91. 
 
 Fig. 92. 
 
 the plate, thereby greatly improving the constancy of the 
 action. Smee's battery has the same arrangement as 
 Wollaston's. 
 
 196. Grove's Gas Battery. This battery is intended more for 
 instruction than use. One of its cells is shewn in fig. 93. 
 Into the two outer necks of a three-necked bottle, two glass 
 tubes are fitted by means of corks through which they pass. 
 Each of these tubes is open below, and a platinum wire enters 
 them hermetically above ; and to this wire a long strip of 
 platinum is soldered, extending nearly to the bottom of the 
 tube. Little cups, containing mercury, stand at the upper 
 ends of these wires. The whole apparatus is filled with slightly 
 
VOLTAIC BATTERIES. 
 
 181 
 
 acid water, and the poles of a voltaic battery are placed in 
 the little cups. Water is thereby decomposed : oxygen forms 
 in the one tube and hydrogen in the other. When the battery 
 wires are removed, no change takes place till metallic connec- 
 tion is established between the cups, and the oxygen and hydro- 
 gen gradually disappear, attended by an 
 electric current which passes from the 
 oxygen to the hydrogen. When several 
 of these are put together in a battery, 
 the connection being always oxygen to 
 hydrogen, they can decompose water. 
 The most important fact illustrated by 
 Grove's battery is, that the oxygen and 
 hydrogen, liberated by galvanic agency, 
 when left to themselves, produce a 
 current the opposite to that which 
 separated them. When the poles of 
 the decomposing battery are in the 
 mercury cups, hydrogen is given off 
 at the , and oxygen at the + 
 pole ; and as opposite electricities 
 attract, it is manifest that the hydro- 
 gen in this action is +, and the 
 oxygen . When the two gases form, 
 by means of the platinum plates, 
 a galvanic pair by themselves, the 
 current must proceed, as in all cases, 
 from the -j- to the within the liquid, and the reverse 
 way between the poles ; but this is the opposite of the 
 direction of the original current. 
 
 Polarisation Constant Batteries. It is therefore manifest 
 that where oxygen or hydrogen is set free at any point in a 
 voltaic circuit, it will tend to send a counter-current. This 
 tendency is called polarisation of the electrodes. This accounts 
 for the fact, that no single cell can decompose water, as 
 the electro-motive force generated is no greater than that of 
 the counter-current which would be produced by the liberated 
 gases. Even two cells produce an insignificant effect. Polar- 
 isation also accounts for the sudden falling off in strength in 
 
 Fig. 93. 
 
182 
 
 ELECTRICITY. 
 
 all voltaic couples where hydrogen is set free at the negative 
 plate. The bubbles of the gas adhering to the plate, not only 
 lessen the surface of contact between the plate and the liquid, 
 but exert an electro-motive force contrary to that of the pair, 
 and this goes on increasing until the action becomes greatly 
 reduced. In all improved forms of the cell, it therefore 
 becomes necessary to adopt some means of preventing the 
 disengagement of hydrogen at the negative plate, and this 
 is done in all constant batteries by employing two fluids 
 instead of one. The best known constant batteries are those 
 of Daniell, Grove, and Bunsen. 
 
 197. Daniell's Battery. A cell of this battery is shewn in 
 fig. 94, and a section of it in fig. 95. The containing vessel, 
 
 Fig. 94. 
 
 Fig. 95. 
 
 c, is of copper, which serves likewise as the negative element 
 of the pair. Inside of this is another vessel, d, of porous 
 unglazed earthenware containing a rod of zinc, z. The space 
 between the copper and the porous cell is filled with a 
 solution of the sulphate of copper, which is kept concen- 
 trated by crystals of the salt lying on a projecting shelf, s, 
 and dilute sulphuric acid is placed with the zinc in the 
 porous cell. The rationale of its action is given as follows : 
 The porous cell which keeps the fluids from mingling does 
 
VOLTAIC BATTERIES. 183 
 
 not hinder the passage of the current ; when the atoms 
 of hydrogen that would ultimately be freed at the copper 
 reach the porous cell, they displace the copper in the 
 sulphate of copper, and copper instead of hydrogen is 
 thrown on the copper plate. The chemical rationale of the 
 action may be given by the following equations. Begin- 
 ning with the copper (Cu) of the outer vessel, and ending 
 with the zinc (Zn) of the rod, and taking | d for diaphragm or 
 porous cell, we have the arrangement before discharge 
 Cu,CuS0 4 CuS0 4 | d H 2 ,S04 H^SO 4 Zn ; and after it, CuCu 
 S0 4 Cu S07TH 2 S0 4 ,H 2 S0 4 Zn. The discharge, therefore, 
 effects a deposition of copper at the copper, and the forma- 
 tion of sulphuric acid at the porous cell, and of sulphate of 
 zinc at the zinc rod. Instead of hydrogen in its nascent 
 state being deposited at the copper, we have copper in the 
 same condition ; but the polarisation caused by the latter is 
 very much inferior to that resulting from the former, and 
 hence the superior electro-motive force of DanielPs cell. The 
 porous cell keeps the sulphate of zinc from reaching the 
 copper, and thus obviates another source of diminished force 
 in the one-fluid battery. The sulphate of zinc once formed, 
 is itself subjected to the decomposing action of the pile, and 
 zinc is deposited on the copper plate, thus tending to give a 
 zinc-zinc instead of a copper-zinc pair. The constancy of 
 Daniell's battery is not unlimited, for the sulphate of zinc 
 which results from the action, being a bad conductor of elec- 
 tricity, enfeebles the current. From its great specific gravity, 
 however, it falls to the bottom of the cell, and may be re- 
 moved by a siphon, and replaced by fresh liquid. The copper 
 of the Daniell's cell is frequently also placed inside the 
 porous vessel, as the platinum in Grove's celL A battery of 
 Daniell's cells is put up in the usual way. 
 
 198. Various Forms of Daniell's Cell Many modifications 
 of Daniell's cell are in use in practical working. The chief 
 of these are the sawdust Daniell and Tray cell, both due to Sir 
 William Thomson. In the sawdust Daniell, sawdust is 
 made to play the part of the ordinary porous cell. On the 
 bottom of a wide glass vessel is placed a copper plate, to the 
 
184 ELECTRICITY. 
 
 edge of which a gutta-percha covered wire is attached, which 
 comes up the side of the vessel and serves as the positive 
 pole. On the top of the copper is placed a layer of moistened 
 crystals of sulphate of copper, and above this a layer of wet 
 sawdust. On the top of this again is spread another layer 
 of sawdust moistened with solution of sulphate of zinc, and 
 on the top of all rests the zinc plate, to which a wire is 
 attached forming the negative pole. This cell is very con- 
 venient when portability is required, and was much used by 
 Sir William Thomson during the laying of the Atlantic 
 cable. The element called Menottis's is precisely similar to 
 the sawdust Daniell. 
 
 The Tray Cell consists of a square wooden tray twenty 
 inches long, lined with sheet-lead, on which a layer of 
 copper is deposited by the electrotype process. The zinc 
 plate is made in the form of a grating, to allow the gas to 
 escape, and is supported on blocks of wood at the four corners 
 of the tray. Sometimes the space between the copper and 
 zinc is filled exactly as in the sawdust Daniell. In other 
 cases a sheet of parchment is stretched below the zinc 
 grating, and then the copper solution is supplied from 
 crystals of sulphate of copper lying all round the edge of the 
 tray, while the solution of sulphate of zkic is poured in 
 between the zinc and parchment. The resistance of this cell 
 is very small, being only *2 ohm. When a strong current is 
 wanted, a number of trays are put the one on the top of the 
 other, the zinc of the one below being in metallic contact 
 with the copper of the next above it. 
 
 199. Grove's Battery consists of platinum-zinc couples. Fig. 
 96 shews an excellent arrangement of a cell of it. The outer 
 cell of glass, g, is filled with dilute sulphuric acid (1 part of 
 acid to 8 of water), in which a cylindrical plate of zinc, z, is 
 immersed. Inside the zinc is a porous cell, d, containing 
 concentrated nitric acid and the platinum plate, p, which is 
 bent into the form of an S (fig. 97), to increase its surface. 
 In the commonly used form of Grove's cell, the zinc plate is 
 made in the form of a U, and incloses a flat porous cell in 
 which is suspended a strip of platinum foil, attached to 
 the zinc plate by a binding screw. Grove's couple is very 
 
VOLTAIC BATTERIES. 185 
 
 much superior in power to any of the preceding, though 
 it is inferior in constancy to Daniell's. When the poles 
 are joined, sulphate of zinc is formed in the outer cell, 
 and the heavy brown gas, peroxide of nitrogen (N 2 4 ), 
 is given off by the nitric acid. As this gas is injurious 
 to the health when breathed for any time, the porous cell is 
 closed with a stopper of wood to prevent or lessen its escape, 
 the connection between the exterior and the platinum plate 
 
 Fig. 96. Fi. 97. 
 
 being made by a strip of inetal passing through the wood. 
 The chemical action of Grove's couple may be shewn in the 
 same way as Daniell's, taking anhydrous nitric acid (N 2 6 ) to 
 be the oxide of the peroxide of nitrogen (N 2 4 ,O). Before 
 discharge, the molecules stand thus, beginning with the plat- 
 
 inum : Ft, Kfi^O N 2 4 ,Q | d H^SO^SO^ Zn ; and after it, 
 
 ; | d H 2 SO^H 2 S0 4 ,Zn. The peroxide of 
 nitrogen discharged at the platinum plate is absorbed by the 
 nitric acid, in which it is soluble, so that the plate is left free. 
 The resulting solution is highly conducting. The peroxide 
 of nitrogen soon spontaneously separates from the nitric acid, 
 giving rise to the dark-brown vapour already mentioned. The 
 cells of a Grove's battery are connected with the platinum of 
 the one to the zinc of the other. 
 
186 ELECTRICITY. 
 
 200. Bunsen's Battery. Bunsen's cell has the same chemical 
 action as Grove's, the platinum being replaced by carbon. 
 There are two forms of the cell the one invented and 
 employed by Professor Bunsen, and generally adopted in 
 Germany ; and the modification introduced by Archerau, 
 generally found in England and France. The Bunsen cell, 
 properly so called, has a carbon cylinder immersed in nitric 
 acid, and the porous cell containing the zinc and sulphuric 
 acid placed within it. Fig. 98 represents a battery of four 
 
 Fig. 98. 
 
 cells, shewing how the different cells are connected : g is the 
 containing glass vessel ; c, the carbon cylinder ; d, the porous 
 cell ; and , the zinc. The other form of the Bunsen cell is 
 shewn in fig. 99. In it the same arrangement is adopted as 
 in Grove's cell. Bunsen's battery, in point of cheapness, 
 is preferable to Grove's, where the platinum forms an ex- 
 pensive item, but is inferior to it in point of compactness. 
 
 Bunsen Goke. The carbons for Bunsen's battery are made 
 by a process invented by Bunsen. The fine dust of coke 
 and caking coal is put into a close iron mould of the shape 
 required for the carbon, and exposed to the heat of a furnace. 
 When taken out, the burned mass is so porous as to be unfit 
 for use, but by repeatedly soaking it in thick syrup, or gas 
 tar, and reheating it, it at length acquires the necessary 
 
VOLTAIC BATTERIES. 
 
 187 
 
 Fig. 99. 
 
 solidity and conducting power. The carbon that forms on 
 the roof of gas-retorts is harder and better than the carbon 
 thus made, but it is difficult to work, and the supply of it is 
 limited. 
 
 201. Iron Battery. Instead 
 of platinum, iron may be used 
 with an equally good result in 
 Grove's battery. Care must be 
 taken that the nitric acid does 
 not become dilute, for in dilute 
 nitric acid the iron is violently 
 attacked. In the electro- chemi- 
 cal table, iron stands much in- 
 ferior to platinum as an electro- 
 negative metal. Its use in the 
 iron battery depends on its 
 becoming highly electro -nega- 
 tive in concentrated nitric acid, 
 or assuming, as it is called, a 
 
 passive condition. The passivity of iron can be produced in 
 various ways. It becomes so when dipped in concentrated 
 nitric acid, when heated in air or oxygen till it changes 
 colour, or when it forms the + pole in the decomposition 
 of water, where ozonised oxygen acts on it. Passive iron 
 suffers no change in dilute nitric acid, which powerfully 
 corrodes active or ordinary iron. The passivity of iron is 
 attributed to the formation on its surface of a very thin 
 layer of oxide, which is insoluble in nitric acid, and electro- 
 negative compared with active iron. Passive iron can be 
 made active by being rubbed with sand-paper, or heated in 
 hydrogen gas. If in the iron battery filled with dilute acid 
 there be any part not passive, that part forms a pair with 
 the passive part, and rapidly dissolves. When the acid is 
 concentrated, however, the surface is kept constantly passive. 
 
 202. Bichromate of Potash Cell This cell was discovered 
 by Bunsen. In it the chromic acid derived from the decom- 
 position of bichromate of potash is made use of as an oxidising 
 agent to prevent a deposit of hydrogen on the electro-negative 
 plate, and thus get rid of the counter electro-motive force of 
 
188 
 
 ELECTRICITY. 
 
 polarisation so detrimental to most forms of one-fluid cell. 
 The cell is represented in section 'dn fig. 100. A globular- 
 shaped vessel of glass, a, is taken with a long, wide, cylindrical 
 neck. Two plates of gas-carbon, c, c, parallel to each other 
 and about an inch apart, are fixed to an ebonite disc, e, which 
 closes the mouth of the glass vessel. These plates are in 
 metallic connection with each other, and with the binding 
 screw, A, which is the positive pole. A plate of zinc, z, the 
 same width as the carbon plates but 
 only half the length, is attached to a 
 brass rod, 6, which can be moved up 
 and down in the socket, s, and fixed 
 in any desired position by a pinching 
 screw. The socket, s, is in metallic 
 connection with the binding screw, 
 which is the negative pole. When in 
 its highest position, the zinc plate is 
 entirely out of the exciting liquid, and 
 the action of the cell is stopped. The 
 liquid consists of a saturated solution 
 (about 4 oz. to a pint) of bichromate 
 of potash in- dilute sulphuric acid, 
 and fills only the globular part of the 
 containing vessel. 
 
 The electro-motive force of this 
 cell is great at first, but it rapidly 
 
 declines when continuously worked through a small external 
 resistance. It rapidly recovers, however, when the cell is 
 out of action ; and hence the reason why this cell is so 
 suitable when a pretty powerful current is wanted fre- 
 quently, but for short periods. It has also the advantage of 
 being entirely free from disagreeable fumes. The chemical 
 action of the cell is represented, according to Niandet, by the 
 equation 
 
 KO,2CrO + 4S0 3 = Cr 2 3 3S0 3 + KO,S0 3 + 3 . 
 
 203. Leclanche Cell. This is, properly speaking, neither a 
 one-fluid nor a two-fluid cell, but something between the 
 two. It is represented in fig. 101. The electro-positive 
 
 Fig. 100. 
 
VOLTAIC BATTERIES. 
 
 189 
 
 element usually consists of a round rod of zinc immersed 
 in a strong solution of sal-ammoniac in water ; while the 
 electro-negative element is an ordinary porous cell, in which 
 is placed a long plate of gas-carbon packed round with a 
 mixture of binoxide of manganese and small fragments of 
 gas-carbon. The top of the porous cell is closed by a layer 
 of melted pitch, and the projecting end of the carbon plate 
 is clamped round by a piece of lead to which a binding-screw 
 is attached. The chemical action which goes on is repre- 
 sented by the equation 
 
 NH 3 HC1 + 2Mn0 2 + Zn = 
 
 ZnCl + NH 3 + HO + Mn 2 3 . 
 
 The electro-motive force of this cell is very small, but 
 permanent. By simply taking care to fill up the outside 
 cell occasionally with water, it can be kept for several years 
 always ready for use. It is in consequence much used for 
 
 Fig. 101. Fig. 102. 
 
 working electric bells and railway signals where a weak 
 current for a short time is often required. It is also very 
 suitable for working telephones with microphone trans- 
 mitters. 
 
 204. Gravitation Batteries. These are forms of the two- 
 fluid cell in which the porous cell is altogether dispensed 
 with, the solutions being kept from mixing in consequence 
 
190 ELECTRICITY. 
 
 of their difference of density. As an example, we shall 
 describe the cell devised by Sir William Thomson, and 
 which is represented in fig. 102. On the bottom of a wide, 
 shallow, c} 7 lindrical glass vessel is placed a circular plate of 
 copper, to which a gutta-percha covered wire is attached. 
 The zinc plate is in the form of a grating, and is supported 
 horizontally by lugs from the edge of the glass vessel at a 
 short distance below its mouth. A glass tube with a funnel- 
 shaped mouth is supported vertically in the centre of the 
 cell, with its lower end just in contact with the copper plate. 
 A glass siphon hangs over the edge of the containing vessel, 
 with the end of its shorter limb midway betweeen the zinc 
 and the copper plates. In charging the cell, a solution of 
 the sulphate of zinc is first poured into the glass vessel till 
 it reaches the zinc plate. Crystals of sulphate of copper are 
 then put into the central tube. These dissolve in the 
 sulphate of zinc solution, and form a solution of greater 
 density, which in consequence spreads over the copper plate. 
 It is evident that, if the cell be kept still, the solutions can 
 only mix by a process of diffusion, and to prevent this as 
 much as possible is the object of the siphon, which is 
 plugged with cotton wick. By capillary action through the 
 cotton, the siphon gradually draws off the sulphate of copper 
 which rises by diffusion, and prevents it from reaching the 
 zinc plate. While the cell is in action, copper is deposited 
 on the copper plate ; while S0 4 finds its way to the zinc plate 
 and combines with it. The copper plate, in this way, 
 gradually gets thicker and the zinc plate thinner ; while 
 the copper solution becomes less dense by the abstraction of 
 copper from it, and the zinc solution more dense by the 
 addition of zinc to it. The tendency is thus for the solu- 
 tions to become of the same density, and to get freely mixed. 
 To avoid this, a plentiful supply of crystals of sulphate of 
 copper must be kept in the central tube, and solution of 
 sulphate of zinc must from time to time be gently poured 
 over the zinc plate. 
 
 In Meidinger's cell, which closely resembles the one just 
 described, the zinc plate is in the form of a ring, which 
 closes the mouth of a glass vessel filled with solution of 
 
VOLTAIC BATTERIES. 191 
 
 sulphate of zinc. At the bottom of the vessel is a shallow 
 glass beaker, which contains a copper ring. The mouth of 
 the beaker is closed by a lid, through the centre of which 
 passes the mouth of an inverted, long-necked, glass balloon. 
 The balloon contains the solution of sulphate of copper, 
 which gradually flows out and spreads over the copper ring. 
 
 205. In the following list, the electro-motive forces of the 
 most common cells are given in volts : 
 
 Volts. 
 
 Daniell Sulphuric add 74 to 1 T079 
 
 Grove do. 1'956 
 
 Bunsen do. 1734 
 
 LeclanchS Solution of sal-ammoniac 1*481 
 
 206. Local Action. This is a defect to which all forms of 
 cell are subject in which zinc and acid are used. It is caused 
 by want of homogeneity in'the zinc plates, which may arise 
 either from actual impurities, such as particles of iron in the 
 zinc, or from the presence here and there of hard and soft 
 parts in the metal. In consequence of these inequalities, one 
 part of the zinc plate is understood to be electro-positive to 
 another, and this, in the presence of dilute acid, sets up a 
 multitude of local circuits, of small electro-motive force but 
 of equally small resistance, which rapidly consume the zinc 
 when the poles are not joined, and which do not contribute 
 in the least to the current when the main circuit is closed. 
 The best remedy for this defect is got by amalgamating 
 the zinc. This is accomplished by first immersing the 
 plates in dilute sulphuric acid, so as thoroughly to clean 
 their surface, and then rubbing mercury over them. In 
 this way the surface assumes a silvery brightness, and 
 becomes so homogeneous in its nature as to preclude local 
 action. If a battery is to be kept in thorough working 
 order, repeated amalgamations of the zinc must be carefully 
 attended to. 
 
192 ELECTRICITY. 
 
 CHAPTER XV. 
 CURRENT RESISTANCE, OHM'S LAW. 
 
 207. Current. If a voltaic cell or battery be in proper working 
 order, no chemical action takes place in the cell until the poles 
 be joined by a wire or other conducting connection. If such 
 a cell be carefully insulated, and the potentials of the copper 
 and zinc plates ascertained by a delicate electrometer, it will 
 be found that the potential of the copper plate exceeds that 
 of the zinc plate by a certain quantity. This difference of 
 potential is the electro-motive force of the cell. It is to be 
 noticed that this difference will be exactly the same, even 
 should the cell be bodily charged with a quantity of elec- 
 tricity from an external source, as thereby the potentials of 
 both the copper and zinc plates will be raised by the same 
 amount. If the copper and zinc plates be joined by a wire, 
 in a very short time a steady current will flow in the wire, 
 positive electricity being carried from the copper to the zinc 
 through the wire, and from the zinc to the copper through 
 the liquid. The current thus forms a complete circuit, as 
 may easily be tested by the following experiment. Place the 
 cell so that the copper and zinc plates face north and south, 
 and let the wire joining them go in the same direction. Now 
 hang a small magnetised needle, first a little below the con- 
 necting wire, and then a little above the liquid. Observe the 
 deflection, and it will be found to be in the same direction in 
 both positions. A reference to the corkscrew rule already 
 given (sect. 184) will immediately shew that this indicates 
 a current flowing as stated. 
 
 208. Graphic representation of OJirrCs Law. If the wire con- 
 necting the poles of the voltaic cell be examined by means 
 of an electrometer at different points of its length, and the 
 potentials noted, it will be seen that the potential gradually 
 falls as we pass from the positive to the negative pole. This 
 can be represented graphically as follows : Let AB (fig. 103) 
 
CURRENT RESISTANCE, OHM'S LAW. 
 
 193 
 
 represent the wire, supposed to be straight, and let it be 
 homogeneous and all at one temperature, A being the 
 positive and B the negative pole. Let the point A be 
 joined by a fine wire to one pair of quadrants of a quad- 
 rant electrometer, the other pair of which is connected with 
 the ground ; and 
 let the potential of 
 A thus ascertained 
 be represented by 
 the line AC drawn 
 perpendicular to 
 AB. Similarly let 
 the potential of B 
 be ascertained and Fig - 103 ' 
 
 represented by the ordinate BZ. Now let any points L 
 and F be taken along the wire, and their potentials ascer- 
 tained and represented by the ordinates LD and FH. It 
 will be found that the straight line joining C and Z 
 will pass through the points D and H. Thus the slope 
 of the line CZ shews the gradual fall of potential along 
 AB. Now the slope of the line CZ will be greater the 
 greater the difference of height between its ends, and 
 the less the horizontal distance between them that is 
 
 CO CO 
 
 to say, the slope is represented by the fraction ^ = ~ 
 
 = tan ^, suppose. If tan 6 is zero, CZ will be hori- 
 zontal, and no current will flow from A to B ; and the 
 greater the value of tan 6 the stronger will be the current. 
 Hence the current may be represented by tan 6. Call it C, 
 
 CO 
 
 and we have C = tan 6 = ?. Now CQ is the difference of 
 
 potential, that is, the electro-motive force acting between A 
 and B. Denote it by E. Similarly CO, DP, and HG are the 
 electro-motive forces between A and L, L and F, F and B, 
 respectively. Denote them by Ej E 2 and E 3 . 
 
 Since the wire AB is homogeneous, its total resistance may 
 be represented by its length, and the resistance of any part by 
 the length of that part. Denoting the whole resistance by R, 
 
194 ELECTRICITY. 
 
 and the resistances of the parts AL, LF, and FB by E x K 2 
 Es we have, from the figure, the following equations : 
 
 f a a n ^_^i_ ?i_ 5?. 
 
 JAi JAij -t\>2 JtVg 
 
 Putting these into another form we get 
 
 E = CK, E! = CE X , E 2 = CR 2 , E 3 = CE 3 , 
 and stating this in words we get the following expression for 
 Ohm's law : 
 
 The electro-motive force acting between the extremities of any 
 part of a circuit is the product of the strength of the current and 
 the resistance of that part of the circuit^ 
 
 The above is to be regarded merely as a graphic representa- 
 tion of Ohm's law. The truth of the law depends upon its 
 perfect accordance with experimental results as far as has yet 
 been ascertained. The law was discovered by Ohm in 1827. 
 
 209. Linear Conductors arranged in Series. By a linear con- 
 ductor is meant one which the current enters and leaves only 
 at two definite points, called the electrodes. Such a conductor 
 is represented by a wire perfectly insulated, except at the 
 ends where the current enters and leaves it. When a number 
 of such conductors are connected end to end, so that the 
 current passes through each in succession, they are said to be 
 arranged in series. Let AB (fig. 104) represent such a com- 
 
 -8- -6- 
 
 Fig. 104. 
 
 pound conductor, consisting, let us suppose, of a length, 
 AC, of copper wire, a length, CD, of iron wire, and a length, 
 DB, of silver wire. Also let E be the total electro-motive 
 force, and E, the total resistance between A and B, E x and Ej, 
 those between A and C, Es and Ea, those between C and D, 
 and E 3 and E 3 , those between D and B. It is evident that 
 the same current must pass through each part of the con- 
 ductor, and Ohm's law applied to the whole and to the 
 several parts gives the equations : 
 
 E = CE, E x = CRy E 2 = CE 2 , E 3 = CE 3 . 
 
CURRENT RESISTANCE, OHM'S LAW. 195 
 
 Adding the last three equations we get 
 
 but E = Ej + E 2 + E 3 . 
 
 .-. OR = C (R! + R 2 + E 3 ), whence 
 
 R = R! + Ra + R 3 that is, 
 
 the resistance of a series of conductors is the sum of the resist- 
 ances of the separate conductors. 
 
 210. Linear Conductors arranged in Multiple Arc. When a 
 set of conductors is arranged side by side so that one end of 
 each is connected with the point where the current enters, 
 and the other end of each with the point where it leaves the 
 system, they are said to be arranged in multiple arc. Such a 
 system is represented in fig. 105. The current denoted, let 
 us suppose, by C, flowing in CA will divide at A, part of it 
 going through each of the conductors, 1, 2, 3. The divided 
 
 Fig. 105. 
 
 current will unite again at B and flow on towards Z. If 
 the resistances of 1, 2, and 3 be all equal, manifestly a third 
 part of the whole current will flow through each of them. 
 Let E be the electro-motive force, and R the resultant resist- 
 ance between A and B. Also let C x be the current, and Rj 
 the resistance in 1, C 2 and R 2 in 2, C 3 and R 3 in 3. Apply- 
 ing Ohm's law to the system, and observing that the electro- 
 motive force between the ends of each conductor is E, we get 
 
 E E E E 
 
 ~ R ' Ul ~ R x ' 2 ~ R 2 ' 3 ~ R 3 ' 
 Adding the last three equations we get 
 
 but 
 
196 ELECTRICITY. 
 
 The fraction -5-, that is, the reciprocal of the resistance of a 
 
 conductor is called the conductivity of the conductor. Hence 
 we may express the above results as follows : 
 
 The conductivity of a multiple conductor is the sum of the 
 conductivities of its separate parts. 
 
 211. Network of Linear Conductors. A network of linear 
 conductors is got by taking any number of points and joining 
 every two by a wire. Such a network for five points, involv- 
 ing ten connecting lines, is represented in fig. 106. (The 
 wires are understood not to touch at the point cc.) The 
 general problem may be thus stated. Given the quantities 
 of electricity which enter each point of the system in a unit 
 of time, the resistance of each branch, and the internal electro- 
 motive force which acts in that branch, it is required to find 
 the difference of potential between each pair of points. 
 Having got this difference, the current in the corresponding 
 branch can be got from Ohm's law. The full investigation of 
 the problem requires the solution of a set of simultaneous 
 equations, and would involve the introduction of too many 
 algebraic symbols to be given here. The general nature of 
 the solution, however, may be stated, and we recommend the 
 actual working out of the problem as a most instructive 
 exercise to the more advanced student. We first observe that 
 there can be no accumulation of electricity at any part of the 
 system, and hence the algebraic sum of all the quantities of 
 electricity which enter it, some being reckoned positive and 
 the rest negative, must be zero. We next notice that the 
 resistance of each branch is the same in whichever direction 
 it is taken, but that the electro-motive forces and currents 
 change sign when their direction is reversed. Then we write 
 down the equations which express the current in each branch 
 in terms of the resistance and the total electro-motive force 
 which acts in that branch. These equations, taken along with 
 the zero relation among the quantities of electricity, give a 
 set of simultaneous equations, involving, as the unknown 
 quantities, the differences of potential between each pair of 
 
CURRENT RESISTANCE, OHM'S LAW. 
 
 197 
 
 points. Solving these equations, we get the difference of 
 potential between each pair of points, from which, knowing 
 the resistance, we find the current in the corresponding 
 branch. 
 
 Kirchoff has given the following laws relating to a network 
 of linear conductors : 
 
 Law I. At any point of the system the sum of all the 
 currents which flow to that point is zero. 
 
 Law II. In any complete circuit formed by the conductors 
 (no matter how many nodes and meshes it may inclose) the 
 sum of the electro-motive forces taken round the circuit is 
 equal to the sum of the products of the current in each con- 
 ductor multiplied by its resistance. 
 
 The first of these laws follows at once from the fact that 
 there can be no accumulation of electricity at any point or 
 node such as A-, fig. 106, and hence as much electricity must 
 leave the system at that point as enters it. This is simply 
 the law of continuity. 
 
 The result stated in the second law may be obtained as 
 follows : 
 
 Let us take the 
 closed circuit A l A% 
 A 3 A 4 inclosing the 
 node As. Let Pj P 2 
 &c. be the potentials 
 at A t A 2 &c. Also 
 let C 12 be the current, 
 and R 12 the resistance 
 of the branch A 12 , and 
 so on of the others. 
 Also let E 12 be 
 the internal electro- Fig. ioe. 
 
 motive force in the 
 
 branch A l A at and so on. These internal electro-motive forces 
 are represented in the figure by the short parallel lines which 
 stand for batteries inserted in the branches. Going round 
 the circuit in the direction Aj A 2 Ag A 4 , and applying Ohm's 
 law to each conductor, we get : 
 
198 ELECTRICITY. 
 
 P 1 - P 2 + E 12 = C 12 R 12 , 
 P 2 P 3 + E 23 = C 23 R 23> 
 
 P 3 - P 4 + E 34 = C 34 E 34 , 
 P 4 - P! + E 41 = C 41 R 41 . 
 By simply adding these equations we get 
 
 E 12 + E 23 + E 34 + E 41 = C 12 E 12 + C 23 R 23 + C 34 E u +C 41 R 41 , 
 
 which is the symbolic expression of Kirchoff's second law. 
 
 One important result regarding a network of linear con- 
 ductors remains to be stated. It is this. If an electro-motive 
 force acting in any branch, such as A^A 2 of the system, 
 causes a certain other electro- motive force, E, to act in 
 another branch, A 4 A 5 , then the same electro-motive force 
 acting in A 4 A 5 will cause an equal electro-motive force, E, to 
 act in AjAg. As a particular case of this, suppose an electro- 
 motive force acting in A!A 2 to cause zero difference of 
 potential between A 4 and A 5 , then the same electro-motive 
 force acting in A 4 A 5 will cause zero difference of potential 
 between A x and A 2 . When this last relation obtains between 
 any two branches, these branches are called conjugate con- 
 ductors. An important case of conjugate conductors will be 
 found when we come to the theory of the Wheatstone 
 Bridge. 
 
 212. Specific Resistance. If we take a unit cube of a sub- 
 stance and measure its resistance, r, to a current passing 
 parallel to one of its edges, then r is called the specific resist- 
 ance of that substance per unit of volume. Suppose we put 
 I of such cubes together so as to form a bar of length I and 
 cross section unity ; then we may treat this bar as a set of I 
 conductors | arranged in series, and the total resistance will 
 be R = Ir. Now put s of these bars side by side, forming a 
 compound bar of length I and cross section s,-and we may 
 treat the bar as a number of equal conductors arranged in 
 multiple arc. If R be the total resistance, we have 
 
 B"T- (1) ' 
 
 Now it is often very difficult to measure accurately the 
 section of a wire, and in these cases it is better to obtain it 
 
CURRENT RESISTANCE, OHM'S LAW. 199 
 
 indirectly from its length, mass, and density. Let I be the 
 length, m the mass, and p the density of the wire under 
 examination ; then since the mass is equal to volume x 
 density, and volume is equal to length x section, we have 
 
 ls p = m, from which we get s = ^. Substituting this in 
 
 72 
 
 equation (1) we get R = rp (2). 
 
 mi 
 
 By making I and m each equal to unity in this equation, we 
 get rp for the resistance of a unit length and unit mass of the 
 substance. Denoting it by r', then / is called the resistance 
 of the substance per unit of weight. Hence in terms of this 
 
 p 
 
 unit we have B, = r'. The relation rp = i / shews how resist- 
 ances expressed in terms of the one unit can be got from 
 those expressed in terms of the other. As an example, the 
 resistance of a column of mercury one metre long and 
 weighing one gramme is 13*071 ohms. Dividing this by 
 13'595, the specific gravity of mercury, we get -96146 ohms, 
 which is the resistance a column one metre long and one 
 square millimetre in section. 
 
 In regard to specific resistance, all ^bodies may be divided 
 into three great classes. The first class includes all those 
 substances whose chemical constitution is unaltered, both 
 throughout their entire mass and at the electrodes, by the 
 passage of a current through 'them. This class embraces all 
 metals with their alloys, gas-carbon, and selenium in the 
 crystalline form. The resistance of all bodies of this class, 
 with very few exceptions, increases with a rise of tempera- 
 ture. 
 
 The second class includes those substances which are 
 decomposed into two chemical constituents by the passage of 
 the current, the one constituent appearing at the positive, and 
 the other at the negative pole. Such substances are called 
 electrolytes (see Electrolysis, Chap. XVI.). Almost all electro- 
 lytes are in the liquid form, with the exception of glass at 
 100 C., and some other substances near the point of fusion 
 which are found to conduct electrolytically. 
 
 The third class includes those substances whose resistance 
 
200 ELECTRICITY. 
 
 is so enormous that the strongest electro-motive force can 
 hardly send the feeblest current through them. These 
 substances are called dielectrics. This class includes air 
 and all gases, glass at its normal temperature, paraffin, shell- 
 lac, ebonite, india-rubber, and some oils. We now come to 
 examine a little more in detail these three classes of bodies. 
 
 213. Specific Resistance of Metals. An important observa- 
 tion regarding metals was first made by Forbes, who found 
 that metals observed the same order as regards conductivity 
 both for heat and electricity a result which has been 
 verified recently, and some new facts added by Tait. Another 
 important property of metals is the increase of resistance by 
 the rise of temperature. This can be shewn very easily by 
 an experiment. Include in the circuit of a battery a galvano- 
 meter and a length of fine iron wire. Observe the deflection 
 of the needle when it has become steady. Now gradually 
 heat the iron wire by a spirit lamp, and the deflection will 
 be observed to decrease on account of the weakening of the 
 current by the increase of resistance produced by heating the 
 wire. This property of metals has been examined experi- 
 mentally with great care by Matthiessen, Siemens, and others. 
 It is found that the rise of resistance is very nearly pro- 
 portional to the increase of temperature from C. to 100 
 C. Beyond that the increase per degree rise gets gradually 
 less than before. Siemens has given the following empirical 
 formula, which connects the specific resistance with change 
 of temperature from C. to 1000 C. : 
 
 r=aTi + /3T + y where T is the temperature calculated 
 from absolute zero that is, from 273 C., and a, /?, and y 
 constants, which depend upon the kind of metal. For copper, 
 a= -026577, (3 = -0031443, and y = - -22751. 
 
 Belying on the truth of the above formula, Siemens has 
 constructed a pyrometer for estimating the temperature of 
 a furnace from the change of resistance experienced by a 
 platinum wire placed in the furnace. 
 
 Metals generally shew a sudden increase of resistance at 
 the melting-point. After that the increase goes on gradually 
 with rise of temperature, but at a less rate per degree rise 
 than before the melting-point was reached. Bismuth and 
 
CURRENT RESISTANCE, OHM'S LAW. 201 
 
 antimony are notable exceptions to this rule, as the specific 
 resistance of both exhibit a sudden fall at the melting-point. 
 
 The specific resistance of alloys has been found to bear no 
 constant relation to the amount and resistance of the metals 
 of which they are composed. Generally, however, the 
 resistance of an alloy is greater than that of a pure metal. 
 It is important to find that the resistance of some alloys 
 varies very little with change of temperature as compared 
 with pure metals, a fact which has been of much service in 
 the construction of standards of resistance. Such an alloy is 
 got from two parts of gold with one of silver. 
 
 Besides heat, several other physical effects produce an 
 alteration in the specific resistance of metals. Putting a 
 wire, for instance, under a state of strain, such as by hanging 
 a heavy weight from it N alters its resistance ; and this altera- 
 tion is more than can be accounted for by the diminution 
 of the section. Sir William Thomson has also noticed that 
 magnetising an iron wire changes its resistance. In the case 
 of crystalline selenium it has been found that light produces 
 a marked effect upon its resistance, and it is now known even 
 that light falling upon selenium can originate a current in it. 
 
 214. Specific Resistance of Electrolytes. The determination 
 of the specific resistance of electrolytes is beset with a 
 peculiar kind of difficulty. This arises from the counter- 
 electromotive force of polarisation, which is set up at the sur- 
 face of contact of the electrolyte with the electrodes. Various 
 methods have been adopted to overcome this difficulty. One 
 is by using what are termed non-polarisable electrodes, such 
 as plates of amalgamated zinc in contact with solution of zinc 
 sulphate. Another is to determine the resistance as far as 
 possible before any great amount of polarisation has had time 
 to take place. This can be accomplished either by using 
 rapidly alternating currents, or by making the surface of 
 the electrodes very large in comparison with the sectional 
 area of the part of the electrolyte whose resistance is being 
 determined. 
 
 In all cases the resistance of electrolytes diminishes with a 
 rise of temperature. 
 
 Paalzow has examined the resistance of various mixtures 
 
202 ELECTRICITY. 
 
 of two different solutions whose individual resistance was 
 known. He finds that the resistance of the mixture is 
 neither the arithmetic nor the geometric mean of the resist- 
 ances of the two solutions ; and also that it does not agree 
 with the result which would be obtained by treating the two 
 solutions as metals connected in multiple are. 
 
 Solutions containing various percentages by weight of the 
 common acids, such as nitric, hydrochloric, sulphuric, &c., 
 have been examined ; and likewise similar solutions of the 
 alkalies and alkaline earths, such as chloride of potassium, 
 sal-ammoniac, &c. 
 
 In the case of all the acids examined, with the exception of 
 oxalic acid, the resistance is found to have a minimum value 
 corresponding to a certain definite percentage of the acid in 
 the solution. That percentage is 297 for nitric, 18'3 for 
 hydrochloric, and 30*4 for sulphuric acid. Sulphuric acid is 
 anomalous inasmuch as it shews two minimum values of the 
 resistance for percentages varying from to 100, the one 
 occurring at 30'4 and the other about 92'5 per cent. 
 
 In the case of the alkalies it is found that they can be 
 divided into two great classes the one class containing those 
 whose solutions do, and the other those whose solutions do 
 not shew a minimum value of the resistance as the percentage 
 is varied up to the saturation point. Examples of the former 
 class are solutions of chloride of potassium and sal-ammoniac ; 
 and of the latter, solutions of common salt, chloride of cal- 
 cium, and chloride of magnesium. 
 
 215. Specific Resistance of Dielectrics. As far as has yet been 
 ascertained, the resistance of all gases and vapours at ordinary 
 pressures and temperatures is practically infinite. Air, for 
 instance, has been found to have a specific resistance which is 
 at least 10 28 times that of copper ; and a similar result has been 
 obtained for steam and the vapours of mercury and sodium. 
 From this it is evident that the gradual loss of electricity 
 which is observed to take place from all charged conductors, 
 however well insulated, cannot be attributed to actual con- 
 duction through the air, but must be due either to conduction 
 through the substance or along the surface of the insulating 
 supports. 
 
CUEEENT EESISTANCB, OHM'S LAW. 203 
 
 The resistance of rarefied gases presents some points of 
 importance. It has been shewn by an experiment due to 
 Varley that 323 Daniell's cells were able to produce a current 
 in a tube containing a certain rarefied gas, but that a less 
 number namely, 304 cells were able to maintain the current 
 after it had been started. When more cells were added, and 
 the current strength tested by a galvanometer, it was found to 
 be proportional to the excess of the number of cells above 
 304. That is to say, suppose the current strength for 304 +8, 
 or 312 cells, to be represented by 9, then the current for 
 304 + 16, or 320 cells, would be represented by 18. From 
 this it would appear that the electro-motive force required 
 to maintain a current through a rarefied gas is made up 
 of the sum of two parts, one of which is constant, and the 
 other connected with the current and resistance by Ohm's 
 law. 
 
 Numerous experiments have been made to determine thy 
 resistance of solid dielectrics such as glass, gutta-percha, 
 india-rubber, &c. With almost no exception the resistance 
 of such bodies diminishes with increase of temperature. 
 This is well shewn in the case of glass, the resistance of which 
 varies from 22,700,000 at 200 G. to 73,500 at 400 C. 
 
 Special attention has been given to the determination of 
 the specific resistance of india-rubber and gutta-percha. 
 This has been caused by the extensive use of these sub- 
 stances as insulating coatings for submarine cables. One 
 notable feature has been observed in regard to them which 
 is, that the resistance varies in a rather uncertain way with 
 time. For instance, in one case the resistance of gutta-percha 
 was observed after the current had flowed, for one minute, 
 for ten minutes, and for nineteen hours ; and it was found 
 that the resistance after ten minutes was four times, and the 
 resistance after nineteen hours twenty-three times what it 
 was after one minute. 
 
 Subjoined is a table of the specific resistance of a few of the 
 more common substances, where t is the temperature at 
 which the resistance is measured, r the resistance in C.G.S. 
 units, and a the percentage of itself by which r varies per 
 degree C. of rise of temperature. 
 
204 
 
 ELECTRICITY. 
 
 
 * 
 
 r 
 
 a, 
 
 
 20 
 
 1521 
 
 37 
 
 Copper (annealed) 
 n (hard drawn) 
 Platinum (annealed) . 
 
 20 
 20 
 
 20 
 
 1615 
 1652 
 
 9158 
 
 38 
 
 Iron (annealed) 
 
 20 
 
 9827 
 
 
 Lead (pressed) 
 
 20 
 
 19850 
 
 38 
 
 
 20 
 
 21170 
 
 04 
 
 Mercury 
 
 20 
 
 96190 
 
 07 
 
 ELSO,. (max.).... 
 
 18 
 
 1-39 xlO 9 
 
 1-5 
 
 NH 4 C1 
 
 18 
 
 2-55 xlO 9 
 
 1-5 
 
 ZnS0 4 (max.) 
 
 10 
 
 26-60 xlO 9 
 
 2-3 
 
 ELSO,, (pure) 
 
 18 
 
 120-20xl0 9 
 
 4-2 
 
 H (pure) 
 
 18 
 
 135 xlO 13 
 
 
 Glass 
 
 200 
 
 227 x 10 14 
 
 
 
 400 
 
 735 x 10 11 
 
 
 Grutta-percha . . . 
 
 24 
 
 353 x 10 21 
 
 
 
 
 
 7xl0 24 
 
 
 
 
 
 
 CHAPTER XVI. 
 MEASUREMENT OF RESISTANCE. 
 
 216. Unit of Resistance. The units of resistance first 
 employed were purely arbitrary, and consisted merely of 
 certain lengths of wire of given material, thickness, and 
 density used always at the same temperature. Examples of 
 such arbitrary units are the ]talon of Jacobi, and the still 
 better known Mercury unit of Siemens the former being 
 the resistance of a copper wire 7*61975 metres long, -667 
 millimetres in diameter, and weighing 22'4932 grammes ; 
 and the latter the resistance of a column of mercury one 
 metre long, and one square millimetre in cross section, the 
 temperature being C. Many obvious disadvantages 
 attended the use of such arbitrary units, one of the chief 
 of which was that they were not universally adopted ; and in 
 consequence the results of one experimenter could not easily 
 be compared with those of another. Hence the necessity 
 
MEASUREMENT OF RESISTANCE. 
 
 205 
 
 very soon arose for some absolute unit which should be 
 universally used by electricians. 
 
 It has already been shewn (sect. 186) that, according to the 
 electro-magnetic system of units, a resistance is a quantity 
 having the same dimensions as a velocity ; and hence, the 
 unit of resistance admits of being expressed by a certain 
 definite absolute velocity. Weber, who was the first to 
 suggest such a system of measurement, adopted as his unit a 
 velocity of one millimetre per second ; and afterwards, Sir 
 William Thomson, in some researches, employed as his unit 
 a velocity of one foot per second. In 1861, acting upon a 
 suggestion of Thomson, the British Association appointed a 
 committee to investigate thoroughly the entire subject of 
 electrical measurements.. In 1864, after much careful experi- 
 menting and deliberation, that committee recommended the 
 adoption of a velocity of 10,000,000 metres, or approximately 
 an earth quadrant per second, as the absolute unit of resist- 
 ance. This unit, called the B. A. unit, 
 or more generally the Ohm, is the one 
 now all but universally used by electri- 
 cians. Having settled upon the abso- 
 lute unit, the committee next set about 
 constructing some material representa- 
 tives of it in the shape of what are 
 known as unit resistance coils. Before 
 doing so, however, they had first to 
 determine the resistance, in absolute 
 measure, of a certain coil of wire. This 
 they did essentially by making the coil 
 revolve at 'a known velocity about a 
 vertical axis, and ascertaining the deflec- 
 tion produced by it upon a magnet deli- 
 cately suspended at the centre of the 
 coil. As will be fully explained when 
 we come to induction of currents, this 
 deflection is due to a current induced 
 in the revolving coil by the earth's Fig. 107. 
 
 magnetism. Having ascertained the 
 resistance of the coil, it was a comparatively easy task to 
 
206 
 
 ELECTRICITY. 
 
 construct from it as a basis a coil whose resistance should be 
 equal to one unit or an Ohm. Several such coils were con- 
 structed, the wire employed being an alloy of platinum and 
 silver, which was chosen because its resistance was found to 
 vary very little with changes of temperature. The wires, 
 which varied in length from one to two metres, and in 
 diameter from *5 to *8 millimetres, were carefully insulated 
 with a double layer of silk, and after being doubled upon 
 themselves were wound upon an elongated brass bobbin as 
 represented in fig. 107. The object of winding the wire 
 double on the bobbin was to insure that at each point of 
 it there should be equal and parallel currents flowing in 
 opposite directions, and so do away with any inductive effect 
 of the one layer of wire upon its neighbour. The wire, after 
 being wound, was carefully imbedded in solid paraffin, its 
 ends being soldered to two stout pieces of copper to serve as 
 electrodes. The whole was then inclosed in a thin casing of 
 sheet-brass to enable it to be immersed in water, and brought 
 to the precise temperature at which the resistance was one 
 Ohm. 
 
 217. Rheostat and Resistance Coils. Having got a unit, the 
 next requisite was a series of graduated resistances so 
 arranged that any required resistance could be readily 
 inserted in a voltaic circuit. One of the earliest methods of 
 obtaining a graduated resistance was by means of the rheostat 
 invented by Wheatstone. It is 
 shewn in fig. 108. Two cylinders, 
 C', C, about 6 inches in length, 
 and 1 inch in diameter, are 
 placed parallel to each other, 
 both being movable round their 
 axes. One of them, C', is of 
 brass, the other, C, is of well- 
 dried wood. The wooden cylin- 
 der has a spiral groove cut into it, 
 making forty turns to the inch, 
 
 in which groove is placed a fine metallic wire. One end of the 
 wire is fixed to a brass ring, which is seen in the figure at the 
 further end of the wooden cylinder ; and its other end is 
 
 
 Fig. 108. 
 
MEASUREMENT OF RESISTANCE. 207 
 
 attached to the nearer end (not seen in the figure) of the brass 
 cylinder, C'. The brass ring just mentioned is connected 
 with the binding screw, S, by a strong metal spring. The 
 further end of the cylinder C' has a similar connection with 
 the binding screw, S'. The key, H, fits the projecting staple 
 of either cylinder, and can consequently turn both. As the 
 brass cylinder, (7, is turned in the same direction as the 
 hands of a watch, it uncoils the wire from the wooden 
 cylinder, (7, making it thereby revolve in the same way. 
 When the wooden cylinder is turned contrary to the hands of 
 a watch, the reverse takes place. The number of revolutions 
 is shewn by a scale placed between the two, and the fraction 
 of a revolution is shewn by a pointer moving on the gradu- 
 ated circle, P. When 'the binding screws, S and S', are 
 included within a circuit, say S with the -|-> and S' with the 
 pole, the current passes along the wire, on the wooden 
 cylinder, C, till it comes to the point where the wire crosses 
 to the brass cylinder, C' ; it then passes up the cylinder C' to 
 the spring and binding screw, S'. The resistance it encounters 
 within the rheostat is met only in wire, for as soon as it 
 reaches the large cylinder, (7, the resistance it encounters up 
 to S' may be considered as nothing. When the rheostat is to 
 be used, the whole of the wire is wound on the wooden 
 cylinder, C, and the binding screws are put into the circuit 
 of a constant cell or battery along with a galvanometer. The 
 rheostat is now seldom used unless for rough work, on account 
 of the resistance at the contact of the wire with the metal 
 cylinder being variable and indeterminate. 
 
 Resistance coils are definite multiples of the Ohm 
 so arranged that they can be at once included or with- 
 drawn from a voltaic circuit without disturbing the resist- 
 ance of the other parts of the circuit. They are con- 
 structed in a way precisely similar to the unit coil, and are 
 usually attached to the under side of a slab of ebonite as 
 represented in fig. 109. One end of each coil is soldered to 
 massive pieces of brass a, 6, c, &c., whose resistance is so small 
 that it may be neglected. Half holes are made in the ends 
 of each of these pieces (C) to admit of conical plugs of brass, 
 p, being inserted between them. When a plug is out of the 
 
208 ELECTRICITY. 
 
 hole between a and &, suppose, the current passing from A to 
 B has to pass through the corresponding coil ; but when it is 
 inserted, the coil is, as it is termed, shunted off, and the 
 
 Fig. 109. 
 
 current passes without resistance through the brass pieces. 
 It is thus easily seen that the resistance inserted in the circuit 
 between A and B is exactly the resistance unplugged ; and 
 to facilitate calculation, the resistance of each coil is engraved 
 upon the corresponding piece of brass. Resistance coils are 
 usually made up in boxes, one of which is represented in fig. 
 113, and in plan in fig. 114, sect. 221. 
 
 218. Comparison of Resistances. The first method of com- 
 paring two resistances was by inserting them successively 
 along with a galvanometer into a voltaic circuit, and observ- 
 ing the corresponding currents. In this way the ratio of the 
 resistances was obtained. Thus, let B be resistance of the 
 battery and its connections, E its electro-motive force, and C 
 the current produced by it. Also let r x and r 2 be the inserted 
 resistances which are to be compared, and C^ and C 2 the 
 corresponding currents, then we have by Ohm's law : 
 
 E = CR = G! (R + rO = C 2 (R + r 2 ). 
 
 From these we get : 
 
 (0 - CO R = Cto 
 (C - C 2 ) R = C 2 r 2 
 
 .-. O = d (C - C 2 ) r, - C 2 (0 - CO r 2 
 
MEASUREMENT OF RESISTANCE. 209 
 
 From this we get the ratio of the two resistances provided 
 we can measure the currents C, Oj, and C 2 . It is to be 
 observed, however, that this supposes the electro-motive force 
 and resistance of the battery to remain constant during the 
 experiment, a thing which we cannot assume, and which is 
 practically found not to be the case. Hence this method is 
 very defective, and is now never employed for accurate work. 
 Fortunately, however, we have two methods for comparing 
 resistances, both entirely independent of the electro-motive 
 force and resistance of the battery. These are the methods 
 by the differential galvanometer, and Wheatstone's Bridge. 
 
 219. Differential Galvanometer. In the differential gal- 
 vanometer there are two independent circuits made by 
 winding side by side upon the bobbin two well-insulated 
 wires, usually of equal length and thickness. The four 
 terminals are so arranged that currents can be sent in 
 opposite directions through the two coils so as to act in 
 opposite directions upon the suspended needle ; and in this 
 way, if the currents are exactly equal, the needle will not be 
 deflected. This is an example of what is called the 'null 
 method ' of comparing resistances, seeing that the thing to be 
 observed is the absence of an effect caused by the action of 
 equal and opposite forces. 
 
 The general arrangement of the differential galvanometer, 
 as used for comparing resistances, is represented in fig. 110. 
 G is the galvanometer, whose coils are M and N. E is a 
 battery, the current, C, from which divides at F, one part 
 going round M, and the other round N, in the directions 
 EFMH and EFNH respectively. Let m be the deflection 
 produced by a unit current in M, and n that produced by 
 a unit current in N ; then, if Cj and C 2 be the currents 
 in the branches containing M and N, and 5 the deflection 
 produced, we have 
 
 * = raCi nC 2 (1). 
 
 Now let A be the total resistance in the branch containing 
 M, r the resistance in the branch HF, including that of the 
 battery, and B -f- x the resistance in the branch containing 
 N, where x is the inserted resistance whose value is to be 
 
210 
 
 ELECTRICITY. 
 
 compared with a known resistance. Let the resistance A be 
 adjusted till there is zero deflection of the needle. Now let x 
 be removed, and known resistances inserted in its place till 
 
 Fig. 110. 
 
 there is again zero deflection. If R be the resistance 
 inserted, x will be equal to R, and in this way x is deter- 
 mined in terms of known quantities. 
 
 As an instructive example of the use of Ohm's Law, we 
 shall find the equations which give C, Q v and C 2 in terms of 
 the given quantities. 
 
 Looking first at the branch EFMH, we have 
 
 E = Cr + C X A 
 
 Looking next at the branch EFBH, we get 
 E = Cr + C 2 (B + x) 
 Also we have evidently 
 
 O = Oj -f- \^2' 
 
 Solving these equations, we easily find 
 A + B + z 
 
 2). 
 
 (3). 
 
 where 
 
 n - "R 
 
 c 2 = n . 
 
 D = A (B + x) + r (A + B + x). 
 
THE 
 
 MEASUREMENT OF RESI 
 
 From (1) we find 
 
 If j = o, then m (B -f a) = nA. 
 
 Now if R inserted for x makes S = 0, then also is 
 m (B + R) = A, 
 
 which shews at once that ce = R. 
 
 220. Wheatstone Bridge. This is another example of the 
 null method of comparing resistances. It was first invented 
 by Christie, although brought to perfection by Wheatstone. 
 It consists essen- 
 tially of a network 
 of six linear con- 
 ductors, having a 
 battery in one 
 branch and a gal- 
 vanometer in the 
 branch conjugate 
 to it. The arrange- 
 ment of the Bridge 
 is shewn in fig. 
 111. 
 
 E is the battery 
 inserted in the 
 branch CE A, whose 
 resistance is represented by r. The current from the 
 battery divides at A, part going round ABC, and the other 
 part round ADC. G is a galvanometer inserted in the 
 branch BD, and delicate enough to detect even the feeblest 
 current in that branch. P, Q, and R are resistances, adjust- 
 able to any known values, inserted in the branches AB, 
 BC, AD ; and x is the unknown resistance, whose value is to 
 be determined, inserted in the branch CD. The remaining 
 parts of the branches are supposed to consist of thick strips 
 of metal whose resistance may be neglected. 
 
 In order to find the value of #, the resistances P, Q, and 
 R are so adjusted that no current passes through the galvano- 
 
 N 
 
 Fig. 111. 
 
212 
 
 ELECTRICITY. 
 
 meter. When this is the case B and D are at the same 
 potential, and from this it follows that the product of the 
 resistances P and x must be equal to the product of Q and R ; 
 that is 
 
 OT? 
 Px = QR, from which we get x = -^-. 
 
 Hence x is expressed in terms of known resistances. 
 
 In order to shew that T*x = QR, we first observe that the 
 fall of potential from A to C is the same whether we go along 
 ABC or ADC. 
 
 Let LH (fig. 112, a), at right angles to LN, represent the 
 
 Fig. 112. 
 
 difference of potential between A and C. Also let LM and 
 MN represent the resistances P and Q. The fall of the 
 potential along ABC is represented by the slope of the line 
 HN. Hence MO will represent the potential at the point B 
 of the bridge. Again, looking at the path ADC, let ST 
 (fig. 112, 6) represent the difference of potential between A and 
 C, and SK and KV the resistances R and x respectively ; then 
 the slope of the line TV represents the fall of potential between 
 A and C, and KF the potential at the point D of the bridge. 
 Now, LH is equal to ST, and MO to KF, seeing that B and D 
 are at the same potential. From fig. 112, a, we get 
 
 LH_ LN _P + Q_P 
 MO~MN~ Q ~Q + 
 
 Similarly, from fig. 112, 6, we get 
 
 ST__ SV_R + a_R 1 
 KF~KV~ x ~ x + 
 
But 
 
 MEASUREMENT OF RESISTANCE. 213 
 
 LH ST 
 
 Therefore ? + 1 = 5 + 1. 
 
 ^ x 
 
 T) T> 
 
 Hence =- ; that is, ~Px = QR. 
 
 The equation Px = QR can also be proved algebraically by 
 the help of KirchofFs laws (sect. 211), and as this affords an 
 excellent example of the use of these laws, we shall give the 
 equations from which the result can be obtained. 
 
 Let GJ be the current in AB (fig. Ill), C 3 that in BO, C 3 
 that in AD, C 4 that in DC, and C 5 that in BD ; also let C be 
 the current from the battery E, and let G denote the galvano- 
 meter resistance. 
 
 By KirchofFs first law, looking at the points A, C, B, and 
 D in succession, we get the equations : 
 
 C 6 = Cj C 2 = C 4 C 3 . 
 
 By KirchofFs second law, looking first at the circuit ABD 
 and then at the circuit BCD, we get 
 
 CjP + C 5 G - C 3 R = ; 
 
 C 2 Q - C 4 z - C 5 G = 0. 
 
 From these equations, by eliminating C x C 2 C 3 and C 4 , we 
 get 
 
 _ Pa-QR 
 
 (P + R) (Q + *) + G(P + Q + 
 
 Hence if the galvanometer shews zero deflection that is, if 
 C 5 = we must have Pee = QR. 
 
 221. Resistance Box. For the practical determination of 
 resistances, a box of resistance coils is usually arranged in the 
 form of a Wheatstone's Bridge. Such a box is represented in 
 fig. 113, and a plan of the top of its lid in fig. 114. The 
 box consists of three parallel rows of coils so connected by 
 stout metal pieces at the ends as to be equivalent to a single 
 long row. The parts AB and BC (fig. 114, a) are called the 
 arms of the bridge. Fig. 114, 6, represents the usual dia- 
 
214 
 
 ELECTRICITY. 
 
 graramatic form of the bridge ; and the letters, in both figures, 
 are made to indicate corresponding parts. The battery is 
 
 Fig. 113. 
 
 usually inserted between A and C, the galvanometer 
 between B and D, and the resistance to be measured 
 
 J 
 
 5000 2000 1000 1000 500 200 100 100 
 
 between C and D. The resist- 
 ance unplugged between A and B 
 corresponds to P, that between 
 B and C to Q, and that in the 
 circuit HLD to R. The equa- 
 tion Px = QR gives at once the 
 
 value of x = -p-. For instance, let the resistances un- 
 plugged in AB and BC respectively be 100 and 10, and 
 
MEASUREMENT OF RESISTANCE. 215 
 
 suppose in order to produce zero deflection in the galvano- 
 meter it is found necessary to unplug 5, 10, and 50 in HLD ; 
 then we have lOOx = 10 (5 -f 10 -f- 50) = 650, which gives 
 x = 6 -5. In order to make the sensibility of the arrange- 
 ment as great as possible, it is best to make the resist- 
 ances in the arms equal and as near to the resistance to be 
 measured as possible. It will be observed that the numbers 
 in HLD are so arranged as to give any resistance up to 10,000 
 Ohms by taking out the proper plugs. 
 
 222. Arrangement of Cells. According to Ohm's law, the 
 current obtained from any particular cell is equal to the 
 quotient which results from dividing the electro-motive force 
 by the total resistance. This resistance arises from two 
 sources ; the first being the resistance within the cell offered 
 by the exciting liquid, and the second the external resistance. 
 If e represent the electro-motive force ; I, the resistance 
 within the cell ; w, the external resistance ; and C, the 
 strength of the current, or the quantity of electricity actually 
 transmitted, the statement of the law for one couple stands 
 
 thus : C = j - . If we increase the number of cells to n, 
 
 L -f- W 
 
 we increase the electro-motive force n times, and at the same 
 time we increase the liquid resistance n times, for the current 
 
 has n times as much of it to travel, then C = -V^ . If w 
 
 nl + w 
 
 be small compared with nl that is, if the external connec- 
 tion be made by a short thick wire it may be neglected, and 
 
 so C = -j = j. This shews that one cell gives in these 
 
 circumstances as powerful a current as a large battery, and 
 that the increased electro-motive force is expended in pushing 
 the current through the liquid in each cell. But if nl be 
 small with respect to w as in the external circuit of an 
 
 electric telegraph battery nl may be neglected, and C = ^. 
 
 Here we learn that the strength of the current increases 
 directly as the number of cells. We may learn from the 
 same that the introduction of the coil of long thin wire 
 of a galvanometer into such a circuit, introducing but a 
 
216 ELECTRICITY. 
 
 comparatively small increase of resistance, causes a very slight 
 diminution of the current strength. If, again, we increase 
 the size of the plates of a cell n times, the section of the 
 liquid is proportionately increased, so that whilst the electro- 
 motive force remains the same, the internal resistance 
 
 diminishes n times ; therefore C = - 7 or C = 7 : . If 
 
 I I + nw 
 
 _+ 
 
 the external resistance is small, nw may be neglected, and 
 C = -y, arid the strength is thus shewn to increase n times. 
 
 223. Suppose now that we have nine cells similar to the 
 one just discussed, the internal resistance of each being '2, 
 the electro-motive force 16, and the external resistance 15. 
 Let us also, for the sake of simplicity, suppose that they 
 are exactly equal, and that results come out exactly in accord- 
 ance with Ohm's law. Practically, this never takes place, 
 but the discrepancies can be easily accounted for, as they 
 originate in the apparatus, or faults of observation, and not 
 in the law. Practical results, however, are so near the law 
 as to leave no doubt of its truth. Let us ascertain how these 
 nine cells would act when differently put up. One cell, 
 
 when w = 0, gives a current C = ^ = 1'05. Let us now 
 
 I D'2i 
 
 put up the nine cells in succession, as in fig. 115. Here the 
 
 Fig. 115. 
 
 electro-motive force of the whole battery is nine times that 
 of one cell, or 144, and the resistance of the whole is also 
 increased nine-fold, or 9 X '2 = 1*8, as the current has in the 
 compound circuit to traverse nine times the amount of liquid 
 
 144 
 it has in one. Thus, C = -=-^ = 8*6, more than eight, 
 
 1 o HP lO 
 
 and nearly nine times the current that one cell can transmit. 
 Instead of the arrangement in s&jfis just investigated, let us 
 
MEASUREMENT OF RESISTANCE. 
 
 217 
 
 have an arrangement of the cells side by side, as in fig. 116. 
 The electro-motive force is not increased, but the resistance 
 
 Fig. 116. 
 
 is nine times diminished, seeing that the whole acts as one 
 
 cell of nine times the surface. Here C 
 
 16 
 
 = T06, 
 
 very little more than that given by one cell Again, put up 
 the nine cells as shewn in fig. 117, where w r e have three 
 batteries of three cells each, each joining to form one current, 
 the whole acting as one battery, with the plates three times 
 
 enlarged. C = = - = 3'1, or about three times the 
 
 current of one cell. Before a large resistance, the surface is 
 best employed by being cut up into 
 small cells, arranged successively, 
 than by having a few large cells. 
 Before a small resistance the reverse 
 holds. The maximum effect is got when 
 the total internal resistance within 
 the battery is equal to the external 
 resistance. This, of course, is only 
 practicable when the external resist- 
 ance is less than the resistance of all 
 the cells put together. 
 
 When continuous work has to be done by a battery, the 
 size of the plates or cells must not be too small, as small cells 
 containing little zinc and acid soon become exhausted. Large 
 cells do not before great resistance give a stronger current 
 than small cells, but they continue in action for a much 
 longer time. 
 
 Fig. 117. 
 
218 
 
 ELECTRICITY. 
 
 224. When cells differing both in electro-motive force and 
 internal resistance are put up successively, we have to add all 
 the electro-motive forces for the electro-motive force, and all 
 the resistances for the resistance of the battery. Thus, if we 
 had six cells with the electro-motive forces 9, 8, 7, 10, 6, 12, 
 and the resistances i, , |, -3-, -5-, 1 5 ^, respectively, the total 
 electro-motive force would be 52, and the total resistance 2, 
 
 52 
 
 and we should have the formula C = 
 
 If the last two 
 
 happened to be reversed and acted in the contrary way, the 
 formula would be C = -=-^ , the total internal resistance 
 being the same as before. 
 
 CHAPTER XVII. 
 
 THE PHYSIOLOGICAL, HEATING, LUMINOUS, AND ELECTRO- 
 LYTIC EFFECTS OF THE GALVANIC CURRENT. 
 
 These are developed by the current in its path. 
 225. The physiological effects, as shewn by the convulsions of 
 Galvani's frog preparation, were the first observed manifesta- 
 tion of the current. Fig. 118 shews how these convulsions are 
 
 obtained. The legs of 
 a recently killed frog 
 are skinned, and the 
 crural nerve laid bare. 
 A zinc wire, BA, holds 
 up the nerve at B, and 
 a copper wire, EA, is 
 Fig. us. made to touch the legs 
 
 at E and D. Each time 
 
 that the zinc and the copper wire are made to join at A, the 
 limbs are convulsed, and the contraction of the muscle throws 
 the legs out to the position //. Frog-lirnbs, as prepared by 
 Galvani, when included in a circuit, form a galvanoscope of 
 excessive sensibility. There is one peculiarity in their action 
 which deserves to be noted. The limbs contract only when 
 
EFFECTS OF THE GALVANIC CURRENT. 219 
 
 the circuit is closed and opened, and remain undisturbed so 
 long as the current passes steadily through them. The more 
 frequently, therefore, the current is stopped and renewed, the 
 greater is the physiological effect. The same is experienced 
 when a current is passed through the human body. When 
 the terminal wires of a battery are lifted one by each hand, 
 except it consist of a very large number of cells, almost the 
 only sensation felt is a slight shock on completing and break- 
 ing the circuit. Du Bois Reymond, the great authority on 
 animal electricity, states that the nerves of motion are affected 
 only by changes in the current, whereas the nerves of sensa- 
 tion, so far as they are affected, are affected not only by these, 
 but also by the steady continuance of the current ; and that 
 the excitation of the nerves dependent on the changes of the 
 current increases with their frequency and suddenness. 
 Frictional electricity in this way owes its superior physio- 
 logical power to the instantaneous nature of its discharge. It 
 is only currents of great tension which can be felt by the 
 living subject. The poles of a battery of fifty Bunsen cells, 
 capable of giving a brilliant electric light, for instance, may 
 be handled without much inconvenience. This may be 
 attributed partly to the non-conducting nature of the skin. 
 If the current enter the body by a cut or wound, the sensa- 
 tion is affected even when the current is weak. The physio- 
 logical effect is also much heightened by moistening the 
 hands with salt and water, or by holding metal handles 
 instead of wires, so as to improve the conducting connection. 
 Another cause of this insensibility may be attributed to the 
 fact that the current is not restricted, as it is in part of the 
 frog preparation, to the nerve, but passes through all the 
 conductors of the system. The nerves of the palate and of 
 sight can be affected by a very feeble current ; those of hearing 
 by a battery of some thirty cells. If two strips 'of silver and 
 zinc be placed the one above, the other below the tongue, and 
 be made to touch, a peculiar taste is experienced ; when the 
 strips are placed between the gums and the cheeks, and 
 joined, a flash of light accompanies each junction. Again, 
 when the poles of a battery of thirty cells are inserted into 
 the ears, a continuous noise is heard. 
 
220 ELECTRICITY. 
 
 226. Heating Effects. When a current passes through a 
 conductor without performing any work either in the circuit 
 or external to it, its energy is entirely converted into heat. 
 Now if E be the electro-motive force and Q the quantity of 
 electricity which passes, the energy is equal to the product 
 EQ. If H be the quantity of heat that is, the number of 
 thermal units produced and if J represent the mechanical 
 equivalent of one thermal unit, the energy is also equal to the 
 product JH. Hence we have the equation, 
 
 JH = EQ (1). 
 
 But by Ohm's law E = CR, and since the quantity of elec- 
 tricity which passes is equal to the product of the current 
 strength and the time during which it flows, 
 
 Q = Ct. 
 Therefore by substituting in (1) we get 
 
 Therefore H = 
 
 From this we see that the heat developed in any conduct- 
 ing wire by an electric current is proportional to the square 
 of the current strength and to the resistance. 
 
 The heat produced by a current can be shewn by passing 
 a strong current through tine wires, when 
 heat is produced sufficient to bring them 
 to a white heat and fuse them. Experi- 
 ments on the heating effects of the current 
 can be made by an apparatus such as that 
 sketched in fig. 119. B is a bottle filled 
 with alcohol (which is non-conducting), 
 and closed with a cork. The thick wires, 
 n, p, passing through the cork, are con- 
 nected with the poles of a battery, and 
 within the bottle they are joined with 
 Fig. 119. a thin spiral wire, www ; t is a delicate 
 
 thermometer. When the circuit is closed, 
 the heat developed in the wire is communicated to the 
 alcohol, the temperature of which is shewn by the ther- 
 mometer. According to the law stated above, the heating 
 
EFFECTS OF THE GALVANIC CURRENT. 221 
 
 effect depends on the strength of the current and the 
 resistance. 
 
 A very pretty illustration of the fact that the heat de- 
 veloped is proportional to the resistance encountered, is 
 offered by a chain, the alternate links of which are made of 
 silver and platinum. When a current of sufficient strength 
 passes through the chain, the silver links remain black while 
 the platinum links become red-hot. 
 
 The application of the heating powers of the current to 
 igniting gunpowder in mining, &c., is detailed in the Practical 
 Applications of Current Electricity. 
 
 227. Galvanic Spark. When the wires connected with a 
 powerful galvanic battery are brought together, no current 
 passes except they'are made to touch, or nearly so. On the 
 separation, a brilliant spark takes place, due, as we shall 
 afterwards find, to induction. According to Sir William 
 Thomson, a battery of 5000 Daniell's cells could not originate 
 a spark, if its poles were placed -^th of an inch apart. In 
 Gassiot's water battery of 3520 well-insulated cells, a spark 
 passed when the poles were brought to *02 of an inch, and con- 
 tinued to do so uninterruptedly for weeks and months to- 
 gether. When the galvanic spark is examined with a micro- 
 scope, it is found that the light only appears at the pole. 
 The electric light, the most splendid exhibition of the light 1 - 
 ing and heating power of the current, will be described under 
 Practical Applications. 
 
 Electrolysis. 
 
 228. Electrolysis is the term used by Faraday to designate 
 that branch of Voltaic Electricity which treats of the laws 
 and conditions of electro-chemical decomposition. As this 
 decomposition is generally attended by electro-chemical com- 
 bination, it is sometimes difficult to distinguish electrolysis 
 from the more general subject of Electro- chemistry, which 
 embraces all chemical changes resulting in or from the 
 galvanic current. Electrolysis is generally understood to 
 treat of the changes effected in a substance subjected to, but 
 not giving rise to the current. 
 
 Faraday's Nomenclature. A. substance capable of decom- 
 
222 
 
 ELECTRICITY. 
 
 position by the current is called an electrolyte (something 
 unbound by electricity). The poles namely, the wires, 
 plates, or the like by which the current enters and leaves the 
 electrolyte are called electrodes (electric ways, from hodos, a 
 way), the -f pole being called the anode (ana, up, and hodos), 
 and the pole the cathode (cata, down, and hodos). The 
 constituents into which the electrolyte is decomposed are 
 called ions (from ion, going) ; the electro-positive substances, 
 or those going to the cathode, are called cations; and the 
 electro-negative substances which go to the anode are called 
 anions. The electro-chemical equivalent of an ion is the 
 quantity of it set free by the passage of a unit quantity of 
 electricity. To electrolyse signifies to decompose by electric 
 agency. 
 
 General Character of Electrolytes. No substance is decom- 
 posed by the current so long as it is in a solid or gaseous 
 state, and it must first be brought to a liquid state, either 
 by solution or fusion, before the current acts on it. There 
 are some unimportant exceptions to this. The passage 
 of electricity through compound gases in a state of great 
 rarity, as in the so-called vacuum tubes, frequently separates 
 them up into their constituents. The electric spark in air 
 effects the combination of oxygen with nitrogen ; nitric acid 
 being produced. Electrolytes must be chemical combinations, 
 as these only can be decomposed. Metallic alloys, when fused, 
 though they conduct the current, are not decomposed by it. 
 
 229. Faraday's Law. Electrolytes are resolved under the 
 action of the current into anions and cations, which appear at 
 their respective electrodes in the proportion of their atomic 
 weights. The action of the current on one or two substances 
 will best illustrate the meaning of this law. 
 
 Electrolytes. 
 
 Composition. 
 
 Cations. 
 
 Anions. 
 
 Relative 
 Proportions. 
 
 Hydrochloric Acid 
 
 HC1 
 
 H 
 
 Cl 
 
 1 to 35-5 
 
 Chloride of Sodium 
 Sulphuric Acid 
 
 NaCl 
 H 2 ,S0 4 
 
 Na 
 
 Hn 
 
 Cl 
 
 S0 4 
 
 23 to 35-5 
 2 to 96 
 
 Sulphate of Sodium 
 Sulphate of Ammonium... 
 Water 
 
 Na 2 ,S0 4 
 (H 4 N) 2 ,S0 4 
 HoO 
 
 wi, 
 
 (H 4 N) 2 
 
 S0 4 
 S0 4 
 
 o 
 
 46 to 96 
 36 to 96 
 2 to 16 
 
 
 
 
 
 
EFFECTS OF THE GALVANIC CURRENT. 
 
 223 
 
 Thus common salt (NaCl) is composed of a simple cation, 
 Na, whose atomic weight is 23, and of a simple anion, 01, 
 whose atomic weight is 35'5. Sulphate of ammonium is 
 composed of two atoms of ammonium (H 4 N) 2 as a complex 
 cation, and one atom of sulphion 
 (SO 4 ) as a complex anion. The 
 atomic weight of ammonium 
 (H 4 N) is 18, and of sulphion 
 (SOJ 96. It will be thus seen 
 that chemical formulae give the 
 electrical as well as chemical 
 composition of electrolytes. In 
 acids, hydrogen forms ,the cation, 
 and the acid radicle, the other 
 constituent, the anion. In the 
 salts of an acid, the metal that 
 takes the place of hydrogen in 
 the acid is the cation of the salt, 
 and the other constituent, the salt 
 radicle, is, as in the acid, the 
 anion. 
 
 The decomposition of water by 
 platinum plates is always taken 
 as the best visible illustration of 
 electrolytic action. Fig. 120 represents a very convenient 
 apparatus for the purpose. A glass basin is made so as to 
 admit a cork below, through which two wires pass having 
 slips of platinum plate soldered to them above. Two glass 
 tubes, open below, are hung over the plates, to hooks pro- 
 jecting from an upright support. The bowl is filled with 
 acidulated water ; and the tubes, after being filled with the 
 same, are inverted, and hung with their lower ends inclosing 
 the plates. When the wires projecting downwards from the 
 cork are connected with the poles of the battery, hydrogen 
 rises from the , and oxygen from the + electrode, to fill 
 each its separate tube. As the decomposition proceeds, twice 
 as much hydrogen is liberated as oxygen. When the tubes 
 are filled, they may be removed and examined. 
 
 Hydrogen is here the type of the metals, or other electro- 
 
 Fig. 120. 
 
224 ELECTRICITY. 
 
 positive substances, disengaged at the pole, and oxygen of 
 the acid and salt radicles, or other electro-negative substances, 
 set free at the -f- pole. Moreover, the proportions of" the 
 volumes of the two gases being that of their chemical com- 
 bining volumes, reminds us that, when a body is decomposed, 
 its components are always separated in the proportions in 
 which they were united, namely, those of their atomic weights. 
 If the tubes of this apparatus be graduated, it will be seen 
 that the volume of hydrogen produced is always double the 
 volume of oxygen produced in the same time. Platinum 
 plates are here .employed because platinum does not enter 
 into combination with either of the gases, so that both are 
 disengaged. The oxygen got by this process smells strongly 
 of ozone. This shews that the gas, when electrically set free, 
 possesses more than usual chemical activity, a characteristic 
 common to the products of electric decomposition. They are 
 set free in what is called their nascent state, in which they 
 form combinations with other substances with more than 
 usual readiness. 
 
 230. Voltameter. This was invented by Faraday for test- 
 ing the strength of a current. Fig. 121 shews how it may be 
 
 Fig. 121. Fig. 122. 
 
 constructed. Two platinum plates, each about half a square inch 
 in size, are placed in a bottle containing water acidulated with 
 sulphuric acid ; the plates are soldered to wires which pass up 
 through the cork of the bottle ; binding screws are attached to 
 the upper ends of these wires ; a glass tube fixed into the cork 
 
EFFECTS OF THE GALVANIC CURRENT. 225 
 
 serves to discharge the gas formed within. When the binding 
 screws are connected with the poles of a battery, the water 
 in the bottle begins to be decomposed, and hydrogen and 
 oxygen rise to the surface. If, now, the outer end of the 
 discharging tube be placed in a trough of mercury (mercury 
 does not dissolve the gases), and a graduated tube (fig. 122), 
 likewise filled with mercury, be placed over it, the mixed 
 gases rise into the tube, and the quantity of gas given off in a 
 given time measures the strength of the current. The unit 
 current may be taken as one which is capable of giving off 
 one cubic centimetre of gas per minute. The voltameter 
 chooses as a test the work which the current can actually 
 perform, and establishes a uniform standard of comparison. 
 The plates of the voltameter must be small, for when they 
 are large, a small quantity of electricity is found to pass 
 without decomposing the water. It is found, also, that a 
 minute quantity of the oxygen forms peroxide of hydrogen 
 (H 2 O 2 ) with the water, and remains in solution, so that 
 when very great accuracy is required the hydrogen alone 
 ought to be measured. 
 
 Secondary Action. When sulphate of copper is decomposed 
 by two copper electrodes, copper is deposited at the pole, 
 and S0 4 enters into combination with the copper of the -f- 
 pole, and neither oxygen nor hydrogen is disengaged. When 
 platinum electrodes are used, copper is deposited at the 
 one and oxygen is disengaged at the other. The reason is 
 this : S0 4 does not enter into combination with platinum, and 
 when set free acts on the water in which the salt is dissolved, 
 forming oxygen and sulphuric acid. Thus, S0 4 + H 2 = 
 H 2 ,S0 4 + O. The liberation of the oxygen thus arises from 
 a purely chemical action, subsequent to electrolytic action. 
 This is called Secondary Action, which denotes, as here, the 
 action of the liberated ions upon the constituents of the 
 solvent or substances present in it. Secondary action is well 
 shewn by the apparatus that Daniell employed for the electro- 
 lysis of salts. This consisted of a voltameter in which the gases 
 were collected separately, having a porous diaphragm dividing 
 it into two compartments. When such an apparatus is filled 
 with a solution, say of sulphate of sodium, and subjected to 
 
226 ELECTRICITY. 
 
 the current, oxygen and hydrogen are set free, as they would 
 be in a voltameter like the one described in fig. 120. At the 
 same time soda is formed in the cathode compartment and 
 sulphuric acid in the other. The current thus seems to do 
 double work ; it appears at the same time to decompose water 
 and the sulphate of sodium. This double action must be 
 attributed to secondary action. Sulphate of sodium, Na 2 S0 4 , 
 is decomposed into the cation Na 2 and the anion S0 4 . Na 2 , 
 in the presence of water, becomes soda, Na 2 0, and liberates 
 hydrogen, thus, Na 2 + H 2 O = Na 2 + H 2 ; and S0 4 , acting 
 also on the water, becomes, as already shewn, sulphuric acid 
 and oxygen. Thus the separation of the constituents of the 
 salt is due to electric action, and the liberation of oxygen and 
 hydrogen to a secondary chemical action. The decomposition 
 of water, in an ordinary voltameter, is very probably due to 
 secondary, not primary action. If it be charged with pure water, 
 little or no decomposition is effected, even when the battery 
 consists of 30 or 40 cells. On the addition of a few drops of 
 oil of vitriol, the gases are disengaged in abundance. It is 
 thus, probably, the sulphuric acid that is decomposed in the 
 first instance, and the water in the second. Electrolytic 
 action splits up H 2 S0 4 into H 2 at the pole, and S0 4 at the 
 + pole ; the former is freed, the latter acting on the water 
 becomes sulphuric acid again, and liberates oxygen in the 
 way just shewn. No sulphuric acid is lost in the operation, 
 but it is constantly unformed and reformed. It is considered 
 by many authorities that water never yields directly to the 
 current that it is not, in fact, an electrolyte. With the 
 exception of the case of fused chlorides, and when one of 
 the poles is eaten away, and the other receives a metallic 
 deposit, electrolysis is almost always accompanied by 
 secondary action, it being frequently a matter of difficulty 
 to unravel the primary from the secondary action in the 
 results. 
 
 When there are several electrolytes in one decomposing cell, all 
 are more or less acted upon when the current is strong ; but 
 when it is weak, the action is confined to the best conductor, 
 or to the one yielding most readily to the current. Water, 
 the usual solvent, is never decomposed directly when it holds 
 
EFFECTS OF THE GALVANIC CURRENT. 227 
 
 an electrolytic salt in solution, the action being expended 
 exclusively on the salt. 
 
 231. When there are several electrolytes each in distinct cells in 
 the same circuit. If, instead of one voltameter included in 
 the circuit, we have several, we find that, whatever amount 
 of gas is liberated in one of these, the same amount is 
 liberated in all, and that independent of the size of the plates 
 and amount of acid in each. We learn, therefore, that the 
 chemical power of the current is the same at every point of 
 the circuit where it is manifested. Suppose, instead of two 
 or three voltameters in the circuit, we have one or two decom- 
 posing cells of the following description. A test tube, having 
 a platinum wire, on which the glass has been fused, passing 
 through the bottom, is partially filled with protochloride of 
 tin, which is kept fused by the heat of a spirit-lamp. The 
 platinum wire at the bottom of the tube forms one electrode, 
 and one descending from the top forms the other, dipping 
 below the fused chloride. If, then, this cell be included 
 in the circuit along with the voltameter, and a similar 
 cell containing fused chloride of lead, so that the current 
 enters the tubes by the upper electrodes, and leaves by the 
 lower, the water, protochloride of tin, and chloride of lead 
 are decomposed simultaneously by the current passing through 
 each. In the voltameter, hydrogen and oxygen are disen- 
 gaged ; in the tubes, metallic tin is deposited at the lower 
 electrode of the one, and lead at the other ; whilst chlorine 
 is liberated at the upper electrodes of both. If, now, the 
 quantity of hydrogen, tin, and lead thus set free be weighed, 
 it will be found that their weights are in the proportion of 
 their chemical equivalents namely, as 1 to 59 to 103. From 
 such experiments as these, Faraday concluded that when the 
 current passes through a series of binary electrolytes, consist- 
 ing of one equivalent of each of the elementary bodies, the 
 quantities of the separated elements of the electrolytes are in 
 the same proportion as their chemical equivalents. It is not 
 only in cells exterior to the battery that this law holds, but 
 in the cells of the battery itself. If the battery which effected 
 the above decomposition consisted of six cells, for each equi- 
 valent of hydrogen, tin, and lead separated without the 
 
228 ELECTRICITY. 
 
 battery, one equivalent of zinc ( = 32) in each cell would have 
 been dissolved, and an equivalent of hydrogen disengaged at 
 each of the copper plates, if the cells were one-fluid. Hence, 
 also, if in any circumstances one cell of say Bunsen's battery 
 gives a current as strong as two cells of a one-fluid arrange- 
 ment, the Bunsen cell would consume but half the zinc con- 
 sumed in the other. Hence the economy of cells of great 
 electro-motive force. 
 
 Faraday's law holds also for binary compounds whose 
 elements do not stand in the relation of an equivalent of the 
 one to an equivalent of the other, but with this modification, 
 that the weights of the electro-negative elements alone, separated 
 in the action, are in the ratio of their equivalents. Thus, if 
 the same current pass through two decomposing cells, one 
 containing a solution of the subchloride of copper (CuCl), 
 consisting of an equivalent of copper and half an equivalent 
 of chlorine, and the other of the chloride of copper (CuCl 2 ), 
 consisting of an equivalent of each, the same quantity of 
 chlorine will be disengaged in both, but twice as much copper 
 is deposited in the first as in the second. Had there been a 
 compound of copper with the formula (CuCl 3 ) containing an 
 equivalent and a half of chlorine capable of decomposition, 
 we should expect in the same way that for one equivalent of 
 chlorine disengaged there would be fds of an equivalent of 
 copper. Becquerel, from such instances, expresses Faraday's 
 law somewhat to this effect : When the same current passes 
 through a series of electrolytes, the weights of the separated 
 anions are to each other as their chemical equivalents. The 
 anions here mentioned may be either simple or complex, 
 although the law at first had reference only to elementary 
 substances. Thus, if one cell' contained tribasic phosphate of 
 sodium (Na 3 P0 4 ) in solution, and the other chloride of sodium 
 (NaCl), one atom of P0 4 being equivalent to three of Cl, 
 then for every atom of P0 4 set free in the one cell, three 
 atoms of Cl would be disengaged in the other. The atomic 
 weight of P0 4 is 95, of 3d 3 times 35'5 namely, 106*5. 
 The cations and anions are disengaged in each cell according 
 to the law (sect. 229). 
 
 The amount of decomposition effected by the current is in 
 
EFFECTS OF THE GALVANIC CURRENT. 229 
 
 proportion to the current strength. This law has been already 
 assumed in the discussion of the voltameter (sect. 230). The 
 accuracy of this law is somewhat compromised by the fact 
 that liquids possess, to a certain extent, the power of con- 
 ducting electricity without electrolytic action, so that all that 
 passes in s this way is chemically lost. Fortunately, the error 
 thus introduced is very small, and can be therefore practi- 
 cally disregarded. 
 
 Electro-metallurgy. The application of electrolysis to the 
 arts will be found in the chapter on Practical Applications. 
 
 CHAPTER XVIII. 
 CONTACT FORCE AND THERMO-ELECTRICITY. 
 
 232. Contact Force. When any two substances are placed 
 in contact there must always be a definite surface of separa- 
 tion between them. It is found that, in almost all cases, an 
 electro-motive force acts across this surface at right angles to 
 it, producing electrical displacement, and making the one 
 substance assume a higher potential than the other. This 
 electro-motive force has received the name of Contact Force ; 
 and if A be the potential of the one substance, and B that of 
 the other, A being the higher, the contact force is represented 
 by the symbol A | B, where it is understood that A | B = 
 B | A. The existence of contact force, in the case of metals, 
 was first clearly pointed out by Volta by an experiment such 
 as the following : 
 
 Suppose we take a delicate condensing electroscope whose 
 lower plate consists of a circular disc of zinc to which a pair 
 of gold leaves is attached, and its upper plate of a similar 
 disc of copper to which an insulating handle is attached. 
 Let the one disc be put on the top of the other with a thin 
 layer of shell-lac varnish between them. In this position let 
 a copper wire be bent round so as to touch simultaneously 
 the upper surface of the copper disc and the lower surface of 
 the zinc. Now remove the copper wire, and raise the copper 
 
230 ELECTRICITY. 
 
 disc by its insulating handle, when the gold leaves will be 
 seen to diverge with positive electricity. The explanation of 
 this experiment is as follows : The contact of the copper 
 wire with the zinc plate produces a definite difference of 
 potential between them, which we may represent by V, and 
 if the copper plate be put in connection with the earth, V 
 will be the potential of the zinc plate. Now when the 
 copper plate is raised, the capacity of the zinc plate is 
 diminished, and its potential V increased in the same pro- 
 portion. Hence the divergence f the gold leaves. 
 
 It is to be borne in mind, however, that in this experiment 
 we have other contacts besides that of zinc and copper, 
 namely, the contacts of air with zinc, and air with copper ; 
 and experiment has not yet clearly shewn what part these 
 contacts play in producing the effect. 
 
 In studying contact "force it may be conveniently divided 
 into three kinds : (1) Contact force of metals with metals ; 
 (2) Contact force of metals with fluids ; (3) Contact force of 
 fluids. 
 
 233. Contact Force of Metals Volta's Law. Volta found 
 that, when any number of metals are joined together in series, 
 the sum of the contact forces between the intermediate metals 
 is equal to the contact force between the two end ones. Thus 
 if A, B, C, D be four metals joined end to end, we have 
 A|B+B|C4-CjD = A|D, which equation can be put 
 into the other two forms : 
 
 A|B + B|C + C|D-A|D = 0, and 
 A|B + B|C + C|D-hD|A = O. 
 
 From the last equation we see that there is no resultant 
 electro-motive force when the metals are joined up so as to 
 make a complete circuit ; and this is exactly what we should 
 expect, as otherwise it would be possible to obtain a current 
 which would produce heat in the circuit, and could be made 
 to do mechanical work without any expenditure of energy, 
 which is of course impossible. It is to be understood, how- 
 ever, that all the junctions must be at the same temperature. 
 Two remarkable illustrations of the contact force between 
 metals have been given by Sir William Thomson. In the 
 
CONTACT FORCE AND THERMO-ELECTRICITY. 231 
 
 one experiment he took a flat circular ring consisting, the one 
 half of zinc and the other of copper soldered together along 
 a line which formed a diameter of the ring. A light flat 
 aluminium index with a counterpoise weight was suspended 
 above the ring and close to it "by a silk fibre, so as to turn 
 about an axis perpendicular to the plane of the ring and 
 passing through its centre. The index was so adjusted as to 
 hang, when in equilibrium, along the line of junction of the 
 two metals. When the index was electrified positively, it 
 turned from the zinc towards the copper ; and when negatively, 
 from the copper towards the zinc ; indicating that the zinc was 
 at a higher potential than the copper in virtue of the contact 
 force at the junction. In the other experiment a cylinder of 
 zinc was suspended vertically from an insulating support. 
 A copper funnel was placed in the upper part of the cylinder 
 so as to have its narrow outlet in the axis of the cylinder 
 and at a point midway between its ends. The funnel was 
 filled with copper filings, which trickled down and were 
 received on an insulated dish in metallic connection with 
 one pair of quadrants of the quadrant electrometer ; the 
 other pair of which was connected to earth. The electro- 
 meter indication shewed that the dish was receiving a con- 
 stantly increasing negative charge. This is explained by the 
 contact force between the copper and zinc rendering the zinc 
 positive and the copper negative. In consequence, each 
 copper filing breaks away with a small negative charge which 
 is increased by the induction between itself and the zinc 
 cylinder, and which it gives up on falling to the insulated 
 dish. This is an example of an electric machine worked by 
 gravitation, inasmuch as the earth's attraction has to over- 
 come the electrical attraction between the zinc cylinder and 
 each copper filing. The filings in this way fall slower than 
 they would do if there were no electrical effect. 
 
 234. Determination of Contact Force. Volta was the first 
 to give values for the contact force of the commoner metals, 
 and although these values are but rough approximations 
 they are still sufficient to illustrate his law. The chemical 
 symbols for the metals being used Zn for zinc, Pb for lead 
 (Latin plumbum), Sn for tin (stannum), Fe for iron (ferrum), 
 
232 ELECTRICITY. 
 
 Cu for copper (cuprum), Ag for silver (argentum) the values 
 are as follows : 
 
 Zn | Pb = 5, Pb | Sn = 1, Sn | Fe = 3, Fe | Cu = 2, 
 Cu | Ag = 1. 
 
 By adding these values we find Zn | Ag =12, which is the 
 value given by Volta. Similarly, "by adding the first four 
 values, we find Zn | Cu = 11, and so on of the others. 
 
 The contact force of metals has been determined in various 
 ways by several experimenters. As an example, we may take 
 the method adopted by Kohlrausch. Two equal circular discs 
 of the metals to be tested are taken : let us suppose of zinc 
 and platinum. These are fixed to insulating supports so as 
 to be opposite each other with their planes vertical, and 
 strictly parallel. An arrangement is also made whereby the 
 discs can be separated and replaced always in the same 
 position. In performing the experiment, the discs are first 
 placed with a thin layer of air between them. A platinum 
 wire is bent so as to touch simultaneously the two plates, the 
 platinum plate being at the same time put to earth. The 
 plates are now separated, and the zinc put in metallic con- 
 nection with an electrometer. Let the electrometer indication 
 be a, the contact force between the zinc and platinum is 
 proportional to a, and may be represented by xa. We have 
 then 
 
 Zn | Pt = xa. (1) 
 
 The plates are next put into the same position as before, 
 but this time they are connected through a Daniell's cell by 
 means of its copper terminals. The plates are again separated 
 as before, and the zinc connected with the electrometer. Let 
 the reading be b. Then we have, if E be the electro-motive 
 force of the Daniell : 
 
 Zn | Cu + E + Cu | Pt = xb; 
 or, by Volta's law, Zn | Pt + E = xb. (2) 
 
 Lastly, the plates are again put in position, connected 
 through the cell, but in the reverse way, and separated as 
 before. Let the reading this time be C ; then 
 
 Zn | Pt - E = xc. (3) 
 
CONTACT FORCE AND THERMO-ELECTRICITY. 
 
 By adding and subtracting (2) and (3) we 
 2Zn | Pt = x (b + c), 
 and 2E = x (b - c). 
 
 By division we have 
 
 Zn ]_Pt _ 6 + c 
 E 
 
 -c 
 
 that is, 
 
 Hence the contact force of zinc and platinum is found in 
 terms of the electro-motive force of a Daniell's cell. By this 
 method Kohlrausch found Zn. | Cu to be equal to *48 of a 
 Daniell's cell, a result which agrees closely with the value, 
 half a Daniell, given by Sir William Thomson. 
 
 235. Contact Force between Metals and Liquids. Although 
 the contact force between metals and liquids is very small, still 
 its existence has been clearly made out by several investigators. 
 It has been found also that the contact forces between a series 
 of metals and liquids do not obey Volta's law that is to say, 
 the contact force between the two end substances joined 
 
 Fig. 123. 
 
 directly is not equal to the sum of the contact forces between 
 the intermediate substances when some of these substances 
 are liquids. The following is Hankel's method of determining 
 the contact force between a metal and a liquid : A (fig. 123) 
 is a glass fuunel with a narrow tube bent twice at a right 
 
234 ELECTRICITY. 
 
 angle, and ending in an enlarged portion, B. A is filled 
 with the liquid to be tested, L, which of course will stand 
 at the same level in B. The metal M to be tested is placed 
 in B. C is a copper disc which can be raised or lowered at 
 pleasure, and can also be fixed at a definite position close to, 
 but not touching, the surface of L, so that the surface of L 
 and the lower surface of C act as the opposed faces of the 
 plates of a condenser. 
 
 In performing an experiment, C and M are first connected 
 by a platinum wire p, and M is at the same time put to earth. 
 The wire p is then removed, and C lifted and put in con- 
 nection with the electrometer. Let the reading be a ; then 
 
 Cu | Pt+Pt | M + M | L = xa; 
 that is, Cu j M + M | L = xa. (1) 
 
 The liquid L is next removed, and a plate of the metal M 
 is placed so that its upper surface is in the same plane as the 
 former surface of the liquid. C is then lowered to its former 
 position, contact is made by p between C and the plate of M, 
 and C raised and connected with the electrometer as before. 
 Let the reading this time be 6, then 
 
 Cu | Pt + Pt | M = Cu | M = xb. (2) 
 
 Lastly, a zinc plate is put in the place of the plate of M, 
 and the same operations repeated. If the reading be now c, 
 we have 
 
 Cu | Pt + Pt | Zn = Cu | Zn = xc. (3) 
 
 From (1) and (2) we have M | L = x (a 6) ; and substituting 
 in this the value of x from (3) we get 
 
 M | L = 5LZ_? Cu | Zn. 
 
 c 
 
 Thus the contact force between the metal and the liquid is 
 determined in terms of that between copper and zinc. 
 
 236. Contact Force between Two Liquids. Although the 
 experiments are somewhat difficult, it has been made out 
 that there is a clear contact force between liquids, and that 
 the contact forces between a series of liquids do not obey 
 Volta's law. The cell of Becquerel is usually given as an 
 
CONTACT FORCE AND THERMO-ELECTRICITY. 235 
 
 example of such contact force. It consists of a porous jar 
 containing a solution of potash immersed in a vessel filled 
 with nitric acid. Strips of platinum are placed in the potash 
 and nitric acid to serve as electrodes, and the current is 
 found to go outside the cell from the potash to the nitric 
 acid. Several examples of similar cells have been given by 
 Faraday and others. 
 
 The contact forces between various liquids have been 
 directly observed by Ayrton and Perry by an elaborate series 
 of experiments conducted in order to ascertain if the resultant 
 electro-motive force in any voltaic arrangement is equal to 
 the sum of the observed electro-motive forces of contact at 
 all the junctions of heterogeneous substances in the circuit. 
 They find this to be the case, to a very close degree of 
 apprpximation, in all the voltaic arrangements which they 
 tested. A few examples will make their results clear. Let 
 C, Z, L represent the copper, zinc, and liquid of a simple 
 cell ; and let L x be the liquid in contact with the copper, and 
 L 2 the liquid in contact with the zinc in a Daniell's cell. 
 Then we have for 
 
 (1) A simple cell with distilled water : 
 
 074 + -126 + 750 = '950. 
 
 Electro-motive force measured directly = '832 to '942 in- 
 creasing slowly. 
 
 (2) A simple cell with nearly pure saturated zinc sulphate 
 solution : 
 
 -113 + -358 + '750 = '995. 
 
 Directly observed E. M. F. = 1*000. 
 
 (3) Daniell with distilled water and pure saturated copper 
 sulphate : 
 
 C | L x + L x | L 2 + L 2 | Z + Z | C 
 028 + -071 + '126 + -750 = '975. 
 Directly observed E. M. F. = '995. 
 
236 ELECTRICITY. 
 
 (4) DanielPs cell with pure saturated copper sulphate and 
 nearly pure saturated zinc sulphate : 
 
 Clln + Lj L 2 + L 2 Z + Z|C 
 028 - -033 + '358 + '750 = 1-103. 
 
 Directly observed E. M. F. = 1-068 to 1-081 increasing 
 slowly. 
 
 Thermo-electricity. 
 
 237. When a circuit is made of a series of different 
 metals all at one temperature, Volta's law holds good, and 
 the contact forces balance each other so that no current is 
 produced in the circuit. If, however, the junctions be at 
 different temperatures, the contact forces do not balance 
 each other, and a current is produced whose direction and 
 strength depend upon the kind of metals and the tempera- 
 ture of the junctions. Currents so produced that is, by 
 heating the junction of different substances were first dis- 
 covered by Seebeck, and are called Thermo-electric currents. 
 Such a current is readily shewn by soldering together a 
 piece of iron and copper wire, and attaching the free ends 
 to the terminals of a galvanometer. On slightly heating the 
 soldered junction, a current will be observed whose direction 
 is from the copper to the iron across the hot junction. 
 Thermo-electric currents are produced not solely by heating 
 the junction of dissimilar metals ; they have also been 
 observed by heating the junction of a liquid and a metal, 
 and also the junction of two liquids. Even in a conductor 
 of one metal such a current can be produced, provided the 
 heat be applied at a point where there is some abrupt change 
 in the nature or form of the material, such as from a soft to 
 a hard, from a strained to an unstrained, or from a thick to 
 a thin part of the conductor. 
 
 238. Thermal Currents with Two Metals. A current is 
 always obtained when the point of junction of any two 
 metals is 'heated. The two metals which shew this pro- 
 perty in the greatest degree are bismuth and antimony. 
 When a bar of antimony, A (fig. 124), is soldered to 
 a bar of bismuth, B, and their free extremities are con- 
 
CONTACT FORCE AND THERMO-ELECTRICITY. 237 
 
 nected with, a galvanometer, G, on the junction being 
 heated, a current passes from, the bismuth to the 
 antimony, as shewn in the figure. When S 
 is chilled by applying ice, or otherwise, a current 
 is also produced, but in the opposite direction. 
 Such a combination constitutes a thermo-electric 
 pair. Applying the same mode of explanation 
 to this pair as to the galvanic pair, we find 
 bismuth is + within and without the pair, anti- 
 mony within and + without the pair. Bismuth 
 thus forms the pole, but + element ; antimony 
 tli6;-f- pole, but element of the pair. The metals 
 may be classed in thermo-electric just as they were 
 in electro-chemical order. The following table 
 gives them in this order, the direction of the arrow 
 shewing how the current goes within the pair : 
 
 HEAT. 
 
 5 
 
 COLD. 
 
 The order and numbers in this table are those given by Dr 
 Mathiessen. The numbers give the relative electro-motive 
 forces, and are calculated on the scale of copper-silver as unity. 
 The greater the difference between the two numbers, the 
 greater the electro-motive force. When two metals with the 
 same sign are associated, the difference of the numbers gives 
 the electro-motive force of the pair, with different signs the sum. 
 Thus the electro-motive force of a bismuth and antimony 
 pair is 25 - (- 10)= 35 ; of bismuth-copper, 25 - 1 = 24 ; 
 
238 
 
 ELECTRICITY. 
 
 of iron-antimony, 5 ( 10) = 5. Tellurium, from its 
 rarity, cannot be practically employed. The structure and 
 purity exercise an important influence on the electro- motive 
 force. The numbers of bismuth and antimony in the table 
 are given for those metals when cast. Commercial pressed 
 wire of bismuth would stand as 36, and antimony as 2. Tem- 
 perature has also an important influence in determining this 
 table. The order and numbers given are for temperatures 
 between 40 and 100 F. For other temperatures, the table 
 would be different for several of the metals. 
 
 It will be seen that metals like bismuth and antimony, 
 which have a crystalline structure, are best suited for a 
 thermo-electric pair. It thus resembles a pyro-electric crystal 
 like tourmaline, which, when heated, shews an opposite 
 electricity at each end. If it had a low conducting power 
 like the metals just named, we might expect from it a 
 thermo-electric current instead of mere polarity. It is pro- 
 bable that the crystalline structure, however, accounts for 
 the appearance of electricity in both cases. 
 
 239. Thermo-electric Battery. One bismuth-antimony pair 
 has very little power. To increase this, 
 several pairs are associated together, as 
 shewn in fig. 125, where the same tension- 
 arrangement is adopted as in a galvanic 
 battery. The heat in this case must be 
 applied only to one row of soldered faces. 
 The current effect depends on the difference 
 of temperature of the two sides. When a 
 strong current is required, the one series 
 must be kept in ice or in a freezing mixture, 
 whilst the other is exposed to heat radiating 
 from a red-hot plate of iron. As in the 
 voltaic pair, the electro-motive force is 
 proportionate to the number of pairs ; the size of the bars, 
 like the size of the plates, merely aiding to diminish 
 the resistance. The electro-motive force of a thermo- 
 electric battery is small ; according to Dr Mathiessen, that 
 of 25 bismuth-tellurium pairs equalling one cell of Daniell's 
 battery when the one series is kept at 32 F. and the other at 
 
CONTACT FORCE AND THERMO-ELECTRICITY. 239 
 
 212 F. In consequence of the low electro-motive force of 
 the thermo-electric battery, the galvanometer to be used with 
 it must introduce as little resist- 
 ance as is consistent with the 
 best effect on the needle. Hence 
 special galvanometers are used, 
 in which the coil wire is short 
 (200 turns) and thick (^ inch) ; 
 these are called thermo-galvano- 
 meters. 
 
 When a great number of pairs 
 are formed into a battery, they 
 
 may be conveniently Arranged as in fig. 126, which shews 
 one of 30 pairs. The odd faces, 1, 3, 5, &c., are exposed on 
 the one side, and the even faces, 2, 4, 6, &c., on the other. 
 The terminal bars are connected with the binding screws 
 n, p. The interstices of the bars are filled with insulating 
 matter (gypsum) to keep them separate, and the frame in 
 which the whole is placed is of non-conducting matter. 
 Such a pile in conjunction with a thermo-galvanometer forms 
 a most delicate thermometer for radiant heat. When placed 
 in a room, the temperature of which is equable all round, 
 no current is produced ; but if heat be radiated more on 
 one side than another, a current ensues. If the hand, for 
 instance, be brought near on the one side, a current in- 
 dicates its radiant power ; or if a piece of ice be brought 
 near, a current is also shewn, but moving in the opposite 
 way. 
 
 240. Thermo-electric Inversion. It was discovered by 
 Gumming that the thermo-electric order of the metals was 
 not the same when the temperature of the junctions was high 
 as when it was low, and that, in certain cases, the order was 
 reversed. For instance, let a closed circuit be formed by 
 soldering together the ends of a piece of iron and copper 
 wire, and let the junctions be denoted by A and B. Also let 
 a galvanometer be included in the circuit. If the junction B 
 be kept at the ordinary temperature, and A raised, a current 
 will be observed passing through A from the copper to the 
 iron. This current will increase as the temperature of A is 
 
240 ELECTRICITY. 
 
 raised, till it attains a maximum at a certain temperature T, 
 and then begins to decrease. By still continuing to raise the 
 temperature of A, the current will become zero, and finally 
 set in the opposite direction. This phenomenon is called 
 thermo-electric inversion, and the temperature T is called the 
 neutral temperature. For a circuit of iron and copper the 
 value of T is 284 C. 
 
 It is found that the current becomes zero when the tem- 
 perature of the one junction is as much above T as the other 
 is below it that is, when the mean of the temperatures of the 
 two junctions is T. Hence, in order to shew the reversal of 
 the current, the easiest way is to heat both junctions, but the 
 one a little more than the other. This may be readily accom- 
 plished by putting both junctions in the same flame, but the 
 one in a slightly hotter part than the other. 
 
 It is evident that if both junctions, A and B, be below 
 284 C., the current will pass from copper to iron across the 
 hot junction ; whereas, if both are above 284 C., the current 
 will pass from iron to copper across the hot junction. Hence, 
 if one of the junctions, A, be at 284 C., and B be either 
 hotter or colder than 284 C., the current will pass from 
 copper to iron across the junction A. 
 
 Professor Tait has examined the whole subject of thermo- 
 electric currents with great care, and has given the following 
 expression for the thermo-electromotive force : 
 
 where a is a constant depending upon the nature of the 
 metals, ^ and 2 the absolute temperatures of the hot and 
 cold junctions respectively, and T the absolute neutral tem- 
 perature. 
 
 241. Reversible Heating Effects Peltier Effect and Thomson 
 Effect. If two different metals be soldered together, and a 
 current from a voltaic cell be sent through the junction, the 
 junction will be heated when the current is in one direction, 
 and cooled when the current is in the opposite direction. This 
 reversible effect was first discovered by Peltier, and is usually 
 called the Peltier effect. It is best seen by sending a current 
 
CONTACT FORCE AND THERMO-ELECTRICITY. 
 
 241 
 
 COLD 
 
 Fig. 127. 
 
 through a bismuth and antimony junction as represented in 
 fig. 127. When the current goes from bismuth to antimony, 
 it cools the junction ; when from antimony to bismuth, it 
 heats the junction. If, for instance, water be 
 placed in a hollow at either junction, cooled to 
 C., it will be frozen when the current passes 
 from bismuth to antimony. When the junc- 
 tion of these two metals is put into the bulb 
 of an air thermometer, so that a current can 
 be sent through it either way, the air expands 
 when the current goes from antimony to bis- 
 muth, and contracts when it goes in the 
 opposite way. 
 
 The Peltier effect can very readily be shewn 
 by means of the thermo-pile as follows : Pass 
 the current from a moderately strong voltaic 
 cell through the thermo-pile for a minute or so, then dis- 
 connect the cell and join the thermo-pile in circuit with 
 a galvanometer. A strong deflection will be observed, 
 due to a thermo-electric current in the circuit ; and this 
 current arises from the opposite faces of the pile having 
 been made to assume different temperatures by the passing 
 of the voltaic current. 
 
 We know that a current in any electrical circuit produces a 
 certain quantity of heat in overcoming the resistance, and 
 that this amount of heat is, by Joule's law (sect. 226), pro- 
 portional jointly to the square of the current strength, the 
 resistance, and the time. Hence the quantity of heat pro- 
 duced in this way is entirely independent of the direction of 
 the current in the circuit. It is different with the heating 
 and cooling produced by the Peltier effect. Since this changes 
 sign when the current is reversed, it obviously cannot be pro- 
 portional to the square or any even power of the current 
 strength, but must be proportional to the first or some odd 
 power of the current strength. It has been found to be 
 simply proportional to the current strength ; and hence, if 
 II denote the coefficient of the Peltier effect for any junction 
 that is to say, the amount of heat absorbed or evolved at 
 the junction by the passing of a unit current in a unit of 
 
242 ELECTRICITY. 
 
 time we have, for the whole heating effect, expressed in 
 mechanical units, produced in a circuit of two metals, the 
 following expression : 
 
 JH = cm* net. 
 
 242. The above equation gives us the means of calculating 
 the value of II, provided we can measure the total amount of 
 heat produced in any circuit by the passage of a known 
 current for a unit of time first, when the current is in one 
 direction, and secondly, when it is in the opposite direction. 
 Let Hj_ and H 2 be the total amounts of heat so produced, then, 
 taking first the upper sign and then the lower, and dividing 
 the whole by J, we have 
 
 UCt 
 
 H >- J J 
 
 By subtracting these equations, we get 
 
 - H 2 = 
 
 from which we have H 
 
 or when the current is of unit strength and the time unity, 
 
 n = i(H 1 -H 2 ). 
 
 Another reversible heating effect was predicted, from theory, 
 by Sir William Thomson, and afterwards verified by him 
 experimentally. It is hence called the Thomson effect. 
 Suppose we have a closed circuit formed of iron and copper 
 wire, and that one of the junctions, A, is at the neutral 
 temperature, and the other, B, at a lower temperature. It is 
 evident that a current will pass from copper to iron through 
 A, and from iron to copper through B. By the Peltier effect 
 there will be an evolution of heat at B. Since the current in 
 the circuit is producing heat, and could be made to do 
 mechanical work, there must be a disappearance of heat 
 equivalent to the mechanical work so done, at some part of 
 the circuit. This disappearance does not take place either 
 at A or B ; and hence, it must be looked for in the copper 
 
CONTACT FORCE AND THERMO-ELECTRICITY. 243 
 
 and iron parts of the circuit themselves. It was found by 
 Thomson that the current carries heat with it in a copper 
 wire when it passes from a hot part to a cold part, and that 
 it carries cold with it in an iron wire when it passes from 
 hot to cold. The nature of the experiment which proves this 
 will be understood from the following description. Insert, in 
 a voltaic circuit, a piece of fine copper wire, and let the two 
 junctions be kept at the freezing point. When the current 
 passes, the wire will be heated, and if there were no reversible 
 heating effect, the point of maximum temperature would be 
 at the middle of the wire, and the temperature would gradu- 
 ally fall down as we approached either junction. As it is, 
 however, the point of maximum temperature is observed to 
 be a little past the middle point in the direction in which the 
 current is going, and to change to the other* side when the 
 current is reversed. The opposite is found to be the case 
 with a fine iron wire in the circuit. 
 
 243. Thermo-electric Diagram. A thermo-electric diagram 
 gives us the means of representing graphically, in a very 
 clear and simple way, the electro-motive force and the 
 Peltier and Thomson effects in any thermo-electric circuit. 
 Such a diagram was first suggested by Sir "William Thomson ; 
 and it has been brought to perfection by Professor Tait. It 
 is constructed as follows : 
 
 Let Ox and Oy be two co-ordinate axes at right angles to 
 each other ; and let distances measured along Ox, that is, the 
 abscissae, represent temperatures reckoned from the absolute 
 zero, that is, 273 C. In order to draw what are called the 
 thermo-electric lines for the several metals, we must first 
 assume some metal as a standard ; and then form thermo- 
 electric circuits with it and each of the other metals in 
 succession. The metal so assumed is usually lead, and for 
 this reason, that the Thomson effect in lead, according to the 
 experiments of Le Roux, is almost nil. Suppose now we wish 
 to draw the thermo-electric line for copper. Having made a 
 circuit of copper and lead, we find, by a series of experiments, 
 the value of the electromotive force in the circuit, when the 
 hot junction is half a degree above, and the cold junction half 
 a degree below each particular temperature from C. up- 
 
244 
 
 ELECTRICITY. 
 
 wards. This is called finding the thermo-electric power of 
 the metal with reference to lead. The values so found are 
 represented in the diagram by vertical ordinates raised at 
 the ends of the abscissae which represent the temperatures ; 
 and when the ends of these ordinates are joined, the curve 
 formed is the thermo-electric line. Professor Tait has shewn 
 that this curve is a straight line for all metals between the 
 limits of temperature C. and 300 C. ; and, hence, in order 
 to simplify the diagram, we can assume Ox as representing 
 the thermo-electric line for lead. The other lines will thus 
 be straight lines inclined to Ox at various angles. 
 
 Let AB represent the copper, and CD the iron line, which 
 
 cut each other at 
 
 N ; the 
 
 OH, of the point 
 N will represent 
 the neutral tem- 
 perature for cop- 
 per and iron. Let 
 the hot junction 
 be at the tempera- 
 ture /3, and the 
 cold junction at 
 the temperature 
 a, represented by 
 OF and OE re- 
 spectively ; then 
 since the line BF 
 
 FIg 128 is the thermo- 
 
 electric power of 
 
 copper, and CF that for iron, each with reference to lead ; it 
 follows that the difference, that is, CB, will represent the 
 thermo-electric power of copper and iron for the mean tem- 
 perature (3. Similarly, DA will represent the thermo- 
 electric power of copper and iron for the temperature a. 
 
 From the points A, B, C, D draw lines parallel to Ox, 
 meeting Oy in a, b, c, d respectively ; then the area ABCD 
 will represent the electro-motive force of a copper and iron 
 circuit, when the hot junction is at /3, and the cold junction 
 
CONTACT FORCE AND THERMO-ELECTRICITY. 245 
 
 is at a ; and under the same circumstances, the area BCc& 
 will be the Peltier effect at the hot junction, the area ADda 
 the Peltier effect at the cold junction, the area BAa& the 
 Thomson effect in copper, and the area GDdc the Thomson 
 effect in iron. 
 
 CHAPTER XIX. 
 
 ELECTRO-MAGNETISM AND MAGNETO-ELECTRIC INDUCTION. 
 
 244. Allusion has already been made (sect. 184) to the dis- 
 covery by Oersted of the action of a wire carrying an electric 
 current on a magnetised needle placed in its neighbourhood. 
 This discovery laid the foundation of the department of 
 electrical science called electro-magnetism. It shews that the 
 space surrounding every closed circuit in which a current is 
 flowing constitutes a magnetic field, through which lines of 
 force are passing, and at any point of which a magnetic pole 
 will be acted upon by a certain resultant electro-magnetic 
 force. It is our object to find, in any case, the direction and 
 intensity of this force in relation to the form of the circuit, 
 the strength of the current in it, and the distance of the 
 magnetic pole from the circuit. This can be done most 
 simply by substituting for the closed circuit what is called 
 its equivalent magnet, or its equivalent magnetic shell. 
 
 245. Equivalent Magnet and Equivalent Magnetic Shell. Sup- 
 pose we have 
 
 a small plane 
 closed cir- 
 cuit AB (fig. 
 129),through 
 which a cur- 
 rent is flow- ^ m 
 
 ing in the direction indicated by the arrow ; and let the dis- 
 tance of this circuit from the magnetic pole m be very great 
 in comparison with the dimensions of the circuit : then, it 
 follows, from the researches of Ampere and Weber, that the 
 action of AB on m is exactly the same as that of a small 
 
246 
 
 ELECTRICITY. 
 
 magnet, SN, inserted perpendicularly through the circuit, 
 subject to two special conditions. These conditions are, 
 first, that the moment of the small magnet be equal to the 
 area of the circuit a multiplied by the strength of the current 
 C on it, that is, to C ; secondly, that the direction of the 
 magnet from south pole to north pole be that of the insertion 
 of a corkscrew through the circuit by rotating the wrist in 
 the direction of the current. Such a magnet is called the 
 equivalent magnet of the circuit. 
 
 Instead of the small magnet SN, we may imagine the 
 whole circuit packed fuli of smaller magnets, provided the 
 sum of the moments of all the magnets be equal to aC. If 
 this were done, we should have all the north poles lying on 
 one surface, and all the south poles on another, producing 
 two parallel layers the one of north magnetism, and the 
 other of south magnetism, having the closed circuit for their 
 common bounding edge. These two layers constitute a 
 magnetic shell of strength C, which is the equivalent magnetic 
 shell of the circuit. 
 
 Now, suppose we have a closed circuit ABCD, of any size 
 
 and form ; and let the space 
 inclosed by it be filled in by 
 a thin membrane of any 
 form upon which we can 
 draw a multitude of inter- 
 secting lines, cutting it 
 up into four-sided spaces. 
 Obviously, if the lines be 
 close enough together, each 
 of these spaces may be 
 regarded as a plane surface. 
 Let now a current of 
 strength C, circulate round 
 each of the small spaces 
 abed, as indicated by the inside arrows. It is evident from 
 inspection that there are two equal and opposite currents 
 in each line which separates one space from another. The 
 effect of these is absolutely zero ; and hence, the whole 
 assemblage of such currents is identically equivalent to a 
 
ELECTRO-MAGNETISM. 247 
 
 single current of strength C, circulating in the same direction 
 round the single circuit ABCD. Conversely, for the current 
 in any circuit ABCD, we can substitute a series of equal 
 currents round the small circuits abed; and from what 
 has been already proved, we can substitute for each such 
 small circuit its equivalent magnetic shell. When this is 
 done, the whole assemblage of magnetic shells combine to 
 form one single magnetic shell, having the circuit ABCD 
 for its bounding edge ; which is consequently the equivalent 
 magnetic shell of the circuit ABCD. To assist the imagina- 
 tion, we may regard this equivalent magnetic shell as a very 
 thin sheet of steel filling up the circuit, having one of its 
 surfaces all north magnetism, and the other all south 
 magnetism. The strength of such a shell at any point 
 is measured by the product of the intensity of the magnetisa- 
 tion at that point into the thickness of the shell at the same 
 point. 
 
 246. Having obtained the equivalent magnetic shell of any 
 closed circuit, we have next to shew how, by means of it, 
 we can get the potential at any point due to a closed circuit 
 carrying a current. Before doing so, however, it will be 
 necessary to explain what is meant by the solid angle sub- 
 tended at a point by a closed circuit, or its equivalent 
 magnetic shell. Let ABCD (fig. 131) be the closed circuit, 
 
 Fig. 131. 
 
 and P the point. From the point P, draw straight lines to 
 every point of the circuit. These will lie on a conical 
 
248 ELECTRICITY. 
 
 surface having its vertex at the point P. With P as a centre, 
 describe a sphere of unit radius which will cut the conical 
 surface. The curved line on the surface of the sphere formed 
 by the intersection of the conical and spherical surfaces will 
 evidently inclose a certain area on the unit sphere. It is 
 this area which represents the solid angle subtended at P by 
 the curve ABCD. 
 
 Now, let a current of strength C, circulate in ABCD ; will 
 also be the strength of the equivalent magnetic shell, having 
 ABCD for its bounding edge. Now, if o> be the value of the 
 solid angle subtended at P by ABCD, then the value of the 
 potential at P, due to the closed circuit, is Cw. We must 
 here attend to certain conventions regarding signs. The 
 solid angle is reckoned + when the area on the unit sphere 
 is to the left of P and to the right of ABCD, and when it is 
 to the right of P and the left of ABCD. It is evident that 
 if P move up to ABCD, the value of w will gradually 
 increase; and when P comes up to the positive side of the 
 shell inclosed by ABCD, o> will be equal to the area of half 
 the surface of the unit sphere, that is, it will be equal to 
 27T. It is equally evident that when P coincides with the 
 negative surface of the inclosed shell, the value of w will be 
 2;r. Hence, at these two points, the values of the potential 
 are respectively + 2?rC and 27rC. Hence we see that if P 
 be carried round the closed circuit from the negative to the 
 positive side, the value of the potential changes from 27rC 
 to + 27rC, that is, it changes by the value 4?rC. Since, in 
 passing from the positive to the negative side of the shell, 
 the potential changes from a positive to a negative value, 
 it is manifest that at some point of the journey the potential 
 must be zero. This will happen, for instance, for a plane 
 closed circuit when the point P is in the plane of the 
 closed circuit, as then the solid angle reduces to being a 
 simple curved line on the unit sphere, which, of course, 
 has no area. 
 
 If a series of surfaces be drawn passing through all those 
 points at which the potential has the same value, these 
 surfaces will be equipotential surfaces, and will all meet in 
 the closed circuit. If lines be drawn everywhere at right 
 
ELECTRO-MAGNETISM. 249 
 
 angles to these surfaces, these will be the lines of force due 
 to the circuit, and will be the lines along which a free 
 magnetic pole will tend to move under the -influence of the 
 electro-magnetic force due to the circuit. 
 
 We are now in a position to employ the results obtained 
 to find the mutual action of currents on magnets, and of 
 currents on other currents. 
 
 247. Long straight Wire carrying a Current. Since every 
 electrical current must form a closed circuit, in order to 
 obtain this case we must conceive the closed circuit to be so 
 large that the part of it which we are considering is entirely 
 beyond the influence of the other parts of the circuit. 
 Perhaps the easiest way of doing this is to imagine the 
 straight wire to form one side of a huge rectangle of wire 
 through which the current is circulating, and that the 
 rectangle is so large that its opposite sides may be con- 
 sidered as infinitely distant from each other. 
 
 Let A and B represent the cross sections of two parallel 
 sides of this rectangle made by the plane of the paper 
 passing perpendicularly through them ; and let P be the 
 point on the plane of the paper at which the potential due 
 to the current in A is required. The current is supposed to 
 
 Fig. 132. 
 
 come vertically upwards through the paper at A, and to 
 descend at B. 
 
 Describe round P a sphere of unit radius, and let the small 
 circle abc be a section of it made by the plane APB. 
 
250 
 
 ELECTRICITY. 
 
 It is evident, on a little reflection, that the solid angle 
 subtended at P by the closed circuit is the area on the unit 
 sphere contained between two planes, perpendicular to the 
 plane of the paper, passing through the lines AP and BP 
 respectively. It thus forms a lime on the unit sphere, and 
 the area of this lune is clearly the same part of the whole 
 surface of the sphere that the angle APB is of four right 
 angles. Now it is known that the area of the surface of a 
 sphere is four times that of its section through the centre, 
 and hence the area of the unit sphere is four times that of 
 the circle dbc, that is, is equal to 47r. If we use circular 
 measure, and denote the angle APB by a, we have for the 
 value of the solid angle subtended at P : 
 
 X 47T = 20. 
 
 2?r 
 
 Now if B be supposed to move parallel to itself away from 
 A, the angle APB will increase, and ultimately become equal 
 to APH, that is, to PAL, which we denote by 0. Hence the 
 true value of the solid angle is 2#, and if C be the current in 
 A, the value of the potential at P due to it is 2$C. 
 
 248. From this we see at once 
 that the potential is the same at 
 every point of the line AP, and 
 hence the equipotential surfaces 
 will be a series of planes passing 
 through A at right angles to the 
 plane of the paper. Since the 
 lines of force are always perpen- 
 dicular to the equipotential sur- 
 faces, they will be a series of 
 concentric circles in planes per- 
 pendicular to the wire, and having 
 the wire passing through their 
 common centre. 
 
 That such is the case can be 
 readily shewn by an experiment. 
 Pass a straight wire, AB (fig. 133), perpendicularly down- 
 wards through the centre of a circle of card-board, CD, 
 
ELECTRO-MAGNETISM. 251 
 
 on which some fine iron filings are scattered. Send a 
 pretty strong current through the wire, and gently tap 
 the card-board, when the filings will be observed to arrange 
 themselves in circles round the wire, tracing out the lines of 
 force. 
 
 Having obtained the potential at P, we have next to obtain 
 the strength of the field, or the magnetic force at that point. 
 This is done by finding the rate of change of the potential 
 along the line of force, PQ, which is part of a circle, with 
 A as its centre. Denoting the magnetic force by H, and 
 the potentials at P and Q respectively, by V x and V 2 , and 
 the angles QAL and PAQ by < and ft, we have : 
 
 IT V -V 2G< - 2C6> 
 
 PQ 
 Now 0-g 
 
 _ _ 20 PQ 20 
 
 = PQ ' PA = PA ; 
 
 that is, the magnetic force varies inversely as the distance of 
 the point from the wire, and acts in a direction at right 
 angles to the wire. 
 
 249. Electrical Circuit placed in a Magnetic Field. We come 
 next to consider the effect produced upon an electric circuit 
 carrying a current, when the circuit is placed in a magnetic 
 field, due either to the presence of a magnet or another 
 electric circuit. For this purpose we substitute for the 
 electric circuit its equivalent magnetic shell, and then we 
 have merely to consider the effect of one magnetic system 
 upon another. It can be shewn mathematically, as has been 
 done by Clerk- Maxwell, that a rigid circuit so placed, and 
 perfectly free to move, will set itself under the influence of 
 the electro-magnetic forces acting upon it, so as to include 
 the greatest possible number of lines of force ; and that the 
 direction of the current in the circuit will be related to the 
 direction of the lines of force according to the cork-screw 
 rule already mentioned. If, instead of being rigid, the 
 circuit be flexible, it will also so set itself, and at the same 
 time so alter its form, as to include the maximum number of 
 
252 
 
 ELECTRICITY. 
 
 lines of force consistent with the geometrical conditions to 
 which it is subject. 
 
 It results from these considerations, that, if an electric 
 circuit experience any displacement in a magnetic field, the 
 displacement will be such as to inclose more lines of force 
 in the circuit ; and that the amount of work done by the 
 electro-magnetic force during the displacement will be 
 proportional to the additional number of lines of force so 
 inclosed. From this we can find the electro-magnetic force 
 acting upon the circuit. 
 
 Let BE (fig. 134) be a part of a circuit carrying a current in 
 the direction of the arrow ; and for simplicity let us suppose 
 
 the plane of the circuit 
 to be perpendicular to 
 the lines of force which 
 are represented by the 
 short parallel arrows. 
 
 Take Pp } an element, 
 that is, a small part of 
 the circuit, supposed 
 straight, and of length 
 equal to a. From P 
 draw PH parallel to the 
 lines of force, and cut off 
 Fig. 134. from it a part, PA, equal 
 
 to the magnetic force, H, 
 
 at the point P. It is evident that if the circuit Pp be moved 
 parallel to itself along PA, no alteration will be made in the 
 number of lines of force passing through it. Hence no work 
 will be done during such motion. The same is the case if 
 the circuit be simply moved round in its own plane. Hence 
 the direction of the electro-magnetic force acting upon Pp 
 must be perpendicular at once to PA and Pp, that is, to the 
 plane PpaA, Aa and pa being drawn parallel respectively to 
 Pp and PA. Let PR be the direction of the resultant 
 electro-magnetic force, and PQ be the displacement parallel 
 to itself produced on the element Pp. Complete the paral- 
 lelogram PQ,qp. Hence if be the current strength in the 
 circuit, the additional number of lines of force included in 
 
ELECTRO-MAGNETISM. 
 
 253 
 
 the circuit by the displacement of Pp is represented by H 
 multiplied by the area of the parallelogram PQqp, that 
 is, by the product H x Pp x PQ. Also, since R is the 
 resultant force, and PQ the space through which it acts, the 
 amount of work done during the displacement is represented 
 by the product R x PQ. Hence we have R x PQ = H x C 
 x Pp x PQ, and therefore R = HC x Pp = HCa. 
 
 Since the direction of the displacement is always such 
 as to include more lines of force, it can, in any case, be 
 determined by the following rule. Place a right-handed 
 cork-screw in the direction of the resultant force PR. Turn 
 the wrist in the direction from Pp to PH, that is, from the 
 direction of the element to the direction of the magnetic 
 force ; then the circuit will be displaced in the direction of 
 the longitudinal motion of the screw. 
 
 250. Two parallel Currents. We shall now apply the above 
 to find- the resultant electro-magnetic force between two 
 parallel currents, one of which is supposed to be infinitely 
 long. 
 
 Let AB be an infinitely 
 long straight wire carry- 
 ing a current C, and DE 
 a parallel wire carrying 
 a current, d, in the same 
 direction, as indicated by 
 the arrows. Let the per- 
 pendicular distance be- 
 tween the two wires be 
 r, and take Pp = a, an 
 element of the circuit 
 DE. 
 
 We have already shewn 
 that the lines of force 
 due to AB are concentric 
 circles in planes perpen- 
 dicular to AB, and having AB passing through their common 
 centre. Hence PH is the direction of the magnetic force 
 H at P. Hence the resultant electro-magnetic force R will 
 be perpendicular to Pp and PH, that is, will be directed 
 
 Fig. 135. 
 
254 
 
 ELECTRICITY. 
 
 towards AB. Also, if we think of the cork-screw being 
 turned from Pp to PH, we see that Pp will move towards 
 AB, that is, there will be an attraction between the wires. 
 For the amount of the attraction we have R, = HC^ct. For 
 
 2C 
 this case H has been shewn (sect. 248) to be equal ' 
 
 Hence we have 
 
 If the direction of the current in DE be reversed, there 
 will be a repulsion instead of an attraction between AB and 
 DE. 
 
 Hence we have the following general law which regulates 
 the action between two parallel currents, namely : That 
 parallel currents in the same direction attract each other, 
 and parallel currents in the opposite direction repel each 
 other. 
 
 251. We come next to the case 
 
 of two straight wires, carrying cur- 
 rents, inclined to each other at an 
 angle, one of the wires being, as 
 before, supposed infinitely long. Let 
 AB be the infinitely long wire car- 
 rying a current from A to B, and 
 DE another wire, carrying a current 
 from D to E, inclined to AB, but in 
 the same plane with it. DE is sup- 
 posed to be insulated from AB at the 
 crossing-point O. 
 
 At P the lines of force due to 
 AB are perpendicular to the plane 
 of the paper, seeing that they are 
 circles in planes perpendicular to 
 the paper. They are also directed 
 through the paper from the reader. Similarly at P x , the 
 lines of force are perpendicular to the plane of the paper 
 and towards the reader. 
 
 Hence at P the direction of the electro-magnetic force is 
 in the line PG, perpendicular to PE. Similarly the force 
 
 A 
 
 Fig. 136. 
 
ELECTRO-MAGNETISM. 
 
 255 
 
 at P t is in the direction P 1 L. These two forces constitute 
 a couple which tends to turn DE about O till it becomes 
 parallel to AB. 
 
 If the current DE be reversed, the motion about O will 
 be reversed. 
 
 Hence follows a second general law, namely That currents 
 inclined to each other at an angle, attract when they both run 
 to or from the crossing point, but repel when they run the one 
 to and the other from the crossing point. 
 
 252. Next let AB be as before an infinitely long straight 
 current, and DE a current at right angles to it, but on one 
 side. At P the lines of force due to AB are perpendicular to 
 the plane of the paper, and directed 
 
 through it. Hence we see at once, 
 by applying the second law, or still 
 better the cork-screw rule, that the 
 direction of the resultant electro- 
 magnetic is that of PL. Hence if 
 DE be free to move parallel to 
 itself, it will move in the direction 
 from A to B, that is, in the same 
 direction as the current in AB. 
 By reversing the current either in 
 AB or DE, DE will move in the 
 opposite direction. From this we 
 have a third general law, which 
 may be thus stated : When one 
 current is perpendicular to another, 
 the former current moves forwards parallel to the latter when it 
 runs from it, and backwards when it runs to it. 
 
 253. The above results can be illustrated experimentally 
 in a variety of ways. The first two may be experimentally 
 illustrated by an apparatus such as that shewn in fig. 138. 
 The rectangle cdef is movable round the pins a and &, 
 resting on two mercury cups, which act as binding screws 
 to complete contact. The arrangement is such that while 
 the rectangle cdef is moving about its axis, a current can 
 continue steadily to flow in it. Further description is 
 unnecessary, as the diagram explains itself. It can be easily 
 
 Fig. 137. 
 
256 
 
 ELECTRICITY. 
 
 Fig. 138. 
 
 understood, that a wire conveying a current may be placed, 
 
 with regard to the different 
 parts of the rectangle, so as 
 to illustrate the first two 
 laws. Thus, if a wire con- 
 ve} 7 ing a downward current 
 be brought near to cd, so as 
 to be parallel to it, attrac- 
 tion will take place ; if it 
 be presented to fe, repulsion 
 will ensue. A current-wire 
 held horizontally with re- 
 spect to cd, can be placed 
 so as to make the currents 
 both tend to the crossing- 
 point between them, or the 
 opposite, so as to illustrate 
 the second law. It may be 
 objected, that in this appar- 
 atus we cannot examine the effect on one part of the current 
 without also taking in the other parts of the rectangle ; but 
 these last may be made to stand comparatively so far off as 
 not to affect the main result. 
 
 254. The third law may be shewn by an apparatus such 
 as that in fig. 139. A is a small circular trench containing 
 mercury, surrounded by a coil of insulated copper wire, ww'. 
 The metal rod, BB, is surmounted by a small cup of 
 mercury. A light copper wire, bacd, is poised on a fine 
 point in the cup n, and its lower ends, d, b, dip into the 
 mercury of the trench. The circuit is so arranged that 
 the current enters at w, traverses the coil, passes to BB 
 (connection not shewn), which it ascends ; at the cup, 
 entering the copper wire, it splits into two branches, 
 descends along ab and cd to the mercury, and leaves finally 
 for the battery at o. As soon as the circuit is closed, the 
 wire, bacd, enters into constant rotation. In the coil, the 
 current moves contrary to the hands of a watch ; the wire, 
 according to the third law, moves backward upon it in the 
 direction of the hands of a watch. In the figure, the 
 
ELECTRO-MAGNETISM. 
 
 257 
 
 Fig. 139. 
 
 horizontal parts of the current, 'na and nc, are so far above the 
 
 current as to affect the motion 
 
 slightly, if at all. But if the 
 
 upright branches ab and cd were 
 
 short, so as to leave the motion 
 
 almost entirely to na and nc, 
 
 the wire would still rotate as 
 
 before ; for the currents na and 
 
 nc are also perpendicular to the 
 
 current of the coil, though in 
 
 a different but parallel plane, 
 
 and both run towards it, thus 
 
 standing in the same relation 
 
 as before. If the current be 
 
 reversed, the motion of the 
 
 wire is also reversed. 
 
 255. A curious consequence 
 is considered to follow from 
 
 the second law namely, that since two parts of a straight 
 line may be regarded as standing at a very obtuse angle to 
 each other with reference to a point in it, any point in the 
 straight line may be looked upon as the crossing-point of its 
 two parts. As at the point taken we find the one part of the 
 current approaching, the other leaving it, the two parts of the 
 current repel each other. Hence the various parts of a current, 
 in a straight line, repel each other. Faraday, in illustration of 
 this, bent a wire in the form of a horseshoe, and made each 
 end of it dip into a separate vessel containing mercury. The 
 wire was partly supported by the mercury, and partly by the 
 beam of a delicate balance. When the poles of a battery are 
 put into the vessels, the wire loses weight, from the repulsion 
 of the mercury conveying the same current as itself. This 
 experiment, it must be confessed, is not quite decisive, as the 
 repulsion may arise from the peculiar action of a fluid on a 
 solid part of the circuit. The mutual action of currents on 
 each other was first elucidated by Ampere in 1825. 
 
 256. Currents on Magnets. If we put a north magnetic 
 pole in the neighbourhood of a straight wire carrying a cur- 
 rent, it will, as we have seen, move round the wire in a circle 
 
258 
 
 ELECTRICITY. 
 
 tracing out a line of force. A south, magnetic pole similarly 
 'placed will also move round the wire, but in the opposite 
 direction. Suppose now that we place near the wire a long, 
 perfectly flexible magnet, such as we may imagine made from 
 a long thin strip of very flexible watch mainspring ; since 
 the north pole goes round the wire in one direction, and the 
 south pole in the other direction, the effect will be that the 
 flexible magnet will become coiled round the wire in the 
 form of a close spiral. Conversely, if we imagine the magnet 
 fixed, and the wire carrying the current flexible and free 
 to move, then the wire will coil itself round the magnet. 
 This last result can be easily illustrated by experiment as 
 follows : 
 
 Let NS be a long strongly magnetised steel bar placed 
 vertically, and let ABC be a long narrow strip 
 of some very flexible metallic foil suspended 
 near the magnet, and through which a current 
 can be passed. When a moderately strong 
 current is sent through ABC, the loose portion 
 of the strip will be seen to coil itself round 
 the pole of the magnet ; and by reversing the 
 current it will uncoil itself, and again coil 
 round the magnet in the opposite direction. 
 
 257. Law of the action of Currents on Magnets. 
 The law of the action of currents on magnets 
 has been investigated experimentally by Biot 
 and Savart in the following way. They sus- 
 pended, by means of a cocoon fibre, a short 
 magnetic needle in the neighbourhood of a 
 straight wire carrying a current of constant 
 strength. By means of a fixed magnet, the action of the 
 earth's magnetism on the movable needle was as far as 
 possible neutralised ; and the whole apparatus was inclosed 
 in a glass case to prevent disturbance from currents of air. 
 They first found that, in all positions, the resultant force, 
 due to the current, acting upon the magnetic + pole, was 
 perpendicular to the plane passing through the wire and the 
 pole. The magnet, in consequence, set itself so that its axis 
 was at right angles to the line drawn from its middle point 
 
 _. 
 
ELECTRO-MAGNETISM. 259 
 
 perpendicular to the wire carrying the current. They next 
 varied the distance of the magnet from the wire, and observed, 
 at the various distances, the period of oscillation of the 
 magnet, when disturbed, under the influence of the current. 
 From this they found that the intensity of the electro- 
 magnetic force acting upon the pole of the magnet varied 
 inversely as the perpendicular distance of the pole from the 
 straight wire. Now, in order to obtain this result for the 
 action of the whole wire, we must suppose that each element 
 of the wire acts upon the pole with a force which varies 
 directly as the length of the element, and inversely as the 
 square of its distance from the pole ; or, to put it otherwise, 
 by making this latter assumption we can shew mathema- 
 tically that the experimental result must follow. The 
 following is the proof usually given. 
 
 Let AB and A'B' be two parallel straight wires carrying 
 equal currents at different 
 perpendicular distances, ME 
 and ME', from the magnetic 
 pole M. Let CD and C'D' 
 be elements of the currents 
 cut off by the lines MCC' 
 and MDD', which are sup- 
 posed inclined to each other 
 at a very small angle. Also A' 
 
 let / and /' denote the forces Fig. 141. 
 
 exerted by the elements CD 
 
 and C'D' respectively upon the magnet-pole M. Then, 
 
 according to the above assumption, we have 
 
 .-..CD C'D' . 
 J ' J ' CM* ' C'M 2 ' 
 
 / CD C'M a 
 that is, 7 = CTJ' ' CAT 
 
 But from similar triangles we have 
 
 CD CM EM 
 C'M ~ E 7 M* 
 Q 
 
ELECTRICITY. 
 
 / EM E'M 2 E'M 
 = ' EM* ~ EM 
 
 that is, 
 
 Hence the forces exerted by the elements CD and C'D' vary 
 inversely as the distances EM and E'M ; and since CD and 
 C'D' are any elements, what is true of them is true of all the 
 others, and hence the forces exerted by the whole wires 
 AB and A'B' vary inversely as the distances EM and E'M. 
 
 Now, so long as we are dealing with the elements of 
 currents merely, it matters not whether we consider them to 
 be elements of straight currents, or elements of currents of 
 any other form ; and hence, by summing up the above 
 results, we have the following expression for the general law 
 which regulates the action of currents, on magnets : The 
 force with which each element (small part) of a current acts on a 
 magnetic pole, stands at right angles to the plane passing 
 through the element and the pole, and is inversely proportional 
 to the square of the distance of the element from the pole. 
 
 258. Circular Current. We can now make use of the 
 above law to find the force exerted by a circular current on 
 a magnetic pole placed at a point on its axis that is, on the 
 straight line drawn perpendicular to the plane of the circle 
 through its centre. 
 
 Let ABC be the circular wire carrying a current, C, 
 
 and let the radius 
 OA = a. Also let 
 AB be an element 
 of the current of 
 length s. Let M 
 be a magnetic pole 
 of strength unity 
 placed on the axis 
 OMF. The force 
 /, exerted by the 
 
 Fig. 142. element AB on M, 
 
 is perpendicular to 
 the plane AMB. Denote it by the line ME of length /. 
 

 ELECTRO-MAGNETISM. 261 
 
 Then, according to the above law, we have / = , when 
 
 r = AM. 
 
 Now, the force /can be resolved into two components, one 
 parallel to OF, and the other perpendicular to it. Let h 
 and g be these components respectively. From the similar 
 
 triangles, FEM and 0AM, we have ^~, = ^|, and therefore 
 
 h a , , , . , of 
 j = that is, h = . 
 
 Cs 
 By substituting for /its value -^, we have 
 
 , ' a Cs Cas 
 
 fl = n- = - o-. 
 
 r r 2 r 3 
 
 Now, it will be at once seen that a precisely similar 
 expression will be got for each element of the circuit, and 
 that the value of r for each element is the same, and hence 
 the value of the total component of the force parallel to OF 
 will be got by summing up all the fractions similar to 
 
 g-. Let H denote this total component, then, 
 
 Ca 
 H = g- X the circumference of circle ABC, 
 
 that is, H = ?^ (1) 
 
 Since each element of the circuit has an equal diametrically 
 opposite element, it is evident that the components, cor- 
 responding to g, due to each pair of such elements, must be 
 equal and opposite forces, and hence will destroy each other. 
 Hence equation (1) gives the total force exerted by the 
 circular circuit on a unit pole at M. 
 
 By supposing M to move up to O, so that r becomes equal 
 to a, we obtain the following expression for the force exerted 
 by a circular current upon a unit pole placed at its centre 
 namely : 
 
 a a 
 
 259. Electro-magnetic Rotations. A great many pieces of 
 
262 
 
 ELECTRICITY. 
 
 Fig. 143. 
 
 apparatus have been devised to illustrate the continuous 
 rotation of magnets under the influence of currents, and vice 
 versd. The apparatus by which Faraday effected these 
 rotations was as follows : 
 
 M and N (fig. 143) are two vessels containing mercury, 
 
 with wires entering them 
 below, so as to effect their 
 communication with the 
 poles of a battery ; 6 is a 
 small powerful magnet, tied 
 by a thread to the wire at 
 the bottom ; F is a magnet, 
 fixed to the bottom of the 
 vessel N ; d is a copper 
 wire, hung by a metal hook. 
 When the current passes, 
 as in the figure, the movable 
 magnet b rotates round the 
 fixed wire e, and the mov- 
 able wire d revolves round the fixed magnet F, in the 
 direction according to the rules just given. If the upper 
 ends of F and b be south poles, the rotation of b will be in 
 the same direction as the hands of a watch, and of d in the 
 opposite way. 
 
 260. Another very instructive piece of apparatus was 
 
 invented 
 by Barlow } 
 and is usu- 
 ally called 
 Barlow's 
 Wheel. It 
 is repre- 
 sented in 
 fig. 144. A 
 is a copper 
 disc mov- 
 able on a 
 stirrup, 
 and having its lower edge dipping in the mercury cup C. 
 
 Fig. 144. 
 
ELECTRO-MAGNETISM. 263 
 
 A powerful horseshoe magnet, NO, is placed so that the 
 wheel is exactly between the poles. The current enters at 
 B, thence to the mercury cup C, from which it ascends a 
 radius of the wheel to the stirrup, and from this to the 
 battery. The lines of force due to the magnet are, at the 
 point where the wheel dips into the mercury, perpen- 
 dicular to the plane of the wheel, and hence perpendicular 
 to the radius along which the current ascends. By reflecting 
 on the rule already given (sect. 249), we see that the wheel 
 will be set in rotation in the direction of the arrow. 
 
 261. Action of the Earth on Currents. The lines of 
 magnetic force on the earth's surface are parallel to the 
 dipping-needle, and currents have a tendency to move at 
 right angles to them. In order to ascertain the action on 
 any portion of a current by the lines of magnetic force, we 
 have simply to project it on a plane at right angles to the 
 lines of force or to the dipping-needle. If the line to be 
 projected lies at right angles to the dipping-needle, then its 
 projection on the plane will be of the same length as itself, 
 and the action of the earth-magnetism will be to urge it 
 perpendicular to the lines of force and to itself, and in a 
 direction determined by the position of the poles of the earth 
 to it. If the line be parallel to the lines of force, then its 
 projection will be a point or the section of the wire ; and it 
 is manifest that the line in this position has no tendency to 
 displacement under magnetic influence. The force of ter- 
 restrial magnetism on it is null. A line between these two 
 positions will appear shortened when projected on the plane, 
 and the direction in which it is urged will be indicated by 
 the perpendicular to the projected line. The shorter the 
 line becomes in projection, the less it is exposed to the 
 displacing influence of terrestrial magnetism. 
 
 Let us apply the principles just stated to the case of the 
 revolving wire, fig. 139, when the coil is placed out of the 
 circuit. Let us suppose the lines of magnetic force resolved 
 into two sets, horizontal and vertical lines. Let us con- 
 fine our attention to one half, nab, of the wire. The 
 vertical lines of force have no influence on the vertical part, 
 ba, because it is parallel with them, and its projection on a 
 
264 ELECTRICITY. 
 
 horizontal plane would be a point. To na, whatever position 
 it occupies in its circle of rotation, the vertical lines will be 
 at right angles, and exert their full force on it. na rotates 
 in presence of the north pole of the earth, which, according to 
 our way of speaking, is a south pole ; it will therefore rotate 
 contrary to the hands of a watch. Let us now see how the 
 horizontal lines act. ab stands always perpendicular to them, 
 whatever be its position. It will accordingly be urged to the 
 right as far as it can go, which is in a position in which it 
 lies east of BB. Here it will be in stable equilibrium, and 
 it will resist being moved westwards one way or other. In 
 this position na would be urged upwards by the horizontal 
 lines, which, from its mode of suspension, cannot take place. 
 The effect of the horizontal lines on na is to move it down- 
 wards in its west, and upwards in its east position, but not 
 to interfere with its motion in a horizontal plane. In the 
 position in which nab stands east of BB, it becomes a question 
 of strength whether na shall carry it on, or ab keep it standing. 
 If it is to rotate, ab must be made shorter than na. If both 
 halves be now taken into account, cd and ab will have a 
 tendency to place themselves both east of BB ; they will 
 therefore counteract each other, and leave the motion of the 
 wire to na and nc, which will keep it in constant motion. 
 
 On a closed circuit, such as that of fig. 138, the effect of 
 terrestrial magnetism will be to place the plane of it at right 
 angles to the magnetic meridian. The horizontal parts will 
 have no effect. The whole will be left to the vertical currents, 
 which, passing, the one up, the other down, will place them- 
 selves, cd to the east, ef to the west. It is from the conflicting 
 action of its parts that a closed circuit, as a whole, cannot con- 
 tinue to rotate in a magnetic field. 
 
 ELECTRO-MAGNETISM. 
 
 Electro-magnetism includes all phenomena where magnetism 
 is produced by an electric current. As of great importance 
 in understanding these phenomena, we must first give the 
 properties of the solenoid. 
 
 262. Solenoid. As originally defined by Ampere, a solenoid 
 consists of an arrangement of circular currents, of infinitely 
 
ELECTRO-MAGNETISM. 
 
 265 
 
 Fig. 146. 
 
 small radius, placed side by side, so that the planes of all 
 the circles are perpendicular to the line passing through 
 their centres. This line is called the axis of the solenoid, 
 and may be either straight or ^ ^ ^ /^ ^ />. /-x 
 curved. When straight, the cir- 1J 1j 1J \J \J t) tj 
 cular currents lie on the surface 
 of a cylinder as represented in 
 
 fig. 145. The currents are also supposed to be all of equal 
 strength, and to flow all in the same direction. 
 
 A solenoid of any size can be imagined as made up of a 
 bundle of such elementary solenoids laid side by side parallel 
 to each other. A section of such a 
 solenoid made by a plane perpendicular 
 to its axis is represented in fig. 146. It 
 will be at once observed that the currents 
 in the adjacent elementary solenoids 
 must destroy each other, seeing that 
 they are equal, and flow in opposite 
 directions ; and that there is left as 
 effective only the current in the external 
 circle ABC. Such a system of external currents is thus 
 equivalent to the whole number of elementary solenoids. 
 
 In order to find the strength of the magnetic field, or, what 
 is the same thing, the intensity of the magnetic force at a 
 point on its axis, due to the solenoid, we proceed as follows : 
 Let PQ be the 
 solenoid, of 
 length I and 
 radius r; and 
 let C be the 
 strength of 
 each circular Fi g< 147. 
 
 current. Let 
 
 M be a unit magnetic pole placed on the axis BAM. We 
 may imagine (sect. 245) each circular current to be replaced 
 by its plane equivalent magnetic shell consisting of two 
 equal layers of magnetism the one, north-magnetism, on the 
 side facing A ; and the other, south-magnetism, on the side 
 facing B. Let cr be the surface-density of each of these 
 
266 ELECTKICITY. 
 
 layers, and r the thickness of the shell, then the strength of 
 the shell is represented by a-r. But this is (sect. 245) also 
 equal to the current strength C. Hence we have VT = C, or 
 
 C 
 
 <r = . Now, for the whole quantity of magnetism on each 
 
 face of the shell, we must multiply cr by the area of the 
 circular face. Denoting this area by a, we have on each 
 magnetic shell a quantity of north-magnetism equal to 
 
 + , on the one side, and a quantity of south-magnetism, 
 
 equal to , on the other side. Now, since the equivalent 
 
 magnetic shells arising from all the circular currents are 
 close together, it is evident that the north-magnetism on the 
 one side of one shell will exactly neutralise the equivalent 
 amount of south-magnetism on the side next to it of the 
 adjacent shell ; and that in consequence there will be left, 
 as effective on external points such as M, only the layer of 
 
 north-magnetism, -| , on the end, A, of the solenoid, arid 
 
 the layer of south-magnetism, , on the other end, B. If 
 n be the number of circular currents in the length I of the 
 solenoid, evidently, T = - ; and since r is the radius of the 
 solenoid, a = Trr 2 . Hence, by substituting, we have for the 
 
 above quantities of magnetism the values + 7rr ^ and 
 
 I 
 
 j respectively. It now only remains to calculate the 
 
 force which these quantities of magnetism together exert on 
 the unit pole placed at M. This will give the strength of 
 the magnetic field at that point which we may denote by H. 
 The calculation requires, however, higher mathematics than 
 can be given here, and hence we give only the result, which 
 is singularly elegant, namely : 
 
ELECTRO-MAGNETISM. 267 
 
 or calling the angles QMB and PMA, x! and x, respectively : 
 H = ?5p5 ( C os xf - cos x). (1) 
 
 The same expression could also be obtained by applying 
 the formula of sect. 258 to each circular current, and adding 
 the results. 
 
 If the unit pole be inside the solenoid, as at M', it is 
 obvious that the angle x becomes obtuse, and its cosine con- 
 sequently negative. Hence for this case, 
 
 H = ^- (cos x,' + cos x). (2) 
 
 When the length of the solenoid is great in comparison to 
 its diameter, the angles z and X, in (2) become very nearly 
 both 0, and their cosines consequently each very nearly 
 equal to 1. Hence for this case, 
 
 (3) 
 
 tl 
 
 This shews that the strength of the field inside a long 
 narrow solenoid is very approximately uniform. 
 
 The solenoids spoken of above are only typical, and cannot 
 be realised in practice. As usually constructed, a solenoid 
 (fig. 148) consists of 
 an insulated copper 
 wire bent in the form 
 of a spiral, and having 
 its ends bent back- 
 wards along the axis 
 to the middle point, 
 and then bent up- Fig. 148. 
 
 wards at right angles 
 
 between two coils of the spiral. It is manifest that in 
 such an arrangement the currents do not exactly fulfil the 
 solenoidal condition inasmuch as their planes are not exactly 
 perpendicular to the axis. We can, however, imagine the 
 current in each coil of the spiral as resolved into two com- 
 ponents, of which the one is a circular current perpendicular 
 
 
268 ELECTRICITY. 
 
 to the axis, and the other a short straight current parallel 
 to the axis. The action of all the straight currents is exactly 
 neutralised by the equal and opposite current along the axis, 
 and hence the arrangement, on the whole, acts precisely as 
 a typical spiral. Such a spiral carrying a current is found 
 experimentally to exhibit all the properties of a straight bar- 
 magnet. If suspended on an Ampere's stand (fig. 138) so as 
 to be movable in a horizontal plane, it sets itself with one end 
 north and the other south, exactly like an ordinary declin- 
 ation needle. If suspended so as to be free to move in the 
 plane of the magnetic meridian, it sets itself parallel to the 
 dipping-needle. The ends of the spiral are also acted upon 
 by, and act upon, a magnet exactly as if it were itself a 
 magnet. Two solenoids also act upon each other as if they 
 were magnets, like solenoid poles repelling, and unlike 
 attracting each other, exactly as is the case with the cor- 
 responding magnet poles. 
 
 263. Ampere's Theory of Magnetism. This theory forms 
 the link between magnetism and current electricity, and 
 gives a simple explanation of the electric action and con- 
 stitution of magnets. Ampere considers that every particle 
 of a magnet has currents circulating about it in the same 
 direction. A section of a magnet, according to this theory, 
 
 is shewn in fig. 149. All the 
 separate currents in the var- 
 
 HftV * ous P art i c l es ma J> however, 
 be considered to be equiva- 
 lent to one strong current 
 
 circulating round the whole 
 Fig. 149. Fig. 150. (fig> 150)> We are to look 
 
 upon a magnet, then, as a system, so to speak, of rings or 
 rectangles, placed side by side, so as to form a cylinder or 
 prism, in each of which a current in the same direction 
 is circulating. Before magnetisation, the currents run in 
 different directions, so that their effect as a system is lost, 
 and the effect of induction is to bring them to run in the 
 same direction. The perfection of magnetisation is to render 
 the various currents parallel to each other. Soft iron, in 
 consequence of its offering no resistance to such a disposition, 
 
 ^^^^ 
 
ELECTRO-MAGNETISM. 
 
 becomes more powerfully magnetic under induction than 
 steel, where such resistance exists. 
 
 Ampere's theory explains very satisfactorily why like poles 
 repel, and unlike attract. Figs. 151 and 152 shew this. Two 
 north poles near each other (fig. 151) have opposite currents 
 
 00 00 
 
 Fig. 151. 
 
 Fig. 152. 
 
 on their adjoining side, and repel each other in consequence. 
 A north and a south have similar currents, and attract (fig. 
 152). 
 
 If the north pole of a magnet were placed parallel to BB 
 in fig. 139, the coil being left out of the circuit, the rotation 
 would take place as shewn in the figure ; if the south pole 
 be put in the same place, the motion of the wire will be 
 reversed. According to Ampere's theory, it may be also 
 easily explained why a closed circuit rests in equilibrium at 
 right angles to the magnetic meridian, and why the axis 
 of a magnet which lies 
 in the axis of a series of 
 such closed circuits places 
 itself in the meridian. The 
 earth, being a magnet, has 
 currents circulating about WES1 
 it, which must be from east 
 to west, the north pole of 
 the earth being, in our way of speaking, a south pole. A 
 magnet, then, will not come to rest till the currents moving 
 below it place themselves parallel to and in the direction 
 of the earth's currents. This is shewn in fig. 153, where a 
 section of a magnet is represented in its position of rest with 
 reference to the earth- current. The upper current being 
 farther away from the earth-current, is less affected by it, 
 and it is the lower current that determines the position. A 
 magnetic needle, therefore, turns towards the north to allow 
 
 Fig. 153. 
 
270 ELECTRICITY. 
 
 the currents moving below it to place themselves parallel to 
 the earth's current. 
 
 264. Electro-magnets. Perhaps the strongest proof of the 
 truth of Ampere's theory is the fact that when a current wire 
 is coiled round a piece of soft iron, the iron becomes for the 
 time powerfully magnetic. This can be shewn by inserting 
 an iron rod in the axis of a solenoid, when the magnetic effect 
 of the latter is seen to be greatly increased, inasmuch as the 
 iron itself becomes magnetic under the influence of the 
 currents surrounding it. The cause of this increase can be 
 readily understood from the results already given. Suppose 
 Q P PQ to be a sole- 
 
 noid of length 
 Z, sectional area 
 a ; and let the 
 number of cir- 
 
 Fig- 154> cular currents 
 
 on it be n. Also 
 
 let AB be an iron rod of length I, and sectional area a', 
 inserted in the axis. Further, let k be the coefficient of 
 magnetic induction of the iron rod ; by which is meant, that k 
 is the quantity of magnetism separated, by unit magnetic 
 force across unit area of any section of the iron rod perpen- 
 dicular to the lines of force, that is, in this case perpendicular 
 to the axis. Now, in order to find the whole quantity of 
 magnetism separated across any section of the rod, we must 
 multiply k by the area of the section, and by the magnetic 
 force acting upon it. The intensity of the magnetic force 
 acting at any point within the solenoid, is given by equation 
 
 (3) (sect. 262), and is equal to ^rS if C be tlie current strength 
 
 I 
 
 in the solenoid. Hence the quantity of magnetism separated 
 across any section of the rod is ~-y a'ifc, But this is also the 
 
 V 
 
 quantity of magnetism across the end section A. Hence the 
 strength of the iron pole A is -, a'k. From sect. 262 we 
 
 find the strength of the solenoid pole to be - ' . By adding 
 
ELECTRO-MAGNETISM. 
 
 271 
 
 these two results, we find the total strength of the pole due to 
 both the iron rod and the solenoid to be 
 
 ^g + t^Srt-SCfr + to^ 
 
 This shews that a marked increase is produced in the 
 strength of the solenoid by the mere insertion of an iron rod 
 in its axis. The general form of an electro-magnet is 
 shewn in fig. 155. It consists of 
 a round bar of soft iron bent into 
 the horseshoe form, with an insu- 
 lated wire coiled round its ex- 
 tremities. When a current passes 
 through the coil, the soft iron 
 bar becomes instantly magnetic, 
 and attracts the armature with a 
 sharp click. When the current 
 is stopped, this power disappears 
 as suddenly as it came. Electro- 
 magnets far outrival permanent 
 magnets in strength. Small 
 electro-magnets have been made 
 by Joule which support 3500 
 times their own weight, a feat immeasurably superior to 
 anything performed by steel magnets. When the current is 
 of moderate strength, and the iron core more than a third of 
 an inch in diameter, the magnetism induced is in proportion 
 to the strength of the current, and of the number of turns in the 
 coil. It is of no importance whether the coils be placed all 
 over the magnet or accumulated at the ends. When the bar 
 is thinner than one-third of an inch, a maximum is soon 
 reached beyond which additional turns of the wire give no 
 additional magnetism ; and even when the core is thick, the 
 advantage gained by increasing the number of coils may be 
 lost by the long circuit reducing the strength of the current. 
 The maximum that can be reached is, in difierent magnets, 
 proportional to the area of section, or to the square of the 
 diameter of the core. It is found also, when the mass of the 
 armature is equal to that of the core, that the weight which the 
 
 Fig. 155. 
 
272 ELECTRICITY. 
 
 magnet sustains is in proportion to the squares of the strengths 
 of the currents. The length of the electro- magnet has no 
 other advantage than that of insulating the poles, the one 
 from the other. When the core consists of a bundle of 
 insulated wires, it is capable of greater magnetisation than 
 when it is solid. The rust that sooner or later forms on iron 
 wires is sufficient insulation. The electro-magnet, from the 
 ease with which it is made to assume or lay aside its 
 magnetism, or to reverse its poles, is of the utmost value in 
 electrical and mechanical contrivances. That the electro- 
 magnet may quickly acquire and as quickly lose its mag- 
 netism on closing and breaking the circuit, it is necessary 
 that the iron be perfectly pure or soft, and well annealed. 
 It is also necessary that the armature be kept just short of 
 touching, for when it is in contact, a residuum of the induced 
 magnetism lingers in it and in the core after the current 
 stops. Under current induction the various molecular 
 currents, according to Ampere's theory, place themselves 
 parallel to each other, and act powerfully in concert. The 
 direction of the current and the nature of the coil being 
 known, the poles are easily determined by the cork-screw rule. 
 265. Magnetic Tick. When an iron rod is made to rest on 
 a sounding-board, such as the body of a fiddle, and placed in 
 the centre of a powerful coil, each time the current is broken 
 a distinct tick is heard from the rod. If a file be placed in 
 the circuit, so that a wire when it slides along will alter- 
 nately close and open the circuit, the rasping noise of the 
 wire sliding along the file will be distinctly rendered by the 
 rod, each interruption giving rise to a tick ; the series of 
 ticks being in the same order exactly as the series of noises at 
 the file. According to Wertheim, the tick is due to the 
 sudden shortening which the rod experiences on being 
 demagnetised. He shewed that at magnetisation the rod was 
 lengthened but very slightly. According to Joule, if the rod 
 be magnetised to saturation, the lengthening amounts to 
 ^i^th of its length. The tick is heard more distinctly if, 
 instead of the rod, a piece of thin sheet-iron be rolled up so 
 that its edges just overlap. The application of this magnetic 
 sound to the conveying of sounds, is described under Telephone. 
 
273 
 
 CHAPTEE XX. 
 GALVANOMETERS. 
 
 266. Galvanometer. A galvanometer is an instrument for 
 measuring the strength of a current by means of the magnetic 
 action which the current exerts. It consists essentially of a 
 coil or coils of wire surrounding a freely suspended magne- 
 tised needle ; and the current strength is deduced from the 
 deflection produced by it on the needle. 
 
 Galvanometers may be divided into two great classes first, 
 those which are used to measure strong currents ; and, 
 secondly, those which are used to detect and measure feeble 
 currents. 
 
 Examples of the first class are the Tangent Galvanometer 
 and the Sine Galvanometer ; of the second class, sometimes 
 also called Sensitive Galvanometers, are the Astatic Galvan- 
 ometer, and Thomson's Reflecting Galvanometer. 
 
 267. Tangent Galvanometer. This instrument is shewn in 
 fig. 156. It consists of a thick 
 
 strip of copper, or of several coils 
 of insulated wire, bent into the 
 form of a circle, from one to two 
 feet in diameter, and with a small 
 magnetic needle moving on a 
 graduated circle at its centre. 
 When the needle is small com- 
 pared with the diameter of the 
 coil, it may be assumed that the 
 needle always moves in a mag- 
 netic field of uniform strength. 
 This being the case, the strength of 
 the current circulating in the ring 
 is proportional to the tangent of 
 the angle of deflection of the needle. 
 The angle of deflection is reckoned 
 from the plane of the ring, which 
 is placed parallel to the magnetic meridian. Fig. 157 shews 
 
 Fig. 156. 
 
274 ELECTRICITY. 
 
 how this may be proved. Let MM be the magnetic meridian, 
 and let AB represent the wire coil looked 
 down upon from above. Let NS be a mag- 
 netised needle, of length 21, suspended at 
 the centre of the coil ; and let the mag- 
 netic strength of each pole be m. Let the 
 angle of deflection of the needle from the 
 plane of the ring be 8. The force exerted 
 by the coil on the pole N is perpendicular 
 to the plane of the coil, and is (sect. 258) 
 
 equal to ) where C is the current 
 
 a 
 
 strength and a the radius of the coil. 
 The moment of this force about O is 
 
 s 
 
 OX = - -I cos 8. Also if H be 
 a a 
 
 Fig. 157. the horizontal component of the earth's 
 
 magnetic force, the moment of the force 
 exerted by the earth on the pole N is Hm x NX= Him sin 8. 
 Now if the needle be in equilibrium, at the deflection 8, 
 under the influence of these two forces, these two moments 
 must be equal. Hence, we have 
 
 I cos 8 = Him sin 8 ; 
 
 w/ 
 
 .-. C = j^ H tan 8. (1) 
 
 If there be n coils of wire in the circular ring, and if a be 
 the mean radius of the ring, this equation becomes : 
 
 2'TrW' 
 
 The above equations are not strictly accurate, seeing that 
 the needle, NS, does not move in a magnetic field of perfectly 
 uniform strength. The farther the needle is deflected from 
 the plane of the coil, the weaker is the action of the current 
 upon it ; and the current strength is not strictly proportional 
 to the tangent of the angle of deflection. In order to do 
 away with this inaccuracy, as far as possible, Helmholtz has 
 adopted the modification of the tangent galvanometer repre- 
 
GALVANOMETERS. 
 
 275 
 
 sented in skeleton in fig. 158 a, and in perspective in 
 fig. 158 6. A and B (fig. a) are two circular coils of equal 
 radius through which the same current flows in the same 
 direction. These coils 
 are placed with their 
 planes vertical and 
 parallel to each other, 
 and the distance, 00', 
 
 Fig. 158 a. 
 
 Fig. 158 b. 
 
 between the centres is made equal to the radius of either coil. 
 The needle, NS, is suspended at the middle point of the 
 common axis, 00', of both coils. With this arrangement, it 
 can be shewn mathematically that the magnetic field sur- 
 rounding NS, provided its length be very short in comparison 
 to the radius of the coils, is very nearly uniform, and hence 
 that the current strength is very nearly proportional to the 
 tangent of the angle of deflection. 
 
 In Gangain's arrangement only one coil, A, is used, all 
 other things remaining the same. 
 
 268. Sine Galvanometer. The construction of the sine 
 galvanometer is very similar to that of the tangent galvan- 
 ometer represented in fig. 158 the essential difference between 
 them being, that, in the sine galvanometer, the wire- coil can 
 be rotated about a vertical axis, and so made to follow the 
 needle during its deflection. The angle of rotation is observed 
 by means of a horizontal scale and vernier. In use the instru- 
 ment is first placed with the plane of the coil parallel to the 
 magnetic meridian, the axis of the needle being then in the 
 plane of the coil. When the current is sent through the coil, 
 the needle is deflected, and then the coil is slowly rotated till 
 its plane again coincides with the axis of the needle. The 
 angle of rotation, 8, is then observed. Let MM (fig. 159) 
 
 B 
 
276 
 
 ELECTRICITY. 
 
 M 
 
 be the magnetic meridian with which the plane of the coil 
 originally coincides ; and let AB and 
 NS be the altered positions of the 
 coil and needle, after rotation through 
 the angle 8. Since the force exerted 
 by the current upon the pole N is 
 always perpendicular to the plane of 
 the coil, the moment of this force 
 
 about O will, in this case, be , 
 
 the letters having the same signifi- 
 cation as before. Also the moment 
 of H, the horizontal component of 
 the earth's magnetic force, about O, 
 is, as before, Him sin 8. These 
 moments being equal in the position 
 of equilibrium, we have 
 
 M 
 
 Fig. 159. 
 
 
 sin S. 
 
 Hence 
 
 C = - H sin 8. 
 
 C is therefore proportional to the sine of the angle of deflec- 
 tion. The sine galvanometer is represented in fig. 160. 
 
 The defect of this instrument is, that the current to be 
 measured must remain constant during the time required 
 to perform the adjustments, which is seldom the case. 
 
 269. The Astatic Galvanometer is used either simply as a 
 galvanoscope, to discover the existence of a current, or as a 
 measurer of the strengths of weak currents. When a needle 
 is placed under a straight wire, through which a current 
 passes, it deflects to a certain extent ; and when the wire is 
 bent, so as also to pass below the needle, it deflects still 
 more. The current in the upper and the lower wire moves 
 in opposite directions ; and the deflection caused by both 
 wires is in the same direction. By thus doubling the 
 wire, we double the deflecting force. If the wire, instead of 
 making only one such circuit round the needle, were to 
 make two, the force would be again doubled, and if several, 
 
GALVANOMETERS. 
 
 277 
 
 the force (leaving out of account the weakening of the cur- 
 rent caused by the addi- 
 tional length of the wire) 
 would be increased in pro- 
 portion. If the circuits of 
 the wire be so multiplied 
 as to form a coil, this force 
 would be enormously in- 
 creased. Two needles, as 
 nearly the same as possible, 
 placed parallel to each other, 
 with their poles in opposite 
 ways, as shewn in fig. 161, 
 and suspended, so as to 
 move freely, by a thread 
 without twist, have little 
 tendency to place themselves 
 in the magnetic meridian, 
 for the one would move 
 in a contrary direction to 
 the other. If they were 
 exactly of the same power, they would remain indifferently 
 in any position. They cannot, however, be so accurately 
 paired as this, so that they always take up a fixed position, 
 arising from the one being 
 somewhat stronger than the 
 other. This position is some- 
 times in the magnetic meridian, 
 sometimes not, according as the 
 needles are less or more per- 
 fectly matched, and their axes 
 lie in the same vertical plane. 
 Such a compound needle is called astatic (Gr. a, privative, 
 and histamai, I stand), as it stands apart from the directing 
 magnetic influence of the earth. If an astatic needle be 
 placed in a coil, as in fig. 162, so that the lower needle 
 be within the coil and the upper one above it, its deflections 
 will be more considerable than a simple needle, for two 
 reasons : in the first place, the power which keeps the 
 
 Fig. 160. 
 
 Fig. 161. 
 
278 
 
 ELECTRICITY. 
 
 needle in its fixed position is small, and the needle is conse- 
 quently more easily influenced ; in the second place, the force 
 of the coil is exerted in the same direction on two needles 
 instead of one, for the upper needle being much nearer the 
 upper part of the coil than the lower, is deflected alone by it, 
 and the deflection is in the same direction as that of the lower 
 needle. An astatic needle so placed in a coil constitutes an 
 astatic galvanometer. One of these instruments is shewn in 
 
 fig. 162. Round an ivory 
 bobbin, AB, a coil of fine 
 copper wire, carefully 
 insulated with silk, is 
 wound, its ends being 
 connected with the bind- 
 
 ing screws, s, 
 
 The 
 
 astatic needle is placed 
 in the bobbin, which is 
 provided with a vertical 
 slit to admit the lower 
 needle, and a lateral 
 slit to allow of its oscil- 
 lations, and is suspended 
 by a cocoon thread from 
 a hook supported by a 
 brass frame. The upper 
 needle moves on a grad- 
 uated circle ; the com- 
 pound needle hangs 
 freely without touching the bobbin. The whole is included 
 in a glass case, and rests on a stand, supported by three 
 levelling screws. When used, the bobbin is turned round by 
 the screw, Q, until the needle stands at the zero point, and 
 the wires through which the current is sent are fixed to the 
 binding screws. The number of degrees that the needle 
 deflects may then be read off. It is manifest that on deflec- 
 tion taking place, the different portions of the coil are 
 differently situated with respect to the needle from what 
 they are at zero ; the deflecting force of the coil, therefore, 
 differs with the position of the needle, so that the angles of 
 
 Fig. 162. 
 
GALVANOMETERS. 
 
 279 
 
 deflection or their functions are not proportional to the 
 different current strengths. Up to from 15 to 20 it is found 
 that, for most instruments, the current strength is proportional 
 to the angle of deflection. Beyond that, the relations of 
 strength indicated by different angles must be ascertained 
 by special experiments. 
 
 270. Thomson's Reflecting Galvanometer. This is by far 
 the most sensitive galvanometer hitherto constructed. It 
 consists of a coil of well-insulated wire, of which a section 
 made by a plane through the axis of the coil is represented 
 in fig. 163. In the centre of the coil is placed a small 
 circular mirror made of .the 
 thinnest microscopic glass 
 silverised. This mirror is 
 suspended by a single cocoon 
 fibre. The magnets, some- 
 times five in number, made 
 of short lengths of the finest 
 hair-spring, and magnetised 
 to saturation, are cemented 
 to the back of the mirror. 
 The whole, magnets and 
 mirror together, weighs less 
 than a grain. The little 
 mirror is usually suspended 
 from the upper side of a 
 cylindrical brass box, which 
 fits into the hole of the coil, 
 and which is closed in front 
 by a lens, or a circle of glass. 
 
 Fig. 163. 
 
 Fig. 164 represents the galvan- 
 ometer, with its lamp and scale, as ready for use. The scale 
 is placed about three or four feet from the mirror, with its 
 zero point a little above the line of the axis of the coil. 
 Below the zero point of the scale is a vertical rectangular 
 slit, and close behind this is placed the clear flame of a 
 paraffin lamp. Suppose the mirror stationary, and perpen- 
 dicular to the axis of the coil. The ray of light from the 
 lamp passing through the slit will then be reflected straight 
 back, and form a bright spot of light on the zero point of the 
 
280 ELECTRICITY. 
 
 scale. When a current is now sent through the coil, the 
 mirror will be deflected, and the spot of light will move 
 towards the one or other end of the scale. According to 
 the optical law of the reflection of light, the angle through 
 
 Fig. 164. 
 
 which the ray of light falling on the mirror is deflected, is 
 double the angle through which the mirror is itself deflected ; 
 and this, combined with the long distance of the scale from 
 the mirror, causes the spot of light to move over a long 
 space for a very small deflection of the mirror. Hence the 
 extreme sensitiveness of the instrument. As this galvan- 
 ometer is very sensitive to even the faintest currents, it is 
 extremely useful, and, in fact, universally employed for 
 determining resistances by means of the null method, such 
 as Wheatstone's Bridge, where the thing to be observed is 
 the absence of any current. 
 
 CHAPTER XXI. 
 CURRENT INDUCTION. 
 
 271. The fundamental fact of current induction may be thus 
 shewn. Two long copper wires, pp and ss (fig. 165), are fixed 
 so as to be parallel and close to each other. The extremities 
 of the one, pp, are in connection with the poles of a galvanic 
 battery, E, and those of the other, ss, with the binding-screws 
 of a galvanometer, G. The instant the circuit of the battery 
 is completed, and the current sent along pp, a current in the 
 opposite direction is induced in the wire ss, which is shewn by 
 
CURRENT INDUCTION. 
 
 281 
 
 the deflection of the needle of the galvanometer. This induced 
 current is only momentary, for though the current continues 
 to circulate in pp 9 the needle soon falls back to its original 
 position of rest, and the wire ss gives free passage to other 
 currents, and appears to be in no way affected. If, now, when 
 the needle is at rest, 
 the battery circuit be 
 broken, and the cur- 
 rent in pp stopped, 
 another momentary 
 current is indicated 
 by the galvanometer 
 needle, but in this case Fig. 165. 
 
 in the same direction 
 
 as the inducing current. The inducing wire and current are 
 called primary, and are so distinguished from the induced 
 wire and current, which are termed secondary. The passive 
 condition of the wire while thus under induction has been 
 described by Faraday as electro-tonic. An electric throb, so 
 to speak, marks the setting in of this state, and another its 
 vanishing ; the former in the opposite direction to that of the 
 inducing current, and the latter in the same direction. If the 
 primary wire, pp, be movable, so that it can be suddenly 
 brought near to and withdrawn from the secondary ss, while 
 the battery current passes steadily, currents are induced as in 
 the former case, the approach of the wire being marked by an 
 inverse current, and its withdrawal by a direct one. As long, 
 however, as the primary wire remains in any one position, all 
 evidence of electricity in the secondary wire disappears ; but 
 if in this position the strength of the primary current should 
 be increased or diminished, momentary currents in the 
 secondary wire would again mark the changes in the primary, 
 the increase causing an inverse, and the decrease a direct 
 current. Hence we conclude, that a current which begins, a 
 current which approaches, or a current which increases in strength, 
 induces an inverse momentary current in a neighbouring conduct- 
 ing circuit; and that a current which stops, a current which 
 retires, or a current which decreases in strength, induces a direct 
 momentary current in a neighbouring circuit. For inverse, the 
 
282 ELECTKICITY. 
 
 word negative, and for direct, the word positive, are frequently 
 employed in reference to induced currents. 
 
 272. In experiments like the above, it is much more con- 
 venient to wind the primary and secondary wires side by side 
 
 round a bobbin, so as to form 
 a coil, as in fig. 166. The wires 
 are insulated from each other 
 by a covering of wool or silk. 
 Not only does such a disposi- 
 tion admit of very long wires 
 being used, but it also disposes 
 the wires employed to greater 
 advantage, for each single turn 
 of the primary wire acts not 
 
 only on the corresponding turn 
 Fig. 166. ;, 
 
 oi the secondary wire, but on 
 
 all the turns near it. The inductive effect of such a coil is 
 much greater than that which would be obtained by the same 
 extent of wires running side by side in a straight or crooked 
 line. It is not even necessary that the two wires be wound 
 round together ; each may be wound on a separate bobbin, and 
 the one placed inside the other as in fig. 167. The primary 
 coil, P, here represented, is made of wire T \th of an inch in 
 diameter, covered with wool ; and the secondary coil, S, of 
 silk-covered wire, about ^th of an inch, and much longer than 
 the primary wire. With two such coils, the illustration of the 
 preceding principles of induction can be conveniently given. 
 If the primary coil be placed in the circuit of a galvanic cell, 
 by two loose and flexible wires, so as to allow of its easy 
 motion, and if the terminal binding-screws of the secondary 
 coil be placed in connection with a galvanometer, when P is 
 inserted into S, a momentary inverse current is indicated, and 
 when it is removed, a momentary direct one ; or if, when P 
 remains in S, the strength of the primary current be altered, 
 the needle announces the induction of currents according to 
 the principles stated above. In order, however, to obtain the 
 greatest effect from the secondary coil S, it is necessary, whilst 
 P remains within it, to have some means of continuously 
 completing and breaking the primary current. A contrivance 
 
CURRENT INDUCTION. 
 
 283 
 
 for this purpose is called a current-break. A simple current- 
 break may be made of a common file, by holding one wire 
 from the battery against the end of the file, and running the 
 other along the teeth, the current being stopped each time the 
 
 Fig. 167. 
 
 wire leaves a tooth. In this way, a rapid series of inter- 
 ruptions is effected, each of which is attended by an inverse 
 and a direct current in the secondary wire. A break of the 
 same description, but more constant, may be also made by 
 causing a metal spring to press against the teeth of a metal 
 wheel, both spring and wheel being connected with the 
 battery. As the wheel is turned by a handle, the spring 
 breaks the contact each time it slips from one tooth to another. 
 The most convenient form of break, however, is one which is 
 made self-acting by the action of an electro-magnet, which 
 receives the name of a magnetic hammer. One form of this 
 instrument is shewn in fig. 272. 
 
 273. In any induction arrangement we can imagine the 
 primary circuit replaced by its equivalent magnetic shell, and 
 hence we are prepared to find that induced currents will be 
 produced in a circuit by the motion of a magnet in its neigh- 
 bourhood, or by in any way altering the strength of the 
 magnetic field in which it is placed. This can be readily 
 
284 ELECTRICITY. 
 
 shewn by experiment as follows : Place the coil S (fig. 167) 
 in circuit with a galvanometer. Insert the north pole of a 
 magnet into the axis of the coil, when a momentary induced 
 current will be observed to pass through the galvanometer. 
 Withdraw the pole, and a current will be observed in the 
 opposite direction. Again, if we place a magnet in the axis 
 of the coil, and alternately increase and diminish its magnet- 
 ism by bringing first the north pole and then the south pole 
 of another magnet up to its south pole, induced currents in 
 opposite directions will be observed to pass through the 
 galvanometer. In fact, the inductive action of a magnet 
 upon any circuit is, in all cases, precisely equal to the 
 inductive action of its equivalent electrical circuit upon the 
 same. 
 
 274. Mutual Induction and Self Induction. Suppose we 
 have two circuits, A and B, it is found by experiment 
 that the induction produced on B by a current, C, in A 
 is equal to the induction produced on A by the same cur- 
 rent, C, in B. This is shewn by first putting the cur- 
 rent C in A, and the galvanometer in B, and then the 
 current C in B, and the same galvanometer in A, when 
 the electro-motive force of induction is found to be the 
 same in the two cases. From this it follows that the num- 
 ber of lines of force inclosed by B, due to a current C in 
 A, is equal to the number of lines of force inclosed by A, due 
 to the same current, C, in B. Hence if the current strength 
 in A be unity, and if M be the number of lines of force due 
 to A inclosed by B, M will also be the number of lines of 
 force inclosed by A due to unit-current in B. The quantity 
 M is called the coefficient of mutual induction between the 
 two circuits ; and it can be shewn mathematically to be equal 
 to the mutual potential of the one circuit on the other. 
 
 Since a circuit carrying a current acts inductively upon 
 every neighbouring circuit, it follows naturally that it must 
 also have a similar action upon the different parts of itself, 
 seeing that these parts may be regarded merely as cases of 
 very near neighbouring circuits. This is found to be actually 
 the case ; and the phenomenon has received the name of 
 Self-induction. The fact of self-induction was first made 
 
CURRENT INDUCTION. 285 
 
 known by Jenkin, who observed that a smart shock could be 
 got from a single voltaic cell by breaking (but not by closing) 
 the circuit, when an electro-magnet was included in the 
 circuit, but that no appreciable shock was got when tiie 
 electro-magnet was excluded. This observation was com- 
 municated to Faraday, who very soon traced it to its true 
 cause in 'the induction of the current on itself.' Self- 
 induction reveals the fact that, when a current circuit is 
 closed, the current does not all at once reach its full strength, 
 but takes some very short time to do so, and that during this 
 time the current is retarded by the opposite current due to 
 self-induction. Similarly, when the circuit is broken, the 
 current strength does not fall to zero all at once, its gradual 
 fall being prolonged by the current due to self-induction, 
 which is, in this case, in the same direction as the main 
 current. The currents due to self-induction are also called 
 extra currents. Now, suppose we <have a circuit, A, carrying 
 a unit current, and that L is the number of lines of force 
 inclosed by A due to self-induction, then L is called the 
 coefficient of self-induction. 
 
 275. Law of Current Induction. The fundamental law of 
 induction has been deduced by Sir William Thomson and 
 Helmholtz from the principle of the conservation of energy, 
 in a way which may be understood from what follows. 
 Suppose we have a circuit placed in a field of uniform 
 magnetic force. Such a circuit may be represented by the 
 
 B' 
 
 Fig. 168. 
 
 horizontal rectangle, A}3FE (fig. 168), placed in the field of 
 force due to the earth's magnetism, where EX and FY are 
 supposed to be two parallel rails joined by the fixed cross- 
 piece EF, and AB to be a movable wire which can slide along 
 
286 ELECTRICITY. 
 
 the rails. Also, let the rails EX, FY, and the cross-piece 
 EF, be of very thick wire, so that their resistance may be 
 neglected ; and let E be the resistance of the sliding piece 
 AB. Let E be the electro- motive force in the direction of 
 the arrows, and C the current in the circuit ABFE ; and let 
 Z represent the vertical component of the earth's magnetism. 
 Then, according to sect. 249, the electro-magnetic force 
 acting upon AB will tend to move it parallel to itself in the 
 direction indicated by the arrow. Let AB move in the small 
 time t into the position A'B 7 ; and let N^ represent the 
 number of lines of force inclosed by the circuit at the 
 beginning, and N 2 the number inclosed at the end of the 
 motion. Then the work done by the electro-magnetic force 
 during the small time t, is represented by (N 2 N X )C. 
 The heat produced by the current in the time t is, by 
 Joule's Law (sect. 226), EC% and the energy drawn from 
 the battery in the same time is EC. But the total work 
 done must be equal to the energy expended, and hence 
 we have 
 
 EC = RC 2 + (N 2 - NO C, 
 
 T* -VT VT 
 
 which gives 
 
 Now, since the electro-motive force E can have any value 
 we please, we may make it zero ; and, if C' be the resulting 
 value of C, C' will represent the induced current produced 
 by the motion of AB across the vertical lines of force. 
 
 Hence 
 
 N, N 
 From this we see that ^7 - 1 is the electro-motive force 
 
 N N 
 of induction. But -~ * is the number of lines of force 
 
 added to the circuit in a unit of time ; and this taken nega- 
 tively is also the rate of decrease in the number of lines 
 of force passing through the circuit. Hence we have the 
 following law as expressed by Clerk-Maxwell : 
 
 The total electro-motive force acting round a circuit at any 
 instant, is measured by the rate of decrease of the number of lines 
 of magnetic force which pass through it. 
 
CURRENT INDUCTION. 287 
 
 We can now find general expressions for the electro-motive 
 force in each of two circuits acting inductively on each 
 other. Let A and B be the two circuits, and let E be the 
 electro-motive force, R the resistance, and C the current in 
 A ; and let E', R', and C' be the same values for B. Also let 
 L and N be the coefficients of self-induction of A and B 
 respectively, and M the coefficient of mutual induction. The 
 total number of lines of force inclosed by A will be the 
 sum of those due to its own self-induction, and those due 
 to B. Hence the value is LC -f MC'. Similarly, the total 
 number inclosed by B is NO' + MC. By taking the rates 
 of decrease of these quantities, we find the induced currents 
 in A and B respectively, and -hence we have 
 
 E rate of increase of (LC + MC') = RC ; 
 E' - rate of increase of (NC' -f MC) = R'C'. 
 
 276. Total Current of Induction. Since the electro-motive 
 force of induction depends on the rate of decrease of the 
 number of lines of force which pass through the circuit, it 
 will only be constant when this decrease is constant that is, 
 when the same number of lines of force is abstracted from 
 the circuit in each unit of time. Also, since the resistance 
 of the circuit is always the same, the induced current will 
 only be constant under the same circumstances. Jn all other 
 cases the current induced in the secondary circuit by the 
 motion of a magnet or primary circuit in its neighbourhood, 
 will continually vary ; and hence, to find the total induced 
 current that is, the whole quantity of electricity conveyed 
 by the induced current, we must sum up all the quantities 
 of electricity conveyed by it during each small element of 
 the time of the motion to which it is due. In order to do so, 
 we proceed as follows : Let the whole time of the motion be 
 divided into a very large number, n, of very small portions, t, 
 each so small that the current during it may be supposed 
 constant. Let N be the number of lines of force inclosed 
 by the circuit at the commencement of the motion ; N x the 
 number inclosed at the end of the first or beginning of the 
 second small time, t ; N 2 the number inclosed at the end of 
 the second or beginning of the third, and so on ; N being 
 
288 ELECTRICITY. 
 
 the number inclosed at the end of the motion. Also, let 
 Cj be the current, and Q x the total current of induction, 
 during the first small portion of time, C 2 and Q 2 the same 
 quantities for the second, and so on. From equation (sect. 
 275) we have : 
 
 But the total quantity of electricity conveyed by a constant 
 current, C^ in the time t is Cj. 
 
 Si -jr. 
 
 Hence, 
 Similarly, 
 
 ^n ^n" T> 
 
 Ja 
 
 To find the total current of induction, which we denote by 
 Qi, we must sum up all these quantities. Hence we have : 
 1 
 
 R * 2 ^ n ~!^ 
 
 Total number of lines of force added 
 
 An example or two of the application of this result to 
 simple cases will help to make the subject clear ; and first 
 let us take the case of the parallel slider represented in fig. 
 168. Let AB move parallel to itself into the position A'B', 
 in the time t; and let the distance BB' equal x. The number 
 of lines of force inclosed by the circuit at the beginning of 
 the motion is equal to Z x the area ABFE ; and the number 
 inclosed at the end is Z x the area A'B'FE. Hence the 
 number of lines of force added to the circuit is the difference 
 of those two quantities that is, is equal to Z x area AA'B'B. 
 Denoting the length of AB by I, we have for E^, the electro- 
 motive force of induction, provided the motion of AB be 
 uniform, the value, 
 
 v *' = - a) 
 
V, 
 
 CURRENT INDUCTION. 289 
 
 Now, is clearly the velocity of AB. Denoting it by v, we 
 
 lj 
 
 have E* = Zlv. Hence the electro- motive force of induc- 
 tion is proportional to the velocity. 
 Also, for Qj, the total current of induction, we have : 
 
 It is important to notice the direction of the induced 
 current. Since the direction of the lines of force is down- 
 wards, the positive direction round the circuit, according to 
 the corkscrew rule, is ABFE. Hence, since the value of E 4 
 is negative, the direction of the induced current is opposite 
 to this that is, is in the direction EFBA. Had AB moved 
 in the opposite direction, the direction of the induced current 
 would have been positive. Hence we see that when the lines 
 of force are increasing, the direction of the induced current 
 is negative, and when decreasing, positive. 
 
 As another example, we shall find the value of the total 
 current of induction in a circular circuit due to the motion 
 of a magnet-pole along its axis. 
 
 Let ABC (fig. 169) be the circular circuit, EF its axis ; and 
 let a magnet-pole of strength m be moved towards the circuit 
 
 Fig. 169. 
 
 from the point P to the point P r The length of the magnet 
 is supposed to be so great that its south pole is at an infinite 
 distance, and has no action lipon the circuit. Now, let V 
 and Vj_ be the potentials in reference to the circuit of a unit- 
 pole placed at P and Pj respectively. Then the number of 
 lines of force inclosed by the circuit at the commencement 
 
290 ELECTRICITY. 
 
 of the motion is mV , and at the end, raVj. Hence, the 
 total current of induction, 
 
 Q. = - g (Vi - V ). 
 
 Now, V is the value of the solid angle subtended by the 
 circuit at the point P ; that is, is equal to the area on a unit- 
 sphere having P for its centre, cut off by a cone which 
 has P for its vertex, and the circuit ABC for its base. The 
 determination of this area is a subject for pure mathema- 
 tics, and is equal to 2?r (1 cos ), where is the angle 
 BPO. Hence V = STT (1 - cos ). Similarly, V x = 27r 
 (1 cos 00, where 0j is the angle BPjO. Hence we have 
 
 <& = - (27T (1 - COS 00 - 27T (1 - COS )} 
 
 2?m (cos - cos 00. (3) 
 
 Several instructive deductions can be drawn from this 
 result. 
 
 (1) Suppose the pole, m, to be suddenly placed at the point 
 Pj. This is the same as supposing the point P to be at an 
 infinite distance to the left of the circuit, and that the pole, 
 m, is gradually moved up from this distance to the point P r 
 But when P is at an infinite distance, = 0, and cos = 1. 
 
 Hence, Q x = - (1 - cos A ). 
 
 (2) Suppose the pole, m, to be suddenly placed at the 
 centre of the circuit O, then B 1 = 90, and cos X = O. 
 
 Hence, Qi = - 
 
 (3) Suppose the pole, m, to be passed along the axis, 
 through the circuit, from an infinite distance on the left to 
 a point, H, on the right, such that OH = OP^ Then 
 
 1 + cos 
 
 (4) Suppose the pole, m, to be passed through the circuit 
 
CURRENT INDUCTION. 291 
 
 from an infinite distance to the left to an infinite distance to 
 the right of the circuit. Since, in this case, becomes 27r, 
 and cos 6 { = 1, we have : 
 
 Ql = _ ? (i + i) = . 
 
 277. Properties of the Induced Current. The following 
 properties of the induced current have been experimentally 
 observed : they can also be deduced from the general law 
 above given. 
 
 (1) The total quantity of electricity conveyed by the 
 induced current at closing the primary circuit, is equal to the 
 total quantity conveyed by the induced current at breaking 
 the primary circuit. Faraday proved this by placing a 
 delicate galvanometer in the secondary circuit, and making 
 and breaking contact very rapidly in the primary circuit. 
 No permanent deflection of the galvanometer needle was 
 observed, which shewed that the jerk given to the needle in 
 one direction by the induced current at make, was exactly 
 counterbalanced by the jerk given in the opposite direction 
 by the induced current at break. Hence the quantities of 
 electricity conveyed by the two currents in opposite direc- 
 tions must have been equal. 
 
 (2) The induced current is independent of the material of 
 which the circuit is composed. To shew this, Faraday 
 twisted together two insulated wires of different materials, 
 but having the same electrical resistance. The wires were 
 soldered together at one end, and the free ends attached to 
 the terminals of a galvanometer. No deflection was pro- 
 duced when the twisted portion was moved rapidly in the 
 magnetic field produced by a powerful electro-magnet, which 
 shews that the induced current in both wires was the same. 
 
 (3) The strength of the induced current is proportional to 
 the strength of the inducing current. This follows at once 
 from the general law, and admits of easy experimental proof 
 by the galvanometer. If the primary circuit consists of n 
 coils of wire each carrying the current C, the induced 
 current is proportional to nC. 
 
 (4) The induction in a coil of ra windings produced by a 
 
 R 
 
292 
 
 ELECTRICITY. 
 
 t I 
 
 coil of n windings is proportional to the product mn. This 
 also follows from the general law. 
 
 278. Lena's Law. Lenz's law is thus expressed by Clerk- 
 Maxwell : 
 
 If a constant current flows in a primary circuit A, and if, by 
 the motion of A, or of the secondary circuit B, a current is 
 induced in B, the direction of this induced current will be such 
 that, by its electro-magnetic action on A, it tends to oppose the 
 relative motion of the circuits. 
 
 A single example will illustrate the law. Let A and B 
 (fig. 170) be two straight parallel circuits, A being the 
 primary, and B the secondary ; and 
 let the current in A be in the 
 direction of the arrow. It will be 
 remembered that the lines of force 
 due to the long straight current 
 A are concentric circles surround- 
 ing it. A number of these lines 
 of force will be inclosed by the 
 secondary circuit B. Now, let A 
 be moved parallel to itself to- 
 wards B. The number of lines 
 of force inclosed by B will be 
 increased by this motion, and, in 
 consequence, an induced current 
 will be produced in B in the direction of the arrow that is, 
 in the opposite direction to the current in A. Now we 
 have here two parallel currents in opposite directions, which 
 we know (sect. 250) repel each other. Hence the electro- 
 magnetic action between A and B opposes the motion which 
 produces the induced current in B. 
 
 Neumann made Lenz's law the foundation of his mathe- 
 matical theory of induction. From it, along with Ampere's 
 expression for the force between the elements of two currents, 
 he deduced, in mathematical form the law of electro-magnetic 
 induction. 
 
 279. Self-Induction, Extra- Current. These have already 
 been shortly alluded to. Suppose we have a single circuit, 
 and let us suppose it placed in a magnetic field of zero 
 
 Fig. 170. 
 
CURRENT INDUCTION. 293 
 
 intensity. Let the electro-motive force acting in the circuit 
 be E, and the resistance K Then, according to Ohm's law, 
 
 E 
 the steady current in the circuit is C = ^. On closing the 
 
 circuit, the current does not increase from zero to its steady 
 value all at once, but takes some time to do so, during which 
 it is gradually increasing. During this time the number of 
 lines of force passing through the circuit is also gradually 
 increasing, and, in consequence, an electro-motive force of 
 induction, E', acts round the circuit in the opposite direction 
 to E, tending to hinder the current attaining its steady value. 
 Now, according to our general law, the value of E' at any time 
 is measured by the rate of decrease of the number of lines of 
 force passing through the circuit that is, it is equal to the 
 negative value of the rate of increase of the number of lines 
 of force passing through the circuit. Now, if C' be the 
 current at the time when the electro-motive force is E, and 
 if L be the coefficient of self-induction, the number of lines 
 of force passing through the circuit at that time is LC'. 
 Hence we have for the current at any time the expression 
 
 ~, E rate of increase of LC' 
 
 The second term on the right-hand side of t^iis equation 
 represents the induced current at the time mentioned. It 
 will become zero, of course, when the current reaches its 
 steady value C, since then the rate of increase of the constant 
 quantity LC is zero. To find the total current of self-induc- 
 tion, we proceed exactly as in the corresponding problem for 
 mutual induction (sect. 276). Denoting it by S;, when S 4 is 
 the total current of self-induction due to closing the circuit, 
 we have 
 
 , number of lines of force added ,,. 
 
 &i = =jj . (1) 
 
 But at closing, the number of lines of force included in the 
 circuit is 0, and when the current has become steady the 
 number included is LC. Hence 
 
 LC-0 LC L E LE 
 
 fo * = IT" = ~" ~W = "" T? ' T? = "" P2' ( 2 ) 
 
294 
 
 ELECTRICITY. 
 
 Next let the circuit be broken after the current has 
 attained its steady value. The current will not fall to zero 
 all at once, but will take some time to do so. During this 
 time the number of lines of force passing through the circuit 
 is gradually decreasing, and, in consequence, an electro- 
 motive force of induction acts round the circuit in the same 
 direction as that of the primary current, tending to hinder 
 the stopping of the current. Proceeding as before, we find 
 the same equation (1) for the total current of self-induction 
 at break. We must remember, however, that in order to 
 get the ' number of lines of force added/ we must in all cases 
 subtract the number inclosed at the beginning from the 
 number inclosed at the end. Now, at breaking the circuit, 
 the number inclosed at the beginning is LC, and at the end 
 O. Hence the number of lines of force added is O LC. 
 Calling Bi the total current of self-induction at break, we 
 have 
 
 O _ LC _ LC _ LE 
 
 t>i T> H TT I ~T>2* 
 
 V S\J V XV 
 
 (3) 
 
 The currents due to self-induction are sometimes called 
 extra-currents ; and from equations (2) 
 and (3), we see that the extra-currents 
 at make and break are equal in quan- 
 tity, but opposite in direction. 
 
 The properties of the currents due 
 to self-induction are the same as those 
 of the currents due to mutual induc- 
 tion. They are, for instance, inde- 
 pendent of the material of which the 
 circuit is made, and are also directly 
 proportional to the strength of the 
 inducing current. 
 
 280. Illustrations of Self-induction. 
 Self-induction can be illustrated ex- 
 perimentally in a variety of ways, of 
 which the following are examples. 
 Let C be a single voltaic cell (fig. 
 171), having in circuit the coil A, whose self-induction is to 
 be observed. Let BE be a cross circuit, having a gap at F, 
 
 Fig. 171. 
 
CUERENT INDUCTION. 295 
 
 into which a wire or galvanometer can be inserted. Also let 
 X be a inake-and-break whereby the current can be rapidly 
 interrupted. When the circuit is closed, part of the current 
 goes through the branch circuit BE, and part through the 
 coil A. Now let a fine platinum wire be inserted at F, 
 and let its resistance be so adjusted that it does not 
 glow by the passing of the steady current through it. 
 Let the circuit be now broken at X. The current due to 
 the self-induction of A cannot pass through the battery, but 
 must all pass through EB in the direction BAEB. This 
 is shewn by the wire at F commencing to glow directly the 
 circuit is broken. Faraday has also shewn, by a similar 
 experiment, that the electrolysis of water can be produced 
 by a single cell, provided the direct current, and the current 
 due to the self-induction of A, be simultaneously sent in the 
 same direction through a voltameter. To shew this experi- 
 ment, the coil A is placed at X, the voltameter at A, and the 
 make-and-break at F. 
 
 281. Two circular Coaxial Solenoids with Iron. Core in the 
 primary circuit. Let A and 
 
 B be two circular coaxial ^~- y 
 
 solenoids A being the / \ / 
 
 primary and B the second- Q I A 
 
 ary circuit. It -is found \ / 
 
 that the induction produced v-2 
 
 in B by the making and F - 172 
 
 breaking of a current in A 
 
 is greatly increased by inserting an iron core in A. The 
 
 reason of this is obvious from sect. 264, which shews that the 
 
 number of lines of force which pass through A is greatly 
 
 increased by the insertion of the iron core. 
 
 Let I be the length of each of the solenoids A and B. Let 
 n be the number of windings per unit-length of A, and n' the 
 number of windings per unit-length of B. Also let B, be the 
 resistance of A, and S the resistance of B ; and let L and N 
 be the coefficients of self-induction of A and B respectively, 
 and M the coefficient of their mutual induction. If the 
 length of A be great in comparison with its diameter, the 
 magnetic field within A, produced by a current circulating in 
 
296 ELECTRICITY. 
 
 it, is very nearly uniform ; and for a unit- current in A, the 
 strength of this field at any point is (sect. 262. 3) equal to 47m. 
 Hence, if a, be the area of the cross section of A, the number 
 of lines of force due to a unit-current inclosed by A is 4-n-na. 
 But this is also the number of lines of force inclosed by each 
 winding of B. But the number of windings in B is In'. 
 Hence the number of lines of force inclosed by all the wind- 
 ings of B is kirnln'o,. Now the number of lines of force 
 inclosed by B, due to unit-current in A, is by definition (sect. 
 274) the coefficient of mutual induction between them. 
 Hence M = ^irnln'a. By inserting an iron rod of cross 
 section a' in A, the number of lines of force which pass 
 through A becomes (sect. 264) 4^rn (a -f- 47r&a')> an ^- hence 
 the value of M becomes M/ = 4-n-nln' (a + 4?rA;a / ), where k is 
 the coefficient of magnetic induction of the iron rod. 
 
 Now let E be the electro-motive force, and the steady 
 current in A, and let t be the very small time which elapses 
 between the instant of closing the circuit and the instant 
 when the current becomes steady. The total current of in- 
 duction Q* in B is given by sect. 276, and is, at make, 
 
 _ number of lines of force added 
 Wi = g 
 
 MC ME 
 
 "s" : "sT 
 
 Similarly at break, the total current of induction Q/ is 
 
 O' 4- ME 
 
 Q * == + sir 
 
 This shews that the total quantities of electricity conveyed 
 by the induced currents at make and break are equal. 
 
 Again, let E' be the average electro-motive force, and C' the 
 average strength of the induced current during the time t. 
 
 Then C/ = f ; 
 
 but evidently Q; = C'$. 
 
 TV/TTi 1 
 
 Therefore Q't = - -^ 
 
 n , ME 
 
 hence ^ "" SS? 
 
CURRENT INDUCTION. 297 
 
 Therefore ?'" ~4B> 
 
 which gives E' = -07 E. 
 
 Now, since t is a very small fraction of a second, this shews 
 that the electro- motive force of induction may be a large 
 number of times greater than the electro-motive force of the 
 battery ; and this accounts for the very great length of spark 
 got between the terminals of the induced circuit, in comparison 
 with the very short spark got at closing and opening the 
 primary circuit. According to Sir William Thomson, it 
 would require 5510 Daniell's cells to produce a spark ^th inch 
 long between two brass terminals, and yet a spark many 
 times that length can be got from an induced current by 
 using even a very few cells in the primary circuit. We shall 
 find great use for this result in explaining the induction coil. 
 
 From the above equation, M = &7rnln'a, we can easily find 
 the value of L. All we have to do is to make n = n', and 
 then suppose the coil B to contract till it coincides with A. 
 The two coils may be then regarded as one, which of course 
 can only have self-induction. We have thus 
 
 L = 4irln 2 a. 
 
 Similarly, by supposing a coil of n' windings per unit- 
 length exterior to B, and then letting the coils coincide, we 
 obtain 
 
 N = 47rlri 2 b, 
 
 where 6 is the sectional area of B. 
 
 282. Electricity induced by the Magnetism of the Earth. 
 Faraday was the first (1831) to obtain electricity from the 
 inductive action of terrestrial magnetism. Terrestrial electric 
 induction may be shewn by such an apparatus as that 
 sketched in fig. 173. If a coil, CC', be made to rotate, as 
 shewn in the figure, round a horizontal axis, and its ends 
 be directly connected with a galvanometer, it will be found 
 that, starting from a certain position, for one half-revolution 
 the needle is deflected one way, and for the other in the 
 opposite way. Suppose the axis to lie at right angles to the 
 magnetic meridian, and that we place the plane of the coil at 
 
298 ELECTRICITY. 
 
 right angles to the dipping-needle, as a starting-point, each 
 half-revolution will occasion a current in an opposite direction. 
 The reason of this is obvious. Through the half-revolution 
 one half of the coil ascends and the other descends, cutting 
 the lines of magnetic force, which are parallel to the dipping- 
 needle in different ways ; opposite currents are thus induced 
 in each half, and these aid each other to form one current. 
 
 Fig. 173. 
 
 The descending half has its current tending eastward, and the 
 ascending half westward. It is easy to see that by the inter- 
 vention of a commutator, as at c, a current in one direction 
 may be obtained through the wires w, w'. The maximum 
 induction takes place when the plane of the coil is parallel 
 to the dipping-needle, for then it cuts the lines of magnetic 
 force at right angles. If the axis of the coil be placed 
 horizontally in the magnetic meridian, the induced electricity 
 will be wholly due to the vertical magnetic lines. If the 
 axis be vertical, the same will be due wholly to the horizontal 
 lines. A comparison of the deflection produced on the 
 galvanometer by a similar rotation in these two positions may 
 be used, according to Weber's suggestion, to determine the 
 magnetic inclination, for the tangent of the angle of inclination 
 is equal to the vertical divided by the horizontal intensity. 
 If the axis be parallel to the dipping-needle, 110 current will 
 be obtained, however fast the rotation. Palmieri, by means 
 
CURRENT INDUCTION. 
 
 299 
 
 of a terrestrial induction machine, produced sparks, shocks, 
 and the decomposition of water. 
 
 283. Induced Currents of Higher Orders. Suppose we have 
 a set of circuits A, B, C, D, &c., B being under the inductive 
 influence of A, C under the inductive influence of B, D under 
 C, and so on. Also suppose a direct primary current be sent 
 for a moment through A ; this will cause an inverse and direct 
 induced current of the first order in B. Now, the inverse 
 current in B will cause a direct and inverse induced current 
 in ; and the direct current in B will cause an inverse and 
 direct current in C. Similarly the direct and inverse currents 
 in C will cause corresponding currents in D, and so on. 
 Thus from the interruption of one current in A, two currents 
 are produced in B, four in C, eight in D, and so on, increasing 
 in geometrical progression. These are called the induced 
 currents of higher orders. As might be expected, they 
 diminish very rapidly in intensity ; but their presence has 
 been detected by their physiological action and otherwise. 
 
 284. Unipolar Induction. This is the name given to a 
 class of phenomena which may be regarded as the converse of 
 the electro-magnetic rotations already alluded to (sect. 259). 
 An example will make the meaning of the term clear. 
 
 Fig. 174. 
 
 Let SN be a cylindrical straight magnet supported on 
 pivots at the ends S and N, so that it can rotate round its 
 axis. Also let A be a circular disc of copper attached to the 
 middle point of the length of the magnet, so that its plane is 
 perpendicular to the axis of the magnet which passes through 
 its centre. Let adN be a conducting circuit attached to the 
 
300 ELECTRICITY. 
 
 pivot at N, and having sliding contact with the copper disc at 
 a. Now, if the current from a cell be sent through the circuit 
 OadN in the direction of the arrows, its electro-magnetic 
 action will cause the magnet and disc to rotate in the direc- 
 tion of the arrow &. And, conversely, if the magnet and disc 
 be rotated in the opposite direction, that is, in the direction 
 of the arrow c, an induced current will be produced in the 
 circuit in the same direction as before, namely, OadN. This 
 is the phenomenon called, rather unfortunately, unipolar 
 induction. 
 
 To find the electro-motive force of the induced current, we 
 proceed as follows. Instead of making the disc A rotate in 
 the direction of the arrow c, we may obviously suppose the 
 disc stationary, and that the circuit Nda with the sliding 
 contact revolves with the same angular velocity in the oppo- 
 site direction. This will clearly produce the same effect. 
 Now suppose the radius Oa, carrying the end of the circuit 
 with it, to revolve in a unit of time from the position Oa to 
 the position Oa' through the angle w. Then o> is the angular 
 velocity, and we have to find the electro-motive force due to 
 this motion. The whole number of 'lines of force inclosed 
 by the circumference of the disc A is 47rm cos <, where 
 m is the strength of the magnet-pole, and < is the angle 
 BNO = BSO. The number of lines of force cut through 
 by the radius Oa in its motion to Oa' is clearly the number 
 included in the sector aOa'. But this number is the same 
 fraction of the whole number that w is of two right angles, 
 that is, of 2?r. Hence the number cut through by Oa in a 
 
 unit of time is -= X 4?rm cos d> = 2 my cos <f>. 
 
 2-7T 
 
 But this is the electro-motive force of induction without 
 regard to sign. Therefore calling it E', we have E' 
 = 2mco cos <j>. 
 
 To get the whole current produced by one revolution of 
 the disc, we must substitute 27r,for to in the above, and divide 
 by the resistance, R, of the circuit. Hence we have for the 
 total current of induction, due to one revolution, the value 
 47rm cos < 
 
CURRENT INDUCTION. 301 
 
 The direction of the induced current is most easily 
 obtained, in any case, by the application of Lenz's law. 
 Observing that the lines of magnetic force go through the 
 disc from S to N, and applying the rule given in sect. 249, 
 we see that the induced current in Oa must be from O to a, 
 in order that it may, by its electro-magnetic action, oppose 
 the motion of Oa into the position Oa'. Hence the direction 
 of the induced current is as indicated. 
 
 CHAPTER XXII. 
 
 ELECTRO-MAGNETIC AND MAGNETO-ELECTRIC INDUCTION 
 APPARATUS. 
 
 285. Since the discovery of current induction by Faraday, a 
 great variety of apparatus has been constructed whereby 
 electric currents can be produced by means of induction. 
 The various kinds of this apparatus can be divided into two 
 great classes first, those in which the induced current 
 is produced by varying the strength of the magnetic field in 
 which the circuit is placed ; and secondly, those in which 
 mechanical work is employed to rotate a coil of wire in a 
 strong magnetic field. An example of the first class is the 
 Induction Coil. Examples of the second are the various 
 machines by means of which mechanical work is converted 
 into the energy of the electric current. These machines will 
 be described in a future chapter. 
 
 286. Induction Coil. The essential parts of this apparatus 
 have been already described. A primary coil with its core 
 of iron wire, and a secondary coil exterior to, and insulated 
 from the primary coil, form the main portions of the 
 instrument. The primary coil is connected with the poles of 
 a galvanic battery, and in the circuit a make-and-break is 
 introduced, to effect the interruptions of the current essential 
 to its inductive action. A commutator and condenser are 
 also essential parts connected with the primary circuit. 
 
 The make-and-break is shewn in fig. 175. A is an iron 
 
302 
 
 ELECTRICITY. 
 
 Fig. 175. 
 
 plate, into which the ends of the iron wires forming the core 
 are fixed, and which serves as an 
 anvil for the hammer H. H has for 
 its shaft the stiff spring D, which 
 keeps p back, and also forms part of 
 the primary circuit, p is a little 
 projecting nipple tipped with plat- 
 inum, e is a screw, the end, p', of 
 which is also tipped with platinum. 
 C, an upright brass standard, also 
 forms part of the circuit. When 
 the circuit is closed, A becomes 
 magnetic, and draws away H from 
 p'. The primary circuit formerly 
 closed at p and p' is now broken. 
 A loses its magnetism, and H, 
 under the influence of the spring D, 
 is taken back to p'. The circuit is again closed, A again 
 becomes magnetic, and thus H is kept oscillating with great 
 
 rapidity between A and p', 
 alternately opening and 
 closing the primary circuit. 
 6 is a screw giving to D 
 the necessary stiffness. 
 
 For large coils, mercury- 
 breaks are almost always 
 employed. A wire is made 
 to dip into a cup of mer- 
 cury and lifted out alter- 
 nately, so as to make and 
 break contact in the primary 
 circuit. The interruption 
 thus made is much improved 
 by pouring alcohol over the 
 mercury ; the spark of the 
 Fig. 176. extra-current taking place 
 
 with more difficulty in 
 
 alcohol than in air. As pure mercury, when thus used, is 
 apt to be broken up into globules under the constant motion, 
 
INDUCTION APPARATUS. 303 
 
 an amalgam of silver or platinum, of a treacly consistence, 
 is substituted with advantage. The mercury-break, sketched 
 in fig. 176, works with singular steadiness and efficiency. A 
 spiral, ssf, of No. 13 copper-wire, made of about an inch in 
 diameter, and six inches in length, is stretched out to about 
 nine inches, and soldered to two rings on the rod p, half an 
 inch in diameter. To shew the construction more clearly, 
 the convolutions are shewn few and far apart. In the appa- 
 ratus itself the spiral hides almost entirely the rod beneath. 
 The rings being wider than the rod, keep the spiral free 
 from it. The lower ring, &, is insulated from the rod; the 
 other, a, being fixed by a binding-screw to it, is in conduct- 
 ing connection with it. The rod is partly of iron, partly of 
 brass, and communicates with the binding-screw, c. A wire, 
 m, is soldered to one of the convolutions a little above the 
 end of the iron part of the rod, and comes out at right angles. 
 It is turned down at the end, so as to dip into a cup of 
 mercury, e, which communicates by the pillar, h, with the 
 binding-screw, d. The break is on a separate stand from the 
 coil, and is so placed in the primary-circuit that each bind- 
 ing-screw is connected with a coating of the condenser. 
 When the commutator turns the current on, the spiral is 
 gently moved by the hand, and if the wire dips into the 
 mercury, continues in constant oscillation. The cup is raised 
 or lowered till the point is got where the best sparks pass 
 between the terminals of the coil, and fixed there with a 
 binding-screw. A spiral, so hung, forms a delicate pendulum, 
 which only requires a small force to keep it in steady motion 
 up and down. This the electric and magnetic action sup- 
 plies. When the current passes, it goes from c up the rod, 
 down the upper part of the spiral into the cup, and thence to 
 the binding- screw, d. The iron rod becomes magnetic, and 
 tends to send the various convolutions at right angles to the 
 lines of magnetic force. Moreover, the various convolutions 
 are the seat of a current moving in the same direction in 
 all, and they consequently attract each other. Under this 
 double action, the dipping-wire is lifted out of the mer- 
 cury, and its own elasticity brings it back, again to com- 
 plete the circuit, again to be lifted out, and so forth. A 
 
304 ELECTRICITY. 
 
 reversal of the current causing a reversal of poles, the action 
 of the spiral is indifferent to the direction of the current. To 
 prevent oxidation, the part of the wire that dips should be of 
 platinum. The alcohol on the surface must be more than an 
 inch deep, otherwise it is scattered about in all directions by 
 the breaking spark. If not, the vessel must be closed with a 
 lid. 
 
 The commutator consists of a cylinder of ivory, with 
 two brass plates attached to its sides, moving on a brass 
 axis, supported by two brass standards. One axis does not 
 go through the whole way, so that two distinct pieces of brass 
 serve as an axis. One of the standards is connected with 
 the +, the other with the pole of the battery. Each plate 
 communicates with one of the standards, so that the plates 
 form the poles. A spring presses against the cylinder, either 
 on the plates or on the ivory. These springs form part of the 
 circuit : when the springs press against the plates, the current 
 flows ; when the plates are reversed by a handle attached to 
 the cylinder, the current is reversed. 
 
 The condenser consists of several sheets of tinfoil and oiled 
 silk, laid alternately the one above the other. The first, 
 third, fifth, &c. sheets of tinfoil are connected by strips of the 
 same material ; so are the second, fourth, sixth, &c. ; the 
 whole forming a condensing apparatus like a Leyden jar, the 
 odd sheets forming the one coating, and the even sheets the 
 other. Each set of sheets is connected with one of the wires 
 of the primary coil. The condenser is generally placed in the 
 sole of the instrument, and does not meet the eye. 
 
 An induction coil, as constructed by Ladd of London, is 
 represented in fig. 177. The forms under which the instru- 
 ment appears are very various, and the one in the figure only 
 serves to shew the general requirements in its construction. 
 The two binding-screws, p and , are for the battery wires ; 
 C is the commutator. The two coils, W, lie horizontally on 
 the sole of the instrument, S. The secondary coil alone is 
 seen, the primary being within it and out of view. The 
 breaking hammer, being behind the coil, is likewise not 
 shewn. The condenser is contained by the box which con- 
 stitutes the sole, and a conducting connection is established 
 
INDUCTION APPAR 
 
 , 
 
 between its coatings and the wires of the^ primary coil. The 
 terminations of the secondary coil are fixed to the heads of 
 the glass pillars, P, F, which are furnished with pointed rods 
 
 Fig. 177. 
 
 capable of universal motion. The excellence of the instru- 
 ment depends on the proper insulation of the secondary coil. 
 The bobbin must be made of glass, gutta-percha, or (best of 
 all) vulcanite, so as to prevent the induced electricity from 
 reaching the ground by the primary coil. Care must also be 
 taken to insulate the different parts of the secondary coil 
 from each other. If this were not done, the spark which 
 completes the secondary current, instead of taking place at 
 the rods, the place at which it is wanted, would pass within 
 the coil itself. It is necessary, in consequence, to have each 
 layer of the coil insulated from the other, by interposing 
 gutta-percha paper, and cementing it with a hot iron to the 
 sides of the bobbin. The induced current must thus pass 
 through all the turns of the wire, and is prevented from 
 shortening its course by leaping over one or more layers of 
 the coil. 
 
 287. In the ordinary construction the wire is coiled first 
 round the centre of the bobbin all the way'along, and layer 
 after layer is put in regular succession, the one above the 
 other, with insulating material between. In this way the 
 greatest difference of potential is between the inside and the 
 outside layers, the poles coming directly from them. In this 
 arrangement it is extremely difficult to maintain proper 
 insulation. The utmost care is needed to keep the electricity 
 
306 ELECTRICITY. 
 
 of the inmost layer of wire from leaping into the primary 
 coil, and even when this is fully accomplished, there is a 
 Leyden-jar action between the inmost layer of the secondary 
 
 and the outmost layer of the 
 primary coil, which hinders the 
 free delivery of the electricity 
 at its pole with which it is 
 charged. We shall mention 
 two ways of obviating this 
 defect. 
 
 Fig. 178 is intended to shew 
 Fi - 178 - the construction of the coil 
 
 devised by Siemens and Halske. PF is the hollow tube in 
 which the primary coil is put. The bobbin is made of 
 ebonite, and the central part is thickest at the ends and 
 thinnest at the middle, being 26 millimetres at the ends and 
 12 at the centre. It is 95 centimetres in length. To this 
 tube are cemented 150 thin discs (only a few are given in the 
 figure) of ebonite at equal distances, dividing the whole 
 length into compartments. Each compartment is filled up 
 with copper wire '14 of a millimetre thick, covered with silk 
 and varnished. The various compartments communicate 
 with each other, so that the whole wire is continuous from 
 end to end. The length of the whole is 129,000 metres. 
 The silk and varnish on the wire are sufficient insulation 
 between the convolutions in each compartment, and the discs 
 are proof against the spark striking through between them. 
 The insulation of the various parts from each other is thus 
 complete. As regards external insulation, least is required for 
 the middle compartments, where there is least danger of the 
 electricity breaking through into the primary coil. Accord- 
 ingly, the tube is thinnest at the middle, and thickest at the 
 ends. The thickness at the ends not only prevents the 
 electricity striking through, but lessens the Leyden-jar action 
 between the ends and the primary coil. With one Burisen 
 cell this coil gives a spark of 21 centimetres ; with six cells, 
 one of 58 centimetres in length. 
 
 The section of the bobbin of a secondary coil (17 inches 
 in length), of much smaller size and of a less expensive 
 
INDUCTION APPARATUS. 307 
 
 character, is given in fig. 179. The coil of which it forms 
 a part was made under the direction of Dr Ferguson. The 
 central tube, PP', is of hardened 
 wood ; d, D, and d' are thick 
 discs of gutta-percha cemented 
 to the tube. The wire is coiled __ ^^^_^__ 
 in two portions, beginning at the JL^^^^^^^^^ P' 
 middle, m ; the one half being 
 coiled to the right, the other to 
 the left. If the whole could be 
 seen, it would look like one coil Fig. 179. 
 
 from end to end with a disc in 
 
 the middle. The two halves communicate by a wire 
 piercing the central disc at m. Gutta-percha paper is 
 wrapped round the tube to a thickness of more than a 
 quarter of an inch before the wire is wound on. Each 
 consecutive layer of wire (copper covered with silk) is sepa- 
 rated from the one above or below by two or three sheets 
 of gutta-percha paper. The coil has the greatest thickness 
 at the middle, and tapers off to the ends. This is done 
 in conformity with a principle discovered by Jacobi and 
 Lenz (1844), namely, that in an electro- magnet, where the 
 wire is uniformly distributed over its length, the inductive 
 power is greatest at the centre, and becomes feeble at the ends. 
 It is sought in this coil to proportion (approximately) the 
 length of the wire coiled in different parts of the bobbin to 
 the electro- motive force of the primary coil at that part. 
 The sparks given off by this coil, which are nearly seven 
 inches in length (with six Bunsen cells), are peculiarly dense, 
 the quality aimed at in the construction. The length of the 
 wire is about seven miles. The double form of the bobbin 
 throws the middle of the wire next the primary coil. Here 
 the potential being least, there is little or no danger of the 
 electricity sparking into the primary coil. As the wire 
 leaves the centre the potential increases, but the insu- 
 lation from the additional sheets of gutta-percha paper 
 between the different layers is also increased. The elec- 
 tricities of the poles are kept from uniting by the thick 
 central disc (1 inch thick and extending l inches beyond 
 
308 ELECTRICITY. 
 
 the coil), and a considerable thickness of gutta-percha 
 placed over them. Within the coil they are kept apart by all 
 the gutta-percha paper on each half of it. To prevent the 
 gutta-percha from altering in the presence of the air, which 
 it usually does, the whole is inclosed in a layer of melted 
 paraffin. 
 
 288. Experiments with the Induction Coil Say that we 
 experiment with a coil like the one shewn in fig. 177, about 
 one foot long and nearly six inches in diameter, which yields 
 readily sparks of from four to five inches with a battery of 
 six Bun sen cells. After connecting the battery wires, and 
 setting the commutator so as to complete the contact, let us 
 place the movable rods within an inch of each other. An 
 uninterrupted rush of sparks is transmitted between the points 
 of the rods. The sparks are not the clear single sparks of the 
 electric machine, but seem to be made up of several sparks 
 occurring at the same instant, which are white and crooked. 
 These are enveloped in a luminous haze, or aureole, which can 
 be blown away by the breath, and thereby separated from the 
 white spark, which cannot be so removed. The aureole is 
 repelled by the poles of a powerful electro-magnet, whilst 
 the white spark is not affected by it. As the rods are with- 
 drawn from each other, it disappears, and \vhen they stand 
 above three inches apart, the spark resembles in every respect 
 the forked single spark of a powerful electric machine. When 
 the points are withdrawn beyond striking distance, electric 
 brushes still play between them, which become visible in a 
 darkened room. If the hand be brought near the rod con- 
 nected with the exterior end of the coil, sharp stinging sparks, 
 two or three inches in length, are got. The rod connected 
 with the inner end does not yield them so readily, and this 
 is the same whether it be the -f- or pole. Each pole of the 
 induction coil is the seat of two opposite electricities, alike 
 in quantity, alternating with each other. A Leyden jar 
 may be charged, but not to the same extent as by the electric 
 machine, if one of the wires be connected with the outer 
 coating, and the other brought within an inch of the 
 knob. The jar on being removed may be discharged by 
 the tongs. When the poles are put in connection with 
 
INDUCTION APPARATUS. 309 
 
 the coatings of a Leyden jar, and the points placed within 
 half an inch of each other, the sparks passing between 
 the points are much more brilliant, and the sharp snap 
 of the simple spark grows into a loud report. The Leyden 
 jar effects a condensation of the electricity of each direct 
 current, and each spark discharge takes place in shorter time, 
 and consequently with greater intensity. The condensed 
 spark punctures paper and the like with great facility, but it 
 is of very low heating power. The uncondensed spark, more 
 particularly the hazy spark, got when the poles are near 
 each other, kindles paper, gunpowder, coal-gas, and other 
 combustibles, with great readiness. The power of the 
 direct induced current of even large induction coils to deflect 
 the magnetic needle, and to effect chemical decomposition, is 
 very insignificant. This shews that it is very much inferior 
 to the inducing current in quantity, however much it may 
 be superior in electro-motive force. The physiological 
 effect, on the other hand, is tremendous, and the experi- 
 menter must take care not to allow any part of his body to 
 form the medium of communication between the poles, as the 
 shock so got might be dangerous, if not fatal. 
 
 289. Large Coil. The Induction Coil has been used very 
 largely of late, in order to obtain information regarding the 
 various forms of disruptive discharge. For this purpose 
 several very large coils have been employed, the largest 
 by far being that lately constructed by Mr Spottiswoode, 
 represented in fig. 180. 
 
 The length of this enormous coil is 4 feet, its diameter 20 
 inches, and its total weight 15 cwt. It is supported at the 
 ends by two massive pillars, and has also a support at the 
 middle to prevent bending. 
 
 There are two primary coils, either of which can be 
 inserted into the secondary the one for producing long 
 sparks, and the other for producing short dense sparks. In 
 the former, which contains an iron core consisting of a 
 bundle of rods, the circuit wire is 660 yards long, '096 inch 
 in diameter, and is wound on in six layers. The resistance is 
 2-3 ohms. In the latter, the iron core is thicker and the 
 wire is wound double to diminish the resistance. 
 
310 
 
 ELECTRICITY. 
 
 The length of wire on the secondary coil is 280 miles, its 
 diameter '0095 inch, and the total number of windings 
 341,850. For better insulation the secondary wire is wound 
 
 Fig. 180. 
 
 in sections separated by discs of vulcanite. The condenser 
 consists of 126 sheets of tinfoil, 18 X 18*25 inches, separated 
 by varnished paper. 
 
 The length of spark got from this coil is very great. 
 With 5 quart Grove cells, the length of spark is 28 inches ; 
 with 10 cells, 35 inches ; and with 30 cells, 42^ inches. 
 This last is by far the longest spark that has ever been 
 produced by artificial means. 
 
 290. Disruptive Discharge, Dielectric Strength. When two 
 electrodes separated by a dielectric are charged to different 
 potentials, the dielectric is, according to Faraday's theory, 
 thrown into a particular state of stress, which is accurately 
 represented by a tension along the lines of force between the 
 electrodes, and an equal pressure in all directions at right 
 angles to these lines. If the dielectric be air, and if p denote 
 this tension, or pressure, we have for the value of p the 
 equation 
 
 p = 27ro- 2 ; (1) 
 
 where cr denotes the quantity of electricity per unit of area 
 on the surface of the electrode. Also if R denote the 
 
INDUCTION APPARATUS. 311 
 
 resultant electric force at a point just outside the conductor, 
 we have (sect. 155) 
 
 E, = 47TO-. (2) 
 
 By combining (1) and (2) we have 
 
 "I- 
 
 If the dielectric be any other medium whose specific induc- 
 tive capacity is K, we have, of course, for p the value 
 
 '-^ 
 
 It is to be observed that p is a force exactly the same in 
 kind as the tension which exists in a cord stretched between 
 two points ; and it can be expressed as so many pounds 
 or grammes weight per unit of area. Hence we can speak of 
 the electric tension of the dielectric, if we understand by that 
 term the quantities represented in equations (3) and (4). 
 
 When the difference of potential between the electrodes is 
 gradually increased, the value of p the electric tension also 
 gradually increases, until a certain limit is reached, when the 
 dielectric gives way under the strain put upon it, and a 
 disruptive discharge, in the form of a spark, takes place 
 between the electrodes. This limiting tension is called the 
 dielectric strength of the medium. 
 
 If the electrodes consist of two parallel circular plates 
 whose diameter is great in comparison to the distance 
 between them, the above expression for p can be put 
 into a slightly different form. For this case E, is constant 
 for every point of the space between the electrodes, unless 
 
 y 
 very near the edges, and (sect. 155) has the value , where V 
 
 is the difference of potential, and t the distance between the 
 electrodes. Hence, if V be the difference of potential, and t 
 the distance between the electrodes when discharge just takes 
 place, the dielectric strength is, for air, 
 
 P = ^. (5) 
 
 87rt 3 
 
 Now if we assume air to be a homogeneous dielectric 
 whose dielectric strength, for given circumstances as to 
 
312 ELECTRICITY. 
 
 pressure, dryness, &c. is constant, this equation (5) shews at 
 once that the spark length, t, is directly proportional to the 
 difference of potential, V. Sir William Thomson, however, 
 has shewn experimentally that this is not the case. He used 
 as electrodes two circular horizontal plates facing each other. 
 The upper plate was made perfectly flat, but the lower one 
 slightly convex upwards like a watch-glass, in order to make 
 the spark always take the same path from centre to centre of 
 the two discs. The difference of potential was measured by 
 the absolute electrometer (sect. 167), and the distance between 
 the plates by a fine micrometer screw. By using equation 
 (5) the dielectric strength, for different thicknesses of the 
 layer of air, was calculated and expressed in C. G. S. units. 
 The result shewed that the dielectric strength was greater for 
 a thin layer of air than for a thick one, or, to put it other- 
 wise, the electro-motive force per inch of air required to 
 produce a spark was greater for thin than for thick layers of 
 air. Kegarding this, Sir William Thomson remarks that it is 
 difficult even to conjecture an explanation. 
 
 By using two balls connected with the opposite coatings of 
 a condenser whose charge was measured by a Lane's jar, 
 Snow Harris found that the length of spark in air and 
 other gases was proportional to the electro-motive force. Later 
 experiments, other than those of Sir William Thomson, have 
 shewn that this law is not strictly accurate for all distances, 
 and that several collateral circumstances, such as the form 
 and size of the electrodes, the sign of the electricity, &c., 
 exert an important influence upon the relation between 
 spark -length and potential-difference. 
 
 Faraday experimented upon the dielectric strength of 
 different gases, but was unable to find any simple law 
 connecting it with any other physical quantity. He gives, 
 however, the following order for the dielectric strength of 
 some of the gases : Hydrogen, oxygen, carbonic acid, air 
 nitrogen hydrogen having the least. This order has been 
 verified by the experiments of Wiedemann. 
 
 It seemed natural to suppose that some relation existed 
 between the dielectric strength and pressure of air or other 
 gaseous medium, and accordingly the discovery of this 
 
INDUCTION APPARATUS. 313 
 
 relation has been made the object of several experimental 
 inquiries. Snow Harris, experimenting with the apparatus 
 already alluded to, found that the length of spark was 
 inversely proportional to the pressure of the air or other 
 gas through which it passed. By recent experiments, this 
 law has been found to be approximately true, but only 
 between the limits of pressure represented by eleven inches 
 of mercury and the ordinary atmospheric pressure. 
 
 Mr Gordon has quite recently examined the subject by 
 means of a large induction coil giving a seventeen-inch 
 spark. Taking the spark between a point and a ball, he 
 finds that the electro-motive force per inch of air required to 
 produce a spark is greater for small than for large pressures 
 a result confirmatory of that of Sir William Thomson. 
 
 When the pressure of the gaseous dielectric is gradually 
 increased above the atmospheric pressure, the dielectric 
 strength also increases until a certain limit is reached, when 
 it appears to become infinite. This has been shewn by 
 M. Cailletet, who found that he could not, by a powerful 
 induction coil, send a spark through half a millimetre of air 
 at a pressure of between forty and fifty atmospheres. 
 
 Also, when the pressure is diminished, the dielectric 
 strength gradually decreases, but not indefinitely so. It 
 appears to reach a minimum value ; and when the vacuum 
 is very perfect, the spark from a powerful source can hardly 
 pass over even a very short distance. In some vacuum 
 tubes constructed by Hittorf and Geissler, a spark which 
 passed readily through fifteen or twenty centimetres of 
 ordinary air, could hardly pass through half a millimetre 
 of the rarefied space. This may be due, however, in great 
 part to a counter electro-motive force set up at the surface of 
 separation between the electrode and the residual gas. 
 
 291. Electric Egg. When the induced current is made to 
 pass through nearly vacuous spaces, a very splendid eifect 
 is produced. The electric egg (fig. 181) is employed to 
 display this. It consists of a glass vessel in the shape of 
 an egg, with an open neck above, and another below. 
 Brass fittings are attached to these. The lower opening 
 is fitted with a stopcock, and can be screwed to the plate 
 
314 
 
 ELECTRICITY. 
 
 of an air-pump. A brass rod and ball rise a short way 
 into the egg. The fittings above are intended to allow of a 
 rod ending in a ball passing up and down air-tight, so that 
 the two balls can be conveniently set at different distances. 
 When the egg is exhausted, and the 
 wires from the coil are attached, the 
 one above and the other below, a lum- 
 inous glow extends between the balls, 
 which is wide in the middle, and con- 
 tracts at either extremity. When the 
 exhaustion has reached one-twelfth of 
 an inch, as shewn by the gauge of the 
 air-pump, black bands are seen to lie 
 horizontally in the light, so as to wear 
 the appearance of stratification, as shewn 
 in the figure. These occur more readily 
 when a drop or two of turpentine, alcohol, 
 or ether have been introduced into the 
 egg. The cause of the stratification is as 
 yet a matter of speculation. The ball 
 which forms the pole is enveloped in 
 a covering of blue light. The glow, 
 which is of a beautiful mauve tint, 
 appears to proceed from the -f ball, 
 and reaches nearly to the ball, from which it is separated 
 by a well-marked non-luminous space. By means of the 
 commutator, these appearances at the balls can be instantly 
 transposed. 
 
 292. Vacuum Tubes. In order to examine the electrical 
 discharge in various gases at different pressures, so-called 
 vacuum tubes are usually employed. They are constructed 
 by hermetically sealing the ends of a glass tube round two 
 pieces of platinum or aluminium wire, which serve as elec- 
 trodes. The tube is exhausted through a short piece of capil- 
 lary tube attached to its side, and put in connection with the 
 air-pump. The exhaustion is usually begun and carried as 
 far as possible by an ordinary air-pump, and then finished by 
 means of the Sprengel mercury pump a form of pump which 
 has been recently so much improved by Crookes, that an 
 
 Fig. 181. 
 
INDUCTION APPARATUS. 315 
 
 exhaustion represented by a small fraction of a millimetre of 
 mercury can be easily obtained. When the exhaustion has been 
 carried as far as required, the capillary tube is melted in the 
 blow-pipe flame and closed a process in which the operator 
 is helped by the pressure of the external air. When tubes 
 containing different residual gases are required, they are first 
 filled with the respective gases and then exhausted, leaving 
 a trace of the gas. When different gaseous pressures in a 
 closed tube are required, the following convenient method is 
 adopted. A small glass bulb containing a piece of potass is 
 attached, by a narrow tubular neck, to a point near the end 
 of the main tube, but clear of its electrode. The potass has 
 the property of absorbing, when cold, the residual gas, especi- 
 ally when carbonic acid gas is used, and of giving it out again 
 when heated. To increase the pressure, the potass bulb is 
 gently heated by a spirit-lamp flame so as to expel the 
 absorbed gas ; and, to diminish the pressure, the bulb is 
 allowed to cool, or cooled artificially, so as to re-absorb more 
 and more of the residual gas. 
 
 When the discharge from the Holtz machine or an induc- 
 tion coil is passed through air at different pressures, the 
 following series of phenomena is observed. 
 
 At the ordinary atmospheric pressure the discharge takes 
 the form of the spark, the brush, the glow, or the band dis- 
 charge according to the electro-motive force of the machine 
 and the distance between the electrodes. 
 
 When the pressure is reduced to about ^\th of an atmo- 
 sphere, the discharge appears as a fine flexible streak of light 
 extending the whole length of the tube, from one electrode 
 to the other. The light is observed to have a reddish tint, 
 which is due to the nitrogen present in the air. 
 
 When the pressure is reduced to ^Vth f an atmosphere, 
 a luminous haze is seen proceeding from the positive elec- 
 trode, and filling the whole of the tube, with the exception 
 of a short dark space in the neighbourhood of the negative 
 electrode, but separated from it by a patch of light of a deep 
 blue colour. An examination of this blue light by the spec- 
 troscope, shews that an increase of temperature has taken 
 place at the negative electrode. 
 
ELECTRICITY. 
 
 316 
 
 When the exhaustion is carried to r^th of an atmosphere, 
 the luminosity proceeding from the positive electrode is seen 
 to be crossed by narrow dark spaces forming what are called 
 
 ; 
 
 Fig. 182. 
 
 striae, while the dark space near the negative electrode shews 
 considerable increase, but is still separated from the electrode 
 by a patch of light. 
 
 When the pressure is still further reduced, the striae 
 become more and more separated, forming detached blocks 
 of light, with distinct dark spaces between them. The dark 
 space near the negative electrode is also still further increased ; 
 and, as the exhaustion proceeds, a second dark space begins 
 to shew itself quite close to the negative electrode, but 
 separated from the first dark space by a solitary luminosity. 
 This second dark space has been recently carefully studied 
 by Crookes, and, after him, has received the name of Crookes' 
 space. 
 
 Fig. 183. 
 
 When the exhaustion is carried still further, and made as 
 complete as possible, the striae are seen gradually to disappear 
 as if they fell one by one into the positive electrode, until, 
 
INDUCTION APPARATUS. 317 
 
 eventually, the Crookes' space has so much increased as to 
 fill the whole length of the tube. In this condition the 
 exhaustion is so perfect, and the number of molecules of 
 residual gas, comparatively speaking, so small, that the 
 molecules are able to proceed in parallel streams from the 
 negative to the positive electrode without coming into col- 
 lision with one another. In the language of the kinetic 
 theory of gases, the length of the mean free path of the 
 molecules is now equal to the length of the tube. In this 
 high vacuum, the stream of molecules proceeding from the 
 negative electrode is observed to go in parallel lines, and to 
 produce a beautiful phosphorescent light where it strikes 
 against the surface of the glass. The colour of this light 
 varies with the kind of glass, but is independent of the 
 nature of the residual gas. With uranium glass, the phos- 
 phorescence is a dark green ; with English glass, blue ; and 
 with soft German glass, a bright apple-green. When the 
 molecular stream is directed against a diamond inclosed in a 
 tube, the diamond phosphoresces with a bright green colour, 
 giving almost as much light as a candle. When the stream 
 falls on a cluster of rubies, each ruby glows with a brilliant 
 red glow. 
 
 By using wide tubes of suitable shape, Mr Crookes has 
 shewn that the shadow of any object placed in the path of 
 the molecules is thrown upon the end of the tube ; and he 
 has also exhibited the curious experiment of making the 
 molecular stream drive a delicately balanced wheel, with 
 mica vanes, supported on pivots inside the tube. 
 
 The character of the discharge in a vacuum tube is found 
 to depend greatly upon the size of the negative terminal. 
 When this is small, the tube appears to expose a resistance to 
 the passage of the discharge, and the striation is formed with 
 greater difficulty. This is shewn by having a tube with one 
 large and one small terminal, and sending the discharge 
 through it alternately in opposite directions. When the 
 small terminal is negative, the striae are very faint, if at all 
 present ; but when the large terminal is negative, they come 
 out with great distinctness. 
 
 Goldstein has recently shewn that the negative terminal, 
 
318 ELECTRICITY. 
 
 though not the positive, can be replaced by a thin sheet or 
 cylinder of non-conducting material, provided it be perforated 
 by a number of small holes. With this form of negative, 
 striation and all the other phenomena of vacuum tubes come 
 out almost as well as with a metallic electrode. 
 
 When a magnet is presented to a vacuum tube through 
 which a discharge is passing, the discharge is seen to be 
 deflected, one pole appearing to attract and the other to repel 
 it. This is obviously analogous to the known action of a 
 magnet upon a movable conductor carrying a current. And 
 not only does the magnet act upon the discharge as a whole, 
 but, when closely examined, it is also found to have a similar 
 action upon each individual stria, giving one the impression 
 that each stria is a complete separate discharge. 
 
 Another remarkable phenomenon connected with the dis- 
 charge in vacuum tubes remains to be noticed the pheno- 
 menon, namely, of the sensitive state. This is the name given 
 to the state of the discharge when it is affected, in the way of 
 being either attracted or repelled by the approach of a con- 
 ductor, such as the tip of the linger, to the side of the tube. 
 
 Fig. 184. 
 
 In all cases the sensitive state is found to be due to the dis- 
 charge being intermittent, and this interniittence is most 
 easily produced by interposing an air-space between the 
 terminal of the machine and the terminal of the tube. This 
 is called including an air-spark in the circuit. When the 
 air-spark is positive that is, when the gap is between the 
 terminal of the tube and the positive terminal of the machine 
 the approach of the conductor causes a repulsion of the dis- 
 charge ; and, when the air-spark is negative, an attraction is 
 produced. The explanation usually given of this phenomenon 
 
INDUCTION APPARATUS. 319 
 
 is as follows : On account of the intermittent nature of the 
 discharge, a greater quantity of electricity is sent through the 
 tube at each discharge than if the discharge were more con- 
 tinuous. This quantity of electricity produces a charge on 
 the inside surface of the glass of the tube, and perhaps also 
 in the particles of the gas themselves. Hence, when a con- 
 ductor connected to earth is brought near to the tube, it is 
 acted upon inductively by the charge on the tube, and a 
 redistribution of the electricity takes place at the point 
 opposite the end of the conductor. In this way the con- 
 ductor conies to act as a second terminal. Now, when the 
 air-spark is positive, the induced electricity on the end of the 
 conductor will be negative, and, in consequence, it will act 
 as a second negative terminal, and produce the usual appear- 
 ance of a dark space which accompanies the negative elec- 
 trode. Hence the charge will seem to be repelled. On the 
 other hand, when the air-spark is negative, the point of the 
 conductor will be positively electrified by induction through 
 the tube, and will act as a positive terminal, producing the 
 usual luminosity and striation which proceed from the positive 
 electrode. Hence, in this case, the discharge will appear to 
 be attracted. The above explanation is not, in all points, 
 "quite satisfactory, and more experimenting is needed to bring 
 out the full explanation of the phenomenon. This subject, 
 along with the whole phenomena of vacuum tubes, has been 
 recently studied with great care by Mr Spottiswood, whose 
 results are to be found in the Philosophical Transactions. 
 
 MAGNETO-ELECTRIC INDUCTION MAGNETO-ELECTRICITY. 
 
 293. Magneto- electricity includes all phenomena where 
 magnetism gives rise to electricity. There are practically 
 two cases of it namely, when the current is induced in a 
 coil of insulated wire, and when it is induced in conducting- 
 plates. 
 
 Currents induced by Magnets in Coils of Wire. 
 
 294. How a Current is induced in a Coil by a Magnet. 
 When a coil, in which a current circulates, is quickly placed 
 
320 
 
 ELECTRICITY. 
 
 within another coil unconnected with it, a contrary induced 
 current in the outer coil marks its entrance, and when it is 
 withdrawn, a direct induced current attends its withdrawal. 
 Change, whether in the position or current strength of the 
 primary coil, induces currents in the secondary coil, and 
 the intensity of the induced current is in proportion to 
 the amount and suddenness of the change. In singular 
 confirmation of Ampere's theory, a permanent bar-magnet 
 may be substituted for the primary coil in these experi- 
 ments, and the same results obtained with greater intensity. 
 When a bar-magnet is introduced into the secondary coil, 
 a current is indicated ; and when it is withdrawn, a current 
 in a contrary direction is observed ; and these currents take 
 place in the directions required by Ampere's theory. A 
 
 change of position of the mag- 
 net is marked by a current, as 
 in the former case. If we had 
 the means of increasing or 
 lessening the magnetism of the 
 bar, currents would be induced 
 the same as those obtained by 
 strengthening or weakening the 
 current in the primary coil. It 
 is this inductive power of iron 
 at the moment that a change 
 takes place in its magnetism, 
 that forms the basis of magneto- 
 electric machines. The manner 
 in which this is taken advantage 
 of will be easily understood by 
 reference to fig. 185. NS is a 
 permanent horseshoe magnet, and let us suppose it to be 
 fixed ; CD is a bar of soft iron, with coils A and B wound 
 round its extremities, and may be looked upon as the 
 armature of the magnet. CD is capable of rotation round 
 the axis EF. So long as CD remains in the position indicated 
 in the figure, no currents are induced in the surrounding 
 coils, for no change takes place in the magnetism induced 
 in it by the action of NS. The moment that the poles 
 
INDUCTION APPARATUS. 321 
 
 of CD leave NS, the magnetism of the soft iron diminishes 
 as its distance from NS increases, and when it stands 
 at right angles to its former position, the magnetism has 
 disappeared. During the first quarter-revolution, therefore, 
 the magnetism of the soft iron diminishes, and this is 
 attended in the coil (for both coils act, in fact, as one) by an 
 electric current, which becomes manifest when the ends, e, e y 
 of the coil are joined by a conductor. During the second 
 quarter-revolution, the magnetism of the armature increases 
 till it reaches a maximum, when its poles are in a line with 
 those of NS. A current also marks this increase, and pro- 
 ceeds in the same direction as before ; for though the mag- 
 netism increases instead of diminishes, which of itself would 
 reverse the induced current, the poles of the revolving 
 armature, in consequence of their change of position with the 
 poles of the permanent magnet, have also been reversed, and 
 this double reversal leaves the current to move as before. For 
 the second half-revolution, the current also proceeds in one 
 direction, but in the opposite way, corresponding to the 
 reversed position of the armature. Thus, in one revolution of 
 a soft iron armature in front of the poles of a permanent magnet, 
 two currents are induced in the coils encircling it, in opposite 
 directions, each lasting half a revolution, starting from the line 
 joining the poles. 
 
 Currents induced by Magnets in Conducting-plates. 
 
 295. The Magnetism of Rotation was discovered by Arago 
 in the years 1824-5. He observed that when a magnetic 
 needle was made to oscillate immediately above a copper 
 plate, it came sooner to rest than it did otherwise. The 
 oscillations were made in the same time as when away from 
 the plate, but they were less in extent : the plate seemed thus 
 to act as a damper to the motions of the needle. This being 
 the action of the plate at rest on the needle in motion, Arago 
 reasoned that the needle at rest would be influenced by the 
 plate in motion. Experiment confirmed this surmise. He 
 made a copper disc revolve with great rapidity under a 
 needle, resting on a membrane placed right over the disc, and 
 quite unconnected with it, the middle of the needle being 
 
322 
 
 ELECTRICITY. 
 
 placed above the centre of the disc. As expected, the needle 
 deflected in the direction of the motion of the disc. The 
 deflection of the needle increased with the rapidity of the 
 motion, and when it reached a sufficient amount, the needle 
 no longer remained in a fixed position, but turned round 
 after the disc. This action of the revolving disc was 
 attributed to what was then called the 'Magnetism of 
 Kotation/ and the name has been since retained. The 
 explanation of this phenomenon was first given by Faraday 
 (1831). He proved it to arise from the reaction of currents 
 induced in the plate in motion by the magnet. 
 
 296. The magnetism of rotation is only one of a very large 
 class of phenomena, in which the motion either of a magnet 
 or a wire conveying a current induces a current in a neigh- 
 bouring conductor. 
 
 With the aid of Lenz's law, we can easily understand the 
 principles at work in Arago's revolving plate. Fig. 186 
 
 represents what takes place in it. 
 The plate, P P, may be regarded 
 as divided into four parts ; those 
 of which n, n', s, sf form the 
 centres. The part n approaches 
 the north pole, N, of the mag- 
 netic needle NS. In order to 
 impede the motion of approach, 
 n must be forced to assume 
 north polar magnetism, the 
 current of which moves, as 
 shewn in the figure, from right 
 to left. The part of which n' is the centre, leaving a south 
 pole, will be induced to assume north polar magnetism 
 to impede the rotation of the disc. The currents of n and n' 
 are coincident at their further ends, but in the middle, as 
 shewn by the dotted lines, they are opposed, the result 
 of which is that one current circulates, as shewn by the 
 continuous line in the left-hand side of the plate. A similar 
 state of things is also found in the right-hand half, as shewn 
 in the figure. The two main currents are coincident in the 
 middle of the plate. It is this conjoined current which 
 
 Fig. 186. 
 
INDUCTION APPARATUS. 
 
 323 
 
 affects the needle ; it runs in a direction a little in advance 
 of the needle, as the inductive power of the magnet takes 
 some time to act. As the induced current lies below the 
 needle, the deflection, according to the rule, takes place in 
 the direction of the motion of the disc. If the disc were 
 stationary, the currents induced in the plates would mani- 
 festly impede the oscillations of the needle. When cuts are 
 made in the disc in the line of the radii, it loses almost 
 entirely its disturbing power ; the currents 
 formed in the whole disc can no longer take 
 place, and those formed in the various sectors 
 are weak in comparison ; by filling up the 
 vacant spaces with solder, the power is nearly 
 restored to it. As is to be expected, the effect 
 of the revolving plate depends on the conduct- 
 ing power of the material of which it is made. 
 It is owing to its high conducting power that 
 copper is so much used in these experiments ; 
 hence, also, it is that copper is so much 
 employed in the construction of magnetic 
 apparatus. A copper compass-box, for instance, 
 is not only desirable, from its being free from 
 iron, but it acts also as a damper to bring the 
 needle quickly to rest when disturbed. 
 
 297. Lenz's law is applicable to all cases 
 when electricity is induced by the motion of a 
 magnet, or of a conducting circuit. We may 
 quote only two other experiments as illustra- 
 tions of it. " In the first experiment, a small 
 cube of copper (fig. 187) is hung by a thread to 
 a frame, and placed between the poles of a powerful electro- 
 magnet ; the cube is sent into rapid rotation by the twist on 
 the thread, previously given it ; it is instantly brought to a 
 halt, when the current is allowed to circulate in the coils of 
 the magnet, and it begins its motion again when the current 
 is turned off. In the second experiment, a disc of copper 
 (fig. 188) is made to rotate rapidly between the poles n, s, of 
 an electro-magnet, by means of a handle and intervening 
 wheelwork turned by the experimenter. When the current 
 
 u 
 
 Fig. 187. 
 
324 ELECTRICITY. 
 
 magnetises the soft iron poles, the disc, moving freely before, 
 appears suddenly to meet with an unseen resistance, and 
 the rotation continues slowly or 
 not at alL If persisted in, the 
 rotation causes the disc to rise 
 in temperature, the rise being 
 proportionate, according to Fou- 
 cault, to the square of the velocity 
 of rotation. As shewn in the 
 figure, the approaching part of 
 the disc has a south pole turned 
 to s and a north pole to n. The 
 Fig. 188. receding part manifests the 
 
 opposite polarity, both polarities 
 
 combining to resist the motion of the disc. The currents 
 marked with dotted lines are not the only currents. There 
 are several such currents in the same direction, extending 
 out like waves on each half, coinciding in the line between 
 the centre and the poles. Hence, if a circuit were formed, 
 including the radius between the centre and the two poles, a 
 current in one direction would be constantly transmitted 
 through it. This may be done by connecting a wire with 
 the axis of the plate, and by making a spring press on the 
 edge of the plate, at the poles, so as to give a path for the 
 current without impeding the plate. To the spring a wire 
 must also be attached. The two wires being connected with 
 a galvanometer, a current in one direction would be indicated 
 by it as the plate revolves. A machine of this kind, invented 
 by Faraday (1831), was-the first form of the magneto- electric 
 machine, Chapter XXII. 
 
 ABSOLUTE ELECTRICAL MEASUREMENTS. 
 
 298. How an Electric Resistance may be expressed as an 
 Absolute Velocity. It has already been shewn (sect. 186) that 
 the dimensions of a resistance are the same as those of a 
 velocity ; and it becomes an important experimental problem 
 to find the velocity which is equivalent to the resistance of a 
 wire of given length, thickness, and material. This has been 
 done by the British Association Committee, in order to find 
 
ABSOLUTE ELECTRICAL MEASUREMENTS. 325 
 
 in absolute measure the value of the ohm or B.A. unit, as it is 
 called. The method adopted will be understood from what 
 follows : Suppose, at any part of the earth's surface, two rails 
 are placed parallel to each other, so that the plane passing 
 through them shall be perpendicular to the magnetic 
 meridian, or to the lines of horizontal force. We may thus 
 put the rails horizontally, the one lying right above the 
 other. Suppose now that a rod, standing vertically, connects 
 these rails, and can be slid along without friction between 
 them. Let the ends of the rails at either termination be 
 connected with a rod of equal length to the slider, and let it 
 be placed in the magnetic meridian, or at right angles to the 
 plane in which the slider moves. Let this rod be bent so as 
 to form an arc of 57| of a circle, the radius of which must 
 be the length of the rod or of the slider, and let a small 
 needle be suspended at the centre. There will be thus a 
 complete conducting circuit formed by one rail, the rod, the 
 other rail, and the slider. Let the resistance, moreover, 
 throughout this circuit be the same, whatever the position of 
 the slider in the rails, or, which is the same thing, let the 
 rails be perfect conductors. When the sliding rod is moved, 
 it cuts the horizontal lines of magnetic force at right angles, 
 and a current is induced by them in it, the strerkgth of which 
 is proportionate to the number of lines cut by it in a given 
 time. The faster, therefore, the rod moves, the greater is the 
 current, and the greater will be the deflection of the small 
 needle. When it is moved with such a velocity that the 
 needle deflects 45, the current in the arc has acquired the 
 same power over the needle as the earth's magnetism. The 
 current induced in the slider is in such a direction that the 
 vertical action between it and the earth's magnetism offers 
 resistance to its further motion, and work therefore has to be 
 expended to move the slider. The work expended in a given 
 time, say a second, in moving the rod, is within the circuit 
 equivalent to the electro-motive force, or the work done in 
 producing the current. If the resistance within the circuit 
 which the electro-motive force has to overcome in generating 
 a current capable of causing a deflection, say of 45, be small, 
 the velocity of the slider will be correspondingly small ; if 
 
326 ELECTRICITY. 
 
 great, correspondingly great. The velocity of the slider thus 
 measures the resistance of the circuit. 
 
 Although this arrangement, which contains the germ of 
 the reasoning, cannot be practically carried out, other 
 arrangements can by calculation be reduced to it. To fix 
 our ideas, let the slider be a metre in length ; let it move, 
 say, 10,000 metres per second to cause a deflection of 45 
 that is, to generate a unit current in the supposed circuit. 
 The slider, in moving at this rate, describes an area of 10,000 
 square metres, which is the measure of the number of lines 
 of force cut, or of the inductive power of the earth's horizontal 
 magnetism in the experiment. It may be obtained, as in 
 this case, by a slider of a metre in length moving at the rate 
 of 10,000 metres per second, or one 100 metres in length 
 moving with T -J- T th part of the velocity that is, 100 metres. 
 
 Suppose, now, I wish to know the resistance offered by a 
 wire of a certain thickness, expressed as a velocity, I bend 
 6-2832 metres of it into the form of a ring of one metre in 
 radius, and make the ring capable of rotation round a vertical, 
 as it is in fig. 188, round a horizontal axis. The induction 
 to which the ring is subjected in its rotation, causes two 
 opposite currents to traverse it in one revolution, the turning- 
 point being when the ring is at right angles to the magnetic 
 meridian ; but since each half changes its side with each 
 change of current, to an observer north or south of the ring 
 the current appears to move always in the same direction, 
 and it consequently affects a needle placed at its centre in the 
 same way. To reduce the motion of the ring to the equiva- 
 lent motion of -the slider, we must project the motion of 
 the ring on a vertical plane at right angles to the magnetic 
 meridian. The semi-revolution of the sphere described 
 by the ring projected on this plane is the area included by 
 the ring, namely, 3-1416 square metres, and by a whole 
 revolution twice this, or 6'2832 square metres. If ten 
 revolutions per second produce a deflection of 45, the 
 effective area is 62 -832, which is equivalent to a metre slider 
 moving at the rate of 62*838 metres per second. But we 
 reckon the current from one metre of it, so that the velocity 
 of the ring must be 6 '2838 times increased to give one metre 
 
ABSOLUTE ELECTEICAL MEASUREMENTS. 327 
 
 the effect of the whole circumference : the equivalent velocity 
 of the metre slider must thus be 394'7. The resistance of 
 6'2832 metres of the wire in question is thus 394*7 metres per 
 second, and we can easily calculate the length of it necessary 
 to produce a resistance of one metre, or of 10,000,000 metres, 
 the B.A. unit. Here we have only given the mere out- 
 line of the process of estimating resistance as an absolute 
 velocity. It was essentially by this method, which is clue to 
 Sir William Thomson, that Messrs Maxwell, Stewart, and 
 Jenkin (1863-4), with almost perfect experimental and 
 mathematical skill, measured the absolute resistance of a 
 coil instead of a ring of copper wire, and thence obtained 
 a material value for a B.A. unit. Should the material 
 standard they found be lost or damaged, it could be again 
 renewed by a new determination. 
 
 299. Relation between the Electro- static and the Electro- 
 magnetic Systems of Units. These systems have already been 
 explained (sects. 183, 185), and it has been shewn (sect. 186) 
 that the ratio of the electro-static to the electro-magnetic unit 
 of quantity of electricity, is a quantity whose dimensions are 
 the same as those of a velocity. Denoting this ratio by v, we 
 can obtain by means of it a set of equations connecting the 
 numbers which express in electro-static and electro-magnetic 
 measure the same quantity of electricity, the same current, 
 the same electro-motive force, the same resistance, and the 
 same capacity. 
 
 (1) Let q and Q be the electro-static and the electro- 
 magnetic measure of the same quantity of electricity. Then 
 evidently we have 
 
 q = vQ. (1) 
 
 (2) Let c and C be the electro-static and the electro- 
 magnetic measure of the same current ; and let q and Q be 
 the electro-static and the electro-magnetic measure of the 
 quantity of electricity conveyed by the current in the time t ; 
 then we have 
 
 q = ct, 
 
 and Q = Ct ; 
 
 but q = vQ by (1). 
 
328 ELECTRICITY. 
 
 Therefore ct = vCt; 
 
 therefore c = vC. (2) 
 
 (3) Let e and E be the electro-static and the electro- 
 magnetic measure of the same electro-motive force, and let q 
 and Q be the electro-static and electro-magnetic measure of 
 the quantity of electricity transferred from one point to 
 another whose difference of potential is e or E ; then the work 
 done is represented by qe or QE. Hence, 
 
 qe = QE - 
 
 but q = vQ. 
 
 Therefore vQe = QE. 
 
 Hence e = |. (3) 
 
 (4) Let r and E, be the electro-static and the electro- 
 magnetic measure of the resistance of the same wire ; and let 
 e and E be the electro-static and electro-magnetic measure of 
 the difference of potential between its ends, and c and C the 
 electro- static and electro-magnetic measure of the current 
 through it ; then, by Ohm's law, we have 
 
 and 
 
 Therefore 7^ = . ^ ; 
 
 \j T Jli 
 
 but c = vC, 
 
 Tfl 
 
 and e = - (3). 
 
 vC E 1 R 
 Therefore -^ = - . - . E . 
 
 -p -p 
 
 Hence v = , that is, r = -^. (4) 
 
 (5) Let s and S be the electro-static and the electro-magnetic 
 measure of the capacity of the same condenser ; and let q and 
 
ABSOLUTE ELECTRICAL MEASUREMENTS. 329 
 
 Q be the electro-static and electro-magnetic measure of the 
 charge in it, and e and E the corresponding measures of the 
 difference of potential ; then 
 
 q = es, 
 
 and Q = ES ; 
 
 but q = -yQ, 
 
 and 
 
 Tjl 
 
 Therefore vQ, = & 
 
 Hence v.ES= .s 
 
 therefore s = -y 2 S. (5) 
 
 The above equations indicate five distinct methods of 
 finding the value of v. 
 
 Weber and Kohlrausch compared the two measures of the 
 same quantity of electricity, that quantity being the charge 
 of a Leyden jar. ;The difference of potential between the 
 coatings was obtained directly by an electrometer. The 
 capacity was expressed in absolute measure by finding the 
 radius of a sphere which had the same capacity* as the jar. 
 The product of these two numbers gave the quantity of 
 electricity in the jar in electro-static measure. The jar was 
 then discharged through the coil of a galvanometer, and, 
 from the swing of the needle, the number representing the 
 electro-magnetic measure of the charge was obtained. The 
 ratio of the two numbers gave the value of v, which was 
 
 v = 3*1704 x 10 10 centimetres per second. 
 
 Sir William Thomson compared the two measures of the 
 same electro-motive force. The electro-motive force in 
 electro-static measure was obtained directly by an electro- 
 meter. The electro-magnetic measure was obtained by 
 observing the current which it could send through a wire of 
 known resistance, and applying Ohm's law. The ratio of the 
 two numbers gave for v the value 
 
 v = 2'93 x 10 10 centimetres per second. 
 
330 ELECTRICITY. 
 
 Clerk Maxwell also compared the two measures of the same 
 electro-motive force, but by a different method. He balanced 
 the electro-static repulsion of two similarly charged insulated 
 discs against the electro-magnetic attraction of two flat spiral 
 coils of known resistance and carrying known currents. This 
 method gave for v the value 
 
 v = 2-8798 x 10 10 centimetres per second. 
 
 The other methods indicated by the above equation have 
 also been employed by different experimenters, and results 
 obtained fairly concordant with the values already given. 
 
 300. Physical meaning of v. An idea of the physical 
 meaning of v may be got as follows. We may evidently 
 regard an electric current as a close succession of statically 
 charged bodies, each containing the quantity of electricity 
 which the current transmits in a second, and all moving with 
 the velocity of electricity. Hence, if we have two bodies 
 statically charged with like electricity, moving in the same 
 direction, and with the same velocity in parallel lines, we see 
 that, at a certain velocity, the electro- static repulsion between 
 the bodies will just be balanced by the electro-magnetic 
 attraction arising from the parallel currents produced by 
 their motion. If V be this velocity, then it can be shewn 
 that V = v. This result was predicted by Clerk Maxwell, 
 and has been so far verified by Professor Kowland, who has 
 shewn that an insulated statically-charged rotating disc has a 
 distinct electro- magnetic action on a freely suspended astatic 
 needle. 
 
331 
 
 Part IV.-PRACTICAL APPLICATIONS OP 
 CURRENT ELECTRICITY. 
 
 CHAPTER XXIII. 
 ELECTRO- METALLURGY. 
 
 301. Electro-metallurgy is the art of depositing, electro- 
 chemically, a coating of metal on a surface prepared to 
 receive it. It may be divided into two great divisions 
 electrotype and electro-plating, gilding, &c. the former 
 including all cases where the coating of metal has to be 
 removed from the surface on which it is deposited, and the 
 latter all cases where the coating remains permanently fixed. 
 Gold, platinum, silver, copper, zinc, tin, lead, cobalt, nickel, 
 can be deposited electrolytically. 
 
 302. Electrotype is the art of copying seals, medals, engraved 
 plates, ornaments, &c., by means of the galvanic current in 
 metal, more especially copper. The manner in which this is 
 done will be best understood by taking a particular instance. 
 Suppose we wish to copy a seal in copper : an impression of 
 it is first taken in gutta-percha, sealing-wax, fusible metal, or 
 other substance which takes, when heated, a sharp impression. 
 While the impression say, in gutta-percha is still soft, we 
 insert a wire into the side of it. As gutta-percha is not a 
 conductor of electricity, it is necessary to make the side on 
 which the impression is taken conducting ; this is done by 
 brushing it over with plumbago by a camel-hair brush. The 
 wire is next attached to the zinc pole of a weakly charged 
 Daniell's cell, and a copper plate is attached by a wire to the 
 copper pole of the cell. When the impression and the copper 
 plate are dipped into a strong solution of the sulphate of 
 copper, they act as the - and + electrodes. The copper of 
 the solution begins to deposit itself on the impression, first at 
 the black-leaded surface in the vicinity of the connecting 
 
332 ELECTRICITY. 
 
 wire, then it gradually creeps over the whole conducting 
 surface. After a day or two, the impression is taken out ; 
 and the copper deposited on it, which has now formed a 
 tolerably strong plate, can be easily removed by inserting the 
 point of a knife between the impression and the edge of the 
 plate. On the side of this plate, next the matrix, we have a 
 perfect copy of the original seal. If a medal or coin is to be 
 taken, we may proceed in the same way, or we may take the 
 medal itself, and lay the copper on it. In the latter case, the 
 first cast, so to speak, that we take of each face is negative, 
 shewing depressions where the medal shews relief ; but this 
 is taken as the matrix for a second copy, which exactly 
 resembles the original. The adhesion between the two is 
 slight, and they can be easily separated. The cell of a battery 
 is not needed to excite the current. 
 A galvanic pair can be made out 
 of the object to be coated and a 
 piece of zinc. Fig. 189 shews how 
 this may be done. B is a glass 
 vessel, containing sulphate of cop- 
 per ; A is another, supported on 
 B by a wire frame, and containing 
 a weak solution of sulphuric acid. 
 The glass vessel, A, is without a 
 bottom, but is closed below by a 
 Fig. 189. bladder. A piece of zinc, Z, is 
 
 put in the sulphuric acid, and a 
 
 wire, D, coated with insulating varnish, establishes a con- 
 nection between it and the impression, C, which is laid below 
 the bladder. Electrotype is of the greatest importance in the 
 arts : by means of it, engraved copper plates may be multi- 
 plied indefinitely, so that proof-impressions need be no rarity ; 
 wood-cuts can be converted into copper; bronzes can be 
 copied ; and several like applications are made of it too 
 numerous to mention. By connecting a copper plate ready 
 for corrosion with the -+- pole, and making it a -f electrode, 
 it can be etched with more certainty than with the simple 
 acid, and without the acid fumes. 
 303. Electro-plating. This is the art of coating the baser 
 
ELECTRO-METALLURGY. 333 
 
 metals with silver by the galvanic current. It is one 
 theoretically of great simplicity, but requires in the successful 
 application of it very considerable experience and skill. 
 Articles that are electro- plated are generally made of brass, 
 bronze, copper, or nickel silver. The best electro-plated 
 goods are of nickel silver. When Britannia metal, iron, zinc, 
 or lead are electro-plated, they must be first electro-coppered, 
 as silver does not adhere to the bare surfaces of these metals. 
 Great care is taken in cleaning the articles previous to electro- 
 plating, for any surface impurity would spoil the success of 
 the operation. They are first boiled in caustic potash, to 
 remove any adhering grease ; they are then immersed in 
 dilute nitric acid, to dissolve any rust or oxide that may be 
 formed on the surface ; and they are lastly scoured with fine 
 sand. Before being put into the silvering bath, they are 
 washed with nitrate of mercury, which leaves a thin film of 
 mercury on them, and this acts as a cement between the 
 article and the silver. The bath where the electro-plating 
 takes place is a large trough of earthenware or other non- 
 conducting substance. It contains a weak solution of cyanide 
 of silver in cyanide of potassium (water, 100 parts ; cyanide 
 of potassium, 10 parts ; cyanide of silver, 1 part). A plate of 
 silver forms the + electrode ; and the articles to be plated, 
 hung by pieces of wire to a metal rod lying across the trough, 
 constitute the electrode. When the plate is connected with 
 the copper or + pole of a one or more celled galvanic battery, 
 according to the strength required, and the rod is joined with 
 the zinc or pole, chemical decomposition immediately 
 ensues in the bath, the silver of the cyanide begins to deposit 
 itself on the suspended objects, and the cyanogen, liberated 
 at the plate, dissolves it, re-forming the cyanide of silver. 
 According, then, as the solution is weakened by the loss of 
 the metal going to form the electro-coating, it is strengthened 
 by the cyanide of silver formed at the plate. The thickness 
 of the plate depends on the time of its immersion. The 
 electric current thus acts as the carrier of the metal of the 
 plate to the objects immersed. In this way, silver becomes 
 perfectly plastic in our hands. We can by this means, 
 without mechanical exertion or the craft of the workman, 
 
334 ELECTRICITY. 
 
 convert a piece of silver of any shape, however irregular, into 
 a uniform plate, which covers, but in no way defaces, objects 
 of the most complicated and delicate forms. When the 
 plated objects are taken from the bath, they appear dull and 
 white ; the dullness is first removed by a small circular brush 
 of brass wire driven by a lathe, and the final polish is given 
 by burnishing. The process of electro-gilding is almost 
 identical with that of electro-plating, only the solution must 
 be kept hot. Success in either is attained by proper 
 attention to the strength of the battery, the strength of the 
 solution, the temperature, and the size of the + electrode. 
 Magneto-electric machines are now used very extensively for 
 furnishing the necessary current in plating. For a description 
 of these machines see Chapter XXIV. 
 
 ELECTRIC LIGHT. 
 
 304 When the ends of two wires which form the poles of 
 a powerful galvanic battery are made to touch, and then are 
 separated for a short distance, the current which passes when 
 the contact is made does not cease with the separation, but 
 forces its way through the intervening air, accompanied with 
 an intense evolution of light and heat. So great is the heat 
 evolved that the most refractory metals are melted by it, and 
 therefore some substance rivalling the metals in conducting 
 power, but much more infusible, must be found to act as the 
 poles, to allow of the continuation of the current in such 
 circumstances. The various forms of carbon are well suited 
 to this purpose ; the more compact forms of charcoal answer 
 very well; baked carbon answers better; but the coke 
 that is sublimed inside the retorts in the distillation of gas, 
 both for durability and conducting power, makes by far the 
 best poles. Sir Humphry Davy (1813) first discovered and 
 described the electric light. Fig. 190 represents a simple 
 arrangement for producing it. The carbon-points, P, N, are 
 fixed into hollow brass rods, which are connected with the 
 battery by wires entering at the binding screws s, s. The 
 rods slide in the heads of the glass pillars A, A, fixed to a 
 stand, so as to admit of the points being placed at different 
 distances. The wires from the battery -poles being properly con- 
 
ELECTRIC LIGHT. 335 
 
 nected, the points are made to touch, and are then withdrawn 
 a line or two, when the most dazzling light ensues, rivalling 
 the light of the sun in purity and splendour. Its intensity is 
 such as to prevent the eye from examining the particulars of 
 
 Fig. 190. 
 
 its production. These, however, may be ascertained by pro- 
 jecting with a lens of short focus the images of the points on 
 a screen, when they are seen as shewn in the figure. The 
 light is found to arise chiefly from the intense whiteness of 
 the tips of the carbon rods, and partially from an arch of 
 flame extending from the one to the other. This arch is 
 called the electric arc. The + pole is the brightest and the 
 hottest ; a fact which may be proved by intercepting the 
 current, when the + pole continues to appear red for some 
 time after the pole has become dark. . 
 
 During the maintenance of the light, a visible change takes 
 place in the condition of the poles. The + pole expe- 
 riences a loss of matter ; particles of carbon pass from it 
 to the pole, which they partly reach, and partly are 
 burned by the oxygen of the air on the way. The same 
 takes place, though to a much less extent, with the pole ; 
 so that while the + pole becomes hollowed out or blunt 
 by its losses, the pole remains pointed by its apparent 
 gains. The wasting away, particularly of the + pole, 
 in a short time renders the distance between the poles too 
 considerable to allow of the passage of the current, and the 
 light is thus suddenly extinguished, until again renewed by 
 contact and removal. The points may be removed with a 
 powerful battery four or five millimetres before the circuit 
 is broken. The transference of matter between the poles 
 is considered to account for the existence of the arc, and 
 
336 ELECTRICITY. 
 
 the passage through the air of the current, as thereby a 
 conducting medium extends between the poles. The heat of 
 this arch of flame, or electric arc, is the most intense that 
 can be produced. Platinum melts in it like wax in the 
 flame of a candle. Quartz, the sapphire, magnesia, lime, and 
 other substances equally refractory, are forced by it into a 
 state of fusion. The diamond, when placed in it, becomes 
 white-hot, swells up, fuses, and is reduced to a black mass 
 resembling coke. In this condition, it is still hard enough to 
 scratch glass, but possesses almost no consistency, giving way 
 to the pressure of the fingers. 
 
 The electric light is caused, not by the combustion of the 
 carbon, but by its being brought into a state of incandescence. 
 The electric light can, in consequence, be produced in a 
 vacuum, and below the surface of water, oils, and other non- 
 conducting liquids. It is thus quite independent of the 
 action of the air, a circumstance which has been turned to 
 useful account. 
 
 With a battery of some fifty Bunsen's elements, a light is 
 produced of very great brilliancy ; but when very great power 
 is to be obtained, as well as brilliancy, twice or thrice that 
 number must be employed. Fifty cells give a current suffi- 
 cient to produce the light. If 150 cells be used, they are best 
 arranged in three batteries, the + poles of all three being 
 joined to form one + pole, and similarly with the poles. 
 With a battery of forty or fifty cells, no pointing of the rods 
 is necessary, as this is done by the action of the electricity 
 itself. 
 
 The spectrum of the electric light is found to abound in 
 violet rays, and hence it is well adapted to photographic 
 purposes. Fizeau and Foucault found that with a battery of 
 46 Bunsen cells, a light was obtained which had 34 times 
 the photographic efficacy of the lime-ball light, both being 
 tested by the effect produced on a plate covered with the 
 iodide of silver. The same electric light, when compared in 
 the same way with the sun, was found to stand as 23 to 100. 
 For the production of the electric light, the various forms 
 of dynamo-machines (Chap. XXIV.) are now all but univer- 
 sally employed. 
 
ELECTRIC LIGHT. 337 
 
 305. Electric Lamps. Various arrangements have been 
 invented for maintaining the steadiness of the electric 
 light. The aim in all such is to keep the carbon points, 
 by some mechanical contrivance, within such a distance of 
 each other that the current can pass between them. Foucault, 
 aided by Duboscq, was the first (1849) who constructed 
 an electric lamp of this description. In it, by aid partly 
 of an electro-magnet, and partly of clock-work, the two 
 points are made to travel towards each other at rates 
 corresponding to those of their consumption, the -f- pole in 
 this way travelling faster than the . A detent is fixed to 
 the keeper of the electro- magnet, which locks the clock-work 
 when the keeper is brought up to the magnet, and withdraws 
 it when it is away from it. The keeper is acted upon by a 
 counter-spring, which draws it away from the magnet when 
 the current does not circulate, or when it is too weak to act 
 effectively. Thus, when the points waste away and separate 
 from each other, the current becomes weaker, and when it 
 gets so weak as to impair the splendour of the light, it is so 
 arranged that the spring draws away the keeper, and thereby 
 liberates the clock-work. The points are now made to 
 approach until the current, by the nearing of the points, 
 acquires sufficient strength to draw the keeper to it and 
 insert the detent. There is thus a constant locking and 
 unlocking of the clockwork, and the points are kept at the 
 distance fitted to produce the most brilliant light. 
 
 The above is an example of one of the earliest forms of 
 what are called focussing arc lamps. They are mostly used 
 for experimental work in the laboratory ; and not for general 
 electric lighting, where it is not essential that the electric arc 
 should always remain exactly at the same place. For the 
 latter purpose, a great variety of non-focussing arc lamps has 
 been devised. In them the upper carbon is allowed to 
 approach the lower merely by the weight of the upper 
 carbon-holder ; and when the requisite distance for the arc 
 to pass is reached, the upper carbon-holder is clamped by 
 means of an electro-magnet actuated by the current itself. 
 When the distance between the carbons becomes too great, 
 the electro-magnet ceases, or partially ceases, to act, and the 
 
338 
 
 ELECTRICITY. 
 
 weight of the carbon-holder again brings it down to the 
 right distance. An early form of this lamp, made by 
 Mr Hart, is represented in fig. 
 191. A is the upper carbon- 
 holder, B the electro-magnet, and 
 D the clamping arrangement 
 worked by the armature F. 
 When the current passes, A is 
 drawn up by the magnet B, and 
 the arc is produced. When the 
 carbons waste, the magnet fails, 
 and the points come together 
 again, and the original process is 
 repeated. 
 
 In Crompton's lamp, now much 
 used, the upper carbon-holder in 
 its descent turns a train of wheel- 
 work, which can be instantly 
 stopped by a friction break 
 applied to the circumference of 
 one of the wheels. The break is 
 worked by an electro-magnet, 
 and the clamping and unclamp- 
 ing take place with great regu- 
 larity, and almost entirely avoid 
 any blinking in the light. 
 
 An ingenious form of arc lamp 
 was invented by Jablochkoff in 
 1876, and is known as Jabloch- 
 koff's candle. It is represented in fig. 192, where C and D 
 are two thin carbon pencils separated by a thin layer of 
 kaolin clay, B. The current, from an alternate-current 
 machine, passes alternately up each carbon, and forms the 
 electric arc at A ; and in this way the two carbons are 
 made to consume equally. Two or more of these candles 
 are usually placed in one lamp, and an arrangement is 
 provided whereby the current is automatically shifted 
 from the one to the other as each in succession burns 
 done. 
 
 Fig. 191. 
 
ELECTRIC LIGHT. 
 
 339 
 
 Another form of arc lamp is represented in fig. 193, 
 called the Wallace-Farmer lamp. A and B are carbon plates, 
 
 the upper of which is controlled by the magnet C, by which 
 
 ' ^U el o/f/T/ 
 
 OF THE 
 
 UHIVERSITY 
 
 Fig. 192. 
 
 Fig. 193. 
 
 it is drawn up when the current passes, and the light springs 
 out at the point where the requisite distance for the arc 
 is found. When this part wastes, the light travels to 
 another, and so on backwards and forwards along the 
 carbons. 
 
 306. Incandescent Lamps. When a strong current passes 
 through a spiral of fine platinum wire, of the requisite 
 resistance, the spiral is raised to a state of bright incan- 
 descence, and so becomes a source of light. This is the 
 simplest example of an incandescent lamp, of which a con- 
 siderable variety now exists. In Mr Swan's lamp the 
 platinum spiral is replaced by a fine fibre of carbon prepared 
 by carbonising a cotton thread at a high temperature, and 
 in space void of air. The ends of the fibre are attached to 
 
340 ELECTRICITY. 
 
 the electrodes, and the fibre is usually bent into a horse-shoe 
 form, with a single spiral coil in the middle. The whole is 
 inclosed in a small glass globe, which is exhausted very 
 perfectly of air, and then hermetically sealed. The object 
 of this is to prevent the rapid oxidation of the carbon when 
 in a state of incandescence, which would soon make it 
 consume away. Such a lamp will burn for 600 or 1000 
 hours without visible deterioration. 
 
 In Mr Edison's incandescent lamp, the carbon fibre is 
 prepared by the carbonising process from a strip of bamboo 
 cane. The other arrangements are similar to those of the 
 Swan lamp. In order to prolong the life of the lamp, Mr 
 Edison makes one end of his carbon fibre a little thicker 
 than the other, and sends the current through the lamp 
 always in the same direction. 
 
 Other examples of incandescent lamps in use are the 
 Maxim and the Lane Fox, which, however, do not differ 
 essentially from those described. 
 
 Incandescent lamps are found very serviceable for house- 
 hold illumination, seeing that a number of them, sometimes 
 as many as forty, can be put upon one circuit, and lit by one 
 machine. 
 
 307. The attempt which has been made to substitute the 
 electric light for coal-gas in lighting up streets and public 
 places, has proved very successful. By contrivances similar 
 to those described above, the light may be continued for 
 hours, and it has been used with excellent effect where a 
 limited space has to be lit up, such as in the construction of 
 bridges, at railway-stations, theatres, &c. It has also been 
 applied with success to lighthouse illumination ; and it has 
 been found that the power of the electric light to penetrate 
 fogs is immensely superior to that of the usual oil-light. At 
 lighthouses the current is got from dynamo-machines, driven 
 by steam-engines. 
 
 EXPLODING GUNPOWDER AT A DISTANCE. 
 
 308. The application of the galvanic current to exploding 
 gunpowder at a distance depends on the power it has to ignite 
 thin wires of comparatively bad conducting metals, such 
 
EXPLODING GUNPOWDER AT A DISTANCE. 
 
 341 
 
 as steel and platinum. The current must be transmitted to 
 the point where the explosion is to take place by good con- 
 ducting wires, and the thin wire is made to connect the two 
 ends of these wires in the gunpowder. A red-heat is thus 
 only developed at the spot where it is required. The circuit 
 is not completed until all arrangements for the blasting are 
 ready, and all persons connected with the preparations are at 
 a safe distance from it. Roberts (1838) devised a method of 
 conducting galvanic blasting which soon became 
 almost universal. It is shewn in fig. 194. A tin 
 tube, 3 inches long and f of an inch wide, is filled 
 with gunpowder, and stopped with a cork at each 
 end. Through one of the corks, two copper wires 
 are inserted, ending in the cartridge in something 
 like a pair of horns. The wires are insulated 
 from each other by woollen yarn. They are con- 
 tinued without the cartridge for about 10 feet, 
 when they part company so as to allow the battery 
 wires to be attached to them. The ends of the 
 horns within the cartridge are connected by a thin 
 steel wire, | an inch in length, wound round and 
 soldered to each of them. At the ends there is of 
 course no insulating matter ; indeed they must be' 
 filed or cleaned so as to make the connection with 
 them and the thin wire complete. When a hole is bored for 
 blasting, say 6 or 7 feet long and 2 inches wide, the charge 
 of powder and the cartridge are inserted so that the cartridge 
 lies in the middle of the charge, and the rest of the bore is 
 filled with straw and sand in the usual way. The 10-foot 
 wires project beyond the hole, and the battery- wires can be 
 conveniently attached to them. When all is ready, the circuit 
 is completed, and the explosion immediately follows. The 
 steel wire is burnt away by the current, but the long copper 
 wires are uninjured, and ready to be fitted up as before. 
 Such cartridges are generally kept ready for use in mining 
 establishments. In long circuits the function of the return 
 wire may be performed by the earth, as in the electric 
 telegraph. 
 
 When several charges have to be fired at once, the whole 
 
 Fig. 194. 
 
342 ELECTRICITY. 
 
 are generally included in one circuit. As there is always 
 some difference in the steel wires, or in the way they are 
 fitted, it not unfrequently happens that one cartridge is fired 
 before the others. The circuit is thus broken, and the others 
 are left unfired. With this arrangement, there is no certainty 
 of a simultaneous discharge. If this is wanted, the galvanic 
 current must be abandoned, and recourse must be had to the 
 electricity of the induction coil. If the ends of the wires 
 within the cartridge be brought so near that the induced cur- 
 rent can leap over the distance between them, no steel wire is 
 needed ; the inductive spark itself can effect the ignition. 
 After explosion, the distance of the ends remains the same, 
 and the sparks continue. If, then, there be several charges 
 to be fired in the same circuit, the firing of one does not stop 
 the current, which continues even after all have been fired. 
 The induction spark does not, however, kindle gunpowder 
 with certainty, so that between the ends some material must 
 be placed more easily ignited than gunpowder such as white 
 gunpowder, gun-cotton, &c. When the number of simulta- 
 neous explosions is great (five or six), some very readily 
 exploded substance, such as fulminating mercury, must be 
 placed in the path of the spark discharge. 
 
 AbeVs fuses give us all that can be wished in the way 
 of certainty and simplicity. Abel does not use a thin 
 platinum wire between the two circuit terminations, but he 
 uses what is in effect the same a mixture that conducts, but 
 conducts with difficulty. His fuses are primed with a 
 mixture of chlorate of potassium, subphosphide of copper, 
 and subsulphide of copper. The conducting ingredient is 
 the subsulphide of copper, which must be added in such a 
 proportion as to render the whole difficultly conducting. 
 When the current passes through the mixture, it develops 
 sufficient heat to explode it, and thereby the charge of gun- 
 powder. Abel's fuses are chiefly intended for the electricity 
 of the magneto-electric machine or of the induction coil, 
 although the ingredients may be so compounded as to serve 
 also for that of the voltaic battery. A very small machine is 
 sufficient for the purpose. The little pocket machines 
 employed for medical purposes fire readily one of these fuses. 
 
EXPLODING GUNPOWDER AT A DISTANCE. 
 
 343 
 
 They are very small, some of them about halt' an inch in 
 length, and half the thickness of an ordinary pencil. From 
 what has been said, the application of electricity to the firing 
 of torpedoes under water can be readily understood. 
 
 ELECTRIC CLOCKS. 
 
 30.9. Electric clocks may be divided into two classes those 
 in which the impulse is given to the pendulum directly by 
 electric power, and those in which it is given by a weight or 
 spring alternately liberated and restrained by electricity. Of 
 the first kind, that invented by Bain (1840) is best known. 
 In the ordinary clock, it is the clock that moves the pen- 
 dulum ; in Bain's clock, it is the pendulum that moves the 
 clock. As the construction of the pendulum is the only part 
 of it connected with electricity, we shall confine our notice 
 to a general description of the pendulum action. The 
 lower part of the pendulum ar- 
 rangement is shewn in fig. 195. +''/'' 
 The bob, B, consists of a bobbin 
 of insulated copper wire, and 
 is hollow in the centre ; the wires 
 w, w from both ends run along 
 each side of the pendulum rod 
 R (the lower part of which alone 
 is seen), and are in metallic connec- 
 tion respectively with the two 
 springs from which the pendulum 
 hangs. Two magnets or bundles of 
 magnetic rods, NS, N'S', are fixed at 
 either side of the bob, and are of 
 
 such dimensions that the hollow bob in its .oscillation can 
 pass a certain way over each without touching. The magnets 
 have their like poles turned towards each other. The two 
 springs of the pendulum rod are in connection with the two 
 poles of a galvanic battery. In the connection between one 
 of these springs and the battery, there is a break (not shewn 
 in the fig.), worked by the pendulum rod. When the pendu- 
 lum is made to move, say towards the right, it shifts a slider, 
 so as to complete the connection between the poles of the 
 
 Fig. 195. 
 
344 ELECTRICITY. 
 
 battery. The current thereupon descends one of the wires of 
 the pendulum, passes through the coil of wire forming the 
 bob, and ascends by the other. In so doing, it converts 
 the bob into a temporary magnet, the south pole towards 
 the right, and the north pole towards the left. In this way, 
 the south pole of the bob is repelled by the south pole,tS, of 
 the right-hand magnet ; and its north pole is attracted by 
 the south pole, S', of the left-hand magnet, so that from this 
 double repulsion and attraction both acting in the same 
 direction, the bob receives an impulse towards the left. 
 Partly, therefore, from this impulse, and partly from its own 
 weight, the pendulum describes its left oscillation ; and when 
 it reaches the end of it, it moves the slider so as to cut off 
 the battery current, and then returns towards the right, 
 under the action simply of its own weight. On reaching the 
 extreme right, as before, it receives a fresh impulse ; and 
 thus, under the electric force exerted during its left oscilla- 
 tion, the motion of the pendulum is maintained. So long as 
 the electricity is supplied, the pendulum will continue to 
 move. The current required is exceedingly weak, and Bain 
 considered that it could be sufficiently excited by a plate of 
 copper and a plate of zinc sunk into the ground, and acted 
 upon by the moisture usually found there. This earth- 
 battery, as he called it, was expected to act steadily for years ; 
 but the result proved far otherwise, for the soil not unfre- 
 quently dried up, leaving no trace of electrical action. The 
 imperfection of the battery has led to a strong prejudice 
 against these clocks stronger, certainly, than they merit. It 
 has been found, however, by those who have employed them 
 for astronomical purposes, that little dependence could be 
 placed on them, and that the proper conditions of pendu- 
 lum motion were, from the unsteady supply of electricity, 
 interfered with ; hence the opinion has been generally 
 accepted, that a pendulum moved immediately by electricity, 
 does not keep very accurate time ; and the efforts that have 
 of late been made in electric clock-making, have aimed at 
 rendering the pendulum independent of the irregularities of 
 the motive agent. 
 
 A very important application of Bain's pendulum has been 
 
ELECTRIC CLOCKS. 345 
 
 made by Mr Jones of Chester. Shortly after the invention 
 of Bain's clock, Professor Wheatstone suggested that any 
 number of such clocks could be made to move simultaneously 
 by the same current of electricity. Mr Jones has turned this 
 idea to account in the following way. A standard clock of the 
 usual construction is made, by regulating the flow of a galvanic 
 current, to control the action of any number of copying 
 clocks, likewise of ordinary construction. The pendulum of 
 the standard clock, itself in no way under electric control, on 
 passing towards the right, touches a spring placed at the side, 
 thereby completing the battery connection, and a current is 
 transmitted to the copying clocks in a certain direction. On 
 passing to the left side, the same takes place, but the current 
 this time is sent through the circuit in the opposite direction. 
 The pendulums of the copying-clocks are made on Bain's 
 principle, but have, of course, no break to move, as the 
 primary pendulum performs that function. Let us suppose, 
 at first, that all the pendulums are at rest ; in this case, no 
 current is transmitted. Let the standard pendulum now be 
 moved to the right, the right spring is touched, and a current 
 at the same instant circulates through the bobs of the copy- 
 ing pendulums, and they thereby receive a simultaneous 
 impulse towards the left. All the pendulums n*ove then to 
 the left ; and on reaching the extremity of this oscillation, the 
 standard pendulum touches the left spring, and the secondary 
 pendulums are now impelled to the right. The motion of 
 each secondary pendulum soon increases, until it reaches its 
 proper extent. The pendulums once set a-going are, how- 
 ever, not intrusted solely to the stimulus of the electricity, but 
 are moved by their own weights, as in ordinary clocks, so that 
 if the electricity ceased to be sent to them, they would go on 
 without it. It might be supposed that a confusion of the two 
 forces, electricity and gravity, would ensue ; such, however, is 
 not the case. While the motion of the clock is intrusted to 
 its own weight, the pendulum submits docilely to the control- 
 ling action of the electricity ; and thus a copying clock of 
 little value may be invested with all the perfection of the 
 most costly observatory clock. The success of Jones's pendu- 
 lum has been severely tested in the arrangement employed by 
 
346 ELECTRICITY. 
 
 Professor Kazzi Smyth for firing the one o'clock time-gun at 
 Edinburgh. A clock in the castle of Edinburgh is made to 
 liberate the trigger of the gun exactly at one o'clock. This 
 clock is regulated on Jones's principle, by a clock at the 
 Observatory on the Calton Hill, nearly a mile distant. The 
 Observatory clock, by means of electricity, sets off a time-ball 
 on Nelson's Monument, about 100 yards off, at the same 
 instant. The fall of the ball, and the flash of the gun, 
 though occasioned each by its own clock, are perfectly 
 simultaneous. 
 
 In the second class of electric clocks, the electricity is not 
 charged immediately with the maintaining of the pendulum 
 motion, but draws up the weight, or liberates the spring which 
 discharges that function. This is the same principle as holds 
 in what is known in horology as the ' remontoir' escapement. 
 Mr Shepherd of London was the first to introduce this prin- 
 ciple into electric clock-making, and one of his clocks on a 
 large scale was exhibited at the Exhibition of 1851. We 
 have now all over the country, clocks regulated to Greenwich 
 time by means of electricity. 
 
 CHAPTER XXIV. 
 
 MACHINES FOR CONVERTING MECHANICAL WORK INTO 
 ELECTRICITY, AND CONVERSELY. 
 
 310. Machines for converting mechanical work into elec- 
 tricity may be divided into two great classes first, those for 
 producing static electricity ; and, secondly, those for producing 
 dynamic or current electricity. 
 
 Of the first class we have two kinds namely, those in 
 which the electrification is produced by friction, and those 
 whose action depends on the principle of electric induction. 
 The most common example of the first class is the ordinary 
 cylinder, or plate-glass electric machine, already described. 
 Here we have a cylinder, or circular plate of glass of suitable 
 thickness, made to revolve against a rubber of silk or amal- 
 gamated leather pressed against it by means of a spring. The 
 
CYLINDER MACHINES. 347 
 
 glass moves away from the rubber with a strong positive 
 charge of electricity, while the rubber receives an equally 
 strong negative one. As the glass moves round it meets, on 
 the side opposite the rubber, a row of points attached to an 
 insulated metallic ball, or cylinder with rounded ends, called 
 the prime conductor. The positive charge on the glass acts, 
 through the thin stratum of air, inductively on these points, 
 and deposits a positive charge of electricity on the prime con- 
 ductor, while a corresponding negative charge passes from the 
 latter to the glass. If we suppose the action of the machine 
 to be theoretically perfect, the glass will leave the row of 
 points and advance towards the rubber with a negative 
 charge, while the glass which leaves it is positively charged. 
 The rubber itself being negatively charged, it is clear that 
 there will be attraction between it and the glass which leaves 
 it, and repulsion between it and the glass approaching. On 
 both accounts the electrical forces must produce a resistance 
 to the revolving plate, or cylinder, and it is the equivalent 
 of the work spent in overcoming this resistance which 
 appears as the energy of the electrification produced in the 
 prime conductor. In any actual case, however, the glass 
 advancing towards the rubber will not be entirely free from 
 a positive charge, but this residual charge will be much less 
 than the charge on the part leaving the rubber, so that the 
 attraction against the motion being more than that favouring 
 it, there will be a balance of resistance requiring to be over- 
 come. 
 
 Besides this resistance there is another, arising from the 
 simple friction between the glass and the rubber. The work 
 done to overcome this directly produces heat, which only 
 warms the surfaces in contact, and is wholly wasted as far as 
 the proper function of the machine is concerned. So great 
 is this waste, in even the best machines of this class, that 
 only a small fraction of the work spent in driving them 
 produces the intended effect. 
 
 If multiplying gear be employed to increase the rate of 
 rotation of the machine, the difference of potential between 
 the glass and rubber is rapidly increased. But a limit to this 
 increase is soon attained, when the attraction between the 
 
348 ELECTRICITY. 
 
 opposite charges on the glass and rubber becomes so great 
 that discharge takes place between them, instead of between 
 the glass and the collecting points. 
 
 311. Another very simple and useful instrument for pro- 
 ducing small quantities of electricity, and which depends, 
 primarily at least, for its action on friction, is the electro- 
 phorus of Volta. This instrument has been already described 
 (sect. 143). 
 
 In order to charge a conductor rapidly by means of the 
 electrophorus, it would be necessary to adopt some mechan- 
 ical arrangement whereby the insulated cover could be 
 rapidly laid on and removed from the resinous plate, and 
 alternately brought into contact with the metallic tray, and 
 with the conductor to be charged. As, however, there would 
 be nothing in the action of such an arrangement to replenish 
 the original charge given to the resin, that charge would be 
 soon dissipated, and all further production of electricity would 
 cease, till the resin was charged afresh from an extraneous 
 source. This is precisely what takes place in the Bertsch 
 machine, represented in fig. 196. 
 
 In this machine we have a circular plate of vulcanite which 
 can be made to revolve on a horizontal axis. At opposite 
 extremities of a vertical diameter there are rows of collecting 
 points, the lower of which we shall suppose is connected 
 with the earth, while the upper is attached to an insulated 
 prime conductor of large capacity. Opposite the lower row 
 of points, and on the other side of the revolving plate from 
 it, is placed a sector of vulcanite which has been negatively 
 charged by friction with flannel. This sector is placed verti- 
 cally, leaving a thin air space between it and the revolving 
 plate. The negative charge on the sector acts inductively 
 on the lower row of points through the air and revolving 
 plate as a kind of compound dielectric. In consequence of 
 this inductive action, the row of points deposits a positive 
 charge on the part of the plate facing it, the corresponding 
 negative charge having been repelled to the earth. When 
 this positively charged part is brought, by the revolution of 
 the plate, opposite the upper row of points, it gives up, 
 through them, its positive electricity to the prime conductor, 
 
THE BEtlTSCH MACHINE. 
 
 349 
 
 and returns ready to receive a fresh charge from the lower 
 row. By rapidly revolving the plate, the prime conductor 
 
 Fig. 196. 
 
 can be charged to a high potential, and a stream of sparks 
 drawn from it to a body in contact with the earth. 
 
 In driving this machine, work has to be done to overcome 
 the attraction of the opposite charges on the electrified sector 
 and the part of the revolving plate which faces it. This 
 attraction will become less and less as the initial charge on 
 the sector gets gradually dissipated, through imperfect 
 insulation, in consequence of no provision having been made 
 in the machine itself for automatically replenishing this 
 charge. 
 
 312. We come next to machines in which ample provision 
 has been made for not only automatically replenishing, but 
 increasing to almost any extent, the initial charge or differ- 
 ence of potential which is given to start them. Examples of 
 such machines are Nicolson's Revolving Doubler, Varley's 
 machine, the Replenisher and Mouse Mill of Sir William 
 Thomson, and the Holtz machine. The action of all these 
 
350 ELECTRICITY. 
 
 depends upon the same principle, which will be best illus- 
 trated by the description of a hypothetical arrangement. 
 
 Suppose we take four similar insulated discs of metal P, Q, 
 R, S, and place them in order round a circle so that P and R 
 may be at the extremities of one diameter, and Q and S at 
 the extremities of the diameter at right angles to the former. 
 Let us call P and R inductors, and Q and S receivers. 
 Further, suppose we have a vertical axis passing through the 
 centre of the circle and carrying a non-conducting cross-piece, 
 to the ends of which are attached two discs similar to the 
 former, which we shall call carriers, and designate by A and 
 B. Let the cross piece and discs be so placed that while the 
 axis revolves, A and B are brought successively opposite, and 
 close to P, Q, R, S, but not into actual contact with any of 
 them, except by means of light metal springs, with Q and S 
 only. Before starting, let P and R receive opposite charges, 
 so that their potentials may be represented by P and R 
 respectively. When A is opposite to P, and B to R, let them 
 be brought by springs into contact with the earth or with 
 each other. Now, if the co-efficient of induction between 
 the inductors and carriers be x, and their capacities each 
 unity, A will move away from P with a charge #P, which it 
 will give up by means of the spring to the receiver Q. 
 Meanwhile B has left R with a charge xR, which it has 
 similarly given to the receiver S. During the next half-turn, 
 B will carry a charge xP to Q, and A a charge ccR to S, so 
 that at the end of one half-revolution Q will have a charge 
 equal to xP, and S a charge equal to ccR. The difference of 
 potentials between the receivers at the end of one half- 
 revolution will thus be x (P R). Manifestly, after each half- 
 revolution the difference will be increased by the same 
 amount, so that it will augment in an arithmetical ratio. 
 
 It will be observed that the charges of P and R have 
 meanwhile remained unchanged, unless in so far as they may 
 have been diminished by imperfect insulation. 
 
 Suppose now that we connect, by a wire, the receiver Q 
 with the inductor R, and the receiver S with the inductor P. 
 It is obvious that this will be precisely the same as if we had 
 originally made Q and R one plate of metal, and similarly 
 
THE REPLENISHER. 351 
 
 of S and P. We shall find, however, that, by this charge, 
 the action of the machine is very much altered. Under- 
 standing that the initial charges of P and R are the same as 
 formerly, let us follow the carriers in their rotation. A will 
 leave P with a charge ccP, which it will give up, by means 
 of the contact spring, to E, thus rendering the potential of 
 R, R xP. Similarly, B will leave R with a charge ccR, 
 which it will give to P, and so make the potential of P, 
 P xR. In this way, after one half-turn, the difference of 
 potential between P and R, instead of being P R as at 
 starting, will be P R (R xP), that is (1 -f x) (P R). 
 Thus, if we know the difference of potential of the inductors 
 after any number of half-turns, the difference after one more 
 half-turn will be found by multiplying the former difference 
 by the factor (1 + x). Thus P -R, being the initial differ- 
 ence, the difference after one half-turn, as we have seen, is 
 (1 + x) (P R) ; after two half-turns, it will be (1 + xf 
 (P R) ; after three half- turns (1 + x) 3 (P R), and so on, 
 thus augmenting in a geometrical ratio. This explains why 
 it is that, in machines of this class, an initial difference of 
 potential, however small, gets rapidly multiplied to an 
 enormous amount. 
 
 The replenisher (sect. 167), invented by 'Sir William 
 Thomson, is almost identical in its action with the arrange- 
 ment we have just described. 
 
 In the large machine of Mr Varley there are two metallic 
 inductors fixed, at some distance apart, to an insulated plate. 
 The carriers consist of pieces of metal attached to a circular 
 sheet of ebonite, which revolves close to and facing the 
 inductors. Pins are provided by which each opposite pair 
 of carriers is brought, in passing, into contact with the 
 inductors, and when fully under cover of the latter, each 
 opposite pair of carriers is also put into contact with each 
 other by means of a wire and contact springs. When the 
 machine is in action, a copious supply of sparks can be drawn 
 from either inductor, or a constant stream of electricity can 
 be made to pass between them. 
 
 In the arrangement called the mouse mill, employed by 
 Sir William Thomson, the carriers are attached to the surface 
 
352 ELECTRICITY. 
 
 of an insulated cylinder which, revolves between inductors 
 forming parts of a concentric cylinder. 
 
 Certainly the most remarkable of all the machines which 
 depend on the principle of electric induction is that designed 
 by Holtz of Berlin, already described (sect. 149). 
 
 313. A most useful modification of the Holtz machine has 
 been recently introduced by Topler, which has the great 
 advantage of not requiring any initial charge to start it. 
 
 Fig. 197. 
 
 In this form of machine a number (usually six) of circular 
 discs of tinfoil, about two inches in diameter, are pasted upon 
 the surface of the revolving glass plate at equal distances 
 from each other. To the centre of each disc a small hemi- 
 spherical metallic button is attached, which, as the plate 
 revolves, comes in contact with a set of metallic brushes. 
 One pair of these brushes is attached, at opposite extrem- 
 ities of a diameter, to the stationary plate, and is in contact 
 with the paper inductors. The other pair is in metallic 
 communication with each other, and is fixed opposite the 
 extremities of a diameter of the revolving plate. In con- 
 nection with this last pair of brushes there are also rows of 
 points similar to the usual rows of points in the Holtz 
 
MAGNETO-ELECTRIC MACHINES. 353 
 
 machine. The inductors are exactly similar to those of the 
 Holtz machine, with the exception, that underneath each 
 there are two circular discs of tinfoil, connected by a tinfoil 
 strip, placed at a distance from each other equal to the dis- 
 tance between the similar discs on the revolving plate. In 
 a dry atmosphere this machine will give readily sparks four 
 or five inches long, without the trouble of initial charging. 
 The machine is represented in fig. 197. 
 
 314. In all these machines work is done against the elec- 
 trical attractions between the inductors and carriers, and as 
 the electrical { charges increase in a geometrical ratio, the 
 attraction, and therefore the work required to overcome it, 
 increases in a like proportion. This is well exemplified in 
 the Holtz machine, when, after a few turns, the attraction 
 between the plates feels like a distinct drag upon the revolv- 
 ing disc. With a plentiful supply of work there is no limit, 
 other than imperfect insulation, to the difference of potential 
 that might be produced by such a machine. Ordinarily, in 
 fair working order, sparks of nine or ten inches are readily 
 obtained from ;it. An interesting experiment, illustrating 
 the transmission of power by static electricity, may be made 
 with two Tb'pler machines. If chains be led from the spark- 
 drawers of the one machine to those of the otlner, and one of 
 the machines turned, the other immediately begins to rotate 
 at a rapid rate. 
 
 315. We now come to the consideration of machines of 
 the second class namely, those for converting mechanical 
 work into current electricity. These machines are either 
 magneto-electric or dynamo-electric machines the former 
 being the name given to machines in which the magnetic field 
 is due to permanent magnets ; the latter, to those in which it 
 is due to electro-magnets excited by the generated current 
 itself. The action of all such machines depends upon the 
 principle of current induction, discovered by Faraday in 
 1831. This was really the first step that led to the con- 
 struction of magneto-electric machines. 
 
 Not long after Faraday's" discovery, the first actual magneto- 
 electric machine was constructed by Rixii of Paris. It con- 
 sisted essentially of a fixed electro-magnet, in front of which 
 
354 ELECTRICITY. 
 
 a permanent magnet was made to revolve, the poles of both 
 magnets lacing each other. As, in the course of rotation, 
 each pole of the steel magnet is brought opposite to the iron 
 cores of the electro-magnet, these cores will be rendered for 
 a moment magnetic, and, in consequence, will induce a 
 momentary current in the surrounding wire coils. At each 
 half- turn the magnetism of the iron cores will obviously be 
 reversed, so that we may look upon the machine as precisely 
 doing at a rapid rate the following operations successively : 
 first, inserting a magnet into the wire coils ; secondly, with- 
 drawing it ; thirdly, inserting it with its poles reversed ; and 
 fourthly, again withdrawing it. There are thus, in one com- 
 plete revolution, four momentary currents produced alter- 
 nately in opposite directions. 
 
 Modifications of this machine were afterwards produced by 
 Paxton and Clarke, who made the permanent magnet fixed, 
 and caused the electro-magnet to revolve. They also sup- 
 plied a commutator to their machines for the purpose of 
 causing the current always to flow in one direction. 
 
 Very large machines on this same principle were con- 
 structed by Holmes of London, and Nollet of Brussels. 
 These were used for producing the electric light in light- 
 houses, and also for the purpose of electro-metallurgy. 
 
 316. Magneto- electric Machine. The general construction 
 of a simple magneto-electric machine is shewn in fig. 198, 
 which is one of the forms of Stohrer's machines. NS 
 is a fixed permanent magnet. BB is a soft iron plate, 
 to which are attached two cylinders of soft iron, round 
 which the coils G and D are wound. CBBD is thus the 
 revolving armature. AA is a brass rod rigidly connected 
 with the armature, and also serving as the rotating axle. 
 F is a cylindrical projection on A A, and is pressed upon 
 by two fork-like springs, H and K, which are also the 
 poles of the machine. The ends, m, n, of the coil are 
 soldered to two metal rings on F, insulated from each other. 
 When the armature revolves, AA and F move with it. F, 
 H, and K are so constructed as to act as a commutator, 
 reversing the current at each semi-revolution. By this 
 arrangement, the opposite currents proceeding from the coil 
 
MAGNETO-ELECTRIC MACHINES. 
 
 355 
 
 at each semi-revolution are so transmitted to H and K 
 that these retain the same names. But for this, the effect 
 of the current derived from 
 one semi-revolution would be 
 reversed by that proceeding 
 from the next. H and K, how- 
 ever, change names with the 
 direction of the rotation of the 
 armature. 
 
 The commutating arrange- 
 ment is shewn in fig. 199. A 
 is the axis of the revolving 
 part, the two black lines under 
 H and K are the two forks of 
 these springs, a and / are pro- 
 jections on a metal tube next 
 the axis, and c and e are pro- 
 jections on another tube insu- 
 lated by boxwood or vulcanite 
 (shewn black in the figure) 
 from the inner tube. Both 
 tubes are fixed to the axis A, 
 and move round with it. The 
 projections a, /, c, e are half- 
 
 Fig. 198. 
 
 rings, a and c being on one side of the axis, and e and / on 
 
 the other. Each tube has the end of one of the coil- wires 
 
 attached to it, so that the tubes 
 
 thus form the terminations of 
 
 the coil. As shewn in the figure, 
 
 the left-hand prong of H rests ^ T 
 
 on a, and the left-hand prong < k 
 
 of K on c ; if a be -}-, c will 
 be . Suppose, now, the half- 
 revolution finished, then 6 will Fig. 199. 
 be on e, and d on /, just when 
 
 the current has begun to flow in the contrary direction, and 
 the tubes have changed signs. Still, however, H is + and 
 K . When the armature is made to revolve with sufficient 
 rapidity, a very energetic and ^teady current is generated, 
 
356 ELECTRICITY. 
 
 which possesses all the properties of the galvanic current. 
 Compared with the galvanic battery, the magneto-electric 
 machine is a readier, steadier, and cleanlier source of electri- 
 city, and is, in consequence, extensively used instead of it. 
 Magneto-electric machines may be made of any strength by 
 increasing the number of magnets and the mechanical force 
 employed. 
 
 In the machine just described, the amount of electricity 
 induced in the coils is at a maximum just when the armature 
 is leaving the poles, and at a minimum when it stands 
 equatorially. The gradual cessation of the magnetism of the 
 core in the first quarter revolution, and the gradual acquisi- 
 tion of it in the second, prevents anything like an instan- 
 taneous stoppage and commencement of the current in the 
 half-revolution. The current is thus tolerably continuous, 
 and when the velocity is great, it is nearly uniform. Hence, 
 when it is sent through the nerves of the body, which are 
 affected by sudden changes of current strength, a slight 
 effect only is felt. When, therefore, physiological effect is 
 wanted, a break must be effected in the current. This is 
 done in Stohrer's machines by making the half-rings overlap 
 a little, so that, at the change of pole, when the current is 
 strongest, the interpolar resistance consists only of the prongs 
 of each fork resting on the two half-rings. As this resistance 
 is indefinitely small, the whole of the current goes by it, and 
 none of it by the body. When one prong of each fork leaves 
 simultaneously its half-ring, the current then passes through 
 the body ; and as the resistance of this last is great, a partial 
 stoppage of the current occurs at the instant of separation, 
 which excites an extra current in the coils of the machine. 
 The tension of the extra current is high, and powerfully 
 affects the nerves. It is felt at each half-revolution. 
 
 In large machines, several magnetic magazines are employed 
 with a corresponding number of armatures and coils. The 
 coils may be arranged like the cells of a galvanic battery, for 
 tension or for quantity. For tension, they are arranged 
 successively, so that they form one compound circuit ; for 
 quantity, each single coil or set of coils contributes to the 
 common current. The electro-motive force, resistance, and 
 
MAGNETO-ELECTRIC MACHINES. 357 
 
 current strength are formed as for a galvanic battery. 
 The thickness of wire is selected according to the object of 
 the machine. For giving shocks, or effecting chemical 
 decomposition, the wire must be long and thin ; for heating 
 platinum wire, thicker and shorter. The electro-motive 
 force increases with the rapidity of rotation. Dove has 
 found that in magneto-electric machines, where the current 
 is primarily induced by magnetism, a solid iron core as an 
 armature gives a better effect than a bundle of iron wires. 
 
 317. Siemens Armature. A very marked improvement in 
 magneto-electric machines was made by Siemens when he 
 introduced his new form of revolving armature (see fig. 
 202). This armature consists of a long bar of iron having 
 somewhat the shape of a piece of an ordinary double-flanged 
 rail. The wire is wound round it longitudinally in the 
 hollow and over the ends, so that when finished the whole 
 has a cylindrical form. This cylinder is made to revolve 
 rapidly between the poles of a set of permanent magnets 
 fixed astride it, and at equal distances from each other. A 
 commutator is supplied for giving the currents one direction. 
 The great advantage of this form of armature is, that it rotates 
 in an intense magnetic field, and can be made to revolve very 
 rapidly, and as a consequence proportionally iutrease the 
 strength of the induced current. As yet, however, increasing 
 the strength of the current depended entirely upon increasing 
 the rate of rotation of the armature. Nothing had been done 
 to increase automatically the magnetism of the magnets which 
 induced the currents in the armature. This was reserved for 
 Wilde, who adopted the ingenious plan of making the current 
 from one machine, after it had been brought into the same 
 direction by a commutator, to circulate round a plate of soft 
 iron, which it converted into a very strong electro-magnet. 
 This electro- magnet he used with another Siemens armature 
 of larger size, the current from which, having been brought 
 to one direction, was made to produce a still larger electro- 
 magnet which acted upon a still larger armature. In this 
 way, a current of enormous strength was finally produced, 
 when sufficient driving power was employed. It is stated 
 that a machine of this kind in full action was able to melt an 
 
358 
 
 ELECTRICITY. 
 
DYNAMO-MACHINES. 
 
 359 
 
 iron rod 15 inches long and a quarter of an inch in diameter, 
 and produced a most brilliant electric light from carbon 
 points. 
 
 318. Wilde's Magneto-electric Machine. Fig. 200 shews 
 a front elevation of a seven-inch machine. It consists of 
 two separate machines a purely magneto-electric machine, 
 and a machine which is both electro-magnetic and magneto- 
 electric. Both machines are in the main very similar, 
 and in many respects identical, the only difference being in 
 size and power. The smaller machine, MM', which is purely 
 magneto-electric, is seen surmounting the other. The horse- 
 shoe permanent magnet, MM', is the foremost of a series of 
 sixteen similar magnets, placed the one behind the other in a 
 horizontal row. Each weighs 3 Ibs., and sustains a weight of 
 20 Ibs. The sixteen magnets are fixed below to the magnet- 
 cylinder, c, shewn on a 
 larger scale in fig. 201. 
 This is partly made up 
 of cast-iron, partly of 
 brass. The two iron 
 components, ii (fig. 201), 
 form the sides of it, and 
 the brass bars, 6&, lie 
 between them. They 
 are bolted firmly to- 
 gether by the brass 
 bolts, rr'. The magnet- 
 cylinder is about 12 
 inches in length ; in 
 
 the centre of it is accurately bored a circular hole, extending 
 the whole way, 2 inches in diameter. The inner side sur- 
 faces of the magnets below are accurately fitted to the upright 
 plane sides of the magnet- cylinder, and are firmly secured 
 to it. By this means the cast-iron portions of the magnet- 
 cylinder, ii, form the polar terminations of the magnetic 
 battery, the brass bars, bb } between them, breaking the 
 magnetic continuity. 
 
 A Siemens armature, aa, of cast-iron is made to revolve 
 within the magnet- cylinder. Its diameter is -^th of an inch 
 
 Fig. 201. 
 
360 
 
 ELECTRICITY. 
 
 less than the diameter of the cylinder, which enables it to 
 revolve without friction in very close proximity to the polar 
 surfaces. The manner in which it is cen- 
 tered is, for the sake of simplicity, not shewn 
 in the upper machine, but it is shewn in 
 the lower machine, where, as is afterwards 
 mentioned, the construction, though larger, 
 is perfectly similar. The framework for 
 sustaining the axis of the armature is firmly 
 bolted at gg. Fig. 201 gives, as just men- 
 tioned, an enlarged cross section ; fig. 202 
 shews an enlarged side-view. Two rectan- 
 gular grooves, wl, are made on opposite 
 sides, giving to it somewhat the appearance 
 of a rail. About 50 feet of insulated 
 copper-wire, ww, is wound lengthwise into 
 these grooves in three coils (shewn in 
 section, fig. 201). The coil thus formed is 
 shut in by wooden packing, IV. In fig. 202 
 this packing is removed from the two ends 
 to shew the longitudinal winding of the coil. 
 To prevent the wires from being driven out 
 by the centrifugal force generated in the 
 rapid rotation of the armature, straps of 
 sheet brass encircle the armature at regular 
 intervals, and are sunk in grooves prepared 
 for them in the cast-iron. Two caps of 
 brass, kk t are fitted to the ends of the arma- 
 ture, and to these are attached the steel 
 journals or axes of rotation, ff. On the 
 further axis (the back axis of fig. 200) the 
 pulley, m, is fixed, round which passes the 
 strap from the steam-engine which works 
 the machine. On the other axis (the front 
 axis of the figure) two rings are put, one, 
 n, insulated from it, and the other, ri, con- 
 Fig. 202. nected with it. One end of the armature 
 coil is in connection with the armature, 
 and thereby with the axis and n' ; the other end is insulated 
 
DTNAMO-MACHINES. 361 
 
 and fixed by a binding- screw with n ; n and ri are thus the 
 terminals of the coil. They are made of hardened steel, and 
 the springs s and s', which press against them are of the 
 same material. 
 
 Starting from the position shewn in fig. 201, the armature 
 in one revolution induces two opposite currents in the coil, 
 one in the first, the other in the second half-revolution. It 
 will be seen (fig. 202) that the separation between n and n' 
 lies obliquely. In this way, each spring, s or s', presses 
 against a different ring at each half-revolution. As n and n' 
 change their electric sign, it is so arranged that they change 
 the spring, s or s', against which they press. Thus s and s' 
 receive their currents always in the same direction, conse- 
 quently the wires, o and o', convey the current away from 
 the machine in a uniform direction. The armature is made 
 to revolve 2500 times per minute, and 5000 waves or cur- 
 rents of electricity are transmitted to the wires, o, o'. 
 
 One advantage of this position lies in the motion of the 
 armature not being resisted by the air. In the ordinary 
 position of the armature, much of the work applied to 
 the rotation is expended in the armature beating the air. 
 There is no such loss in Wilde's machine. Another advan- 
 tage is derived from the inductive action 01 the magnet 
 being exerted directly on the coil, as well as through the 
 intervention of the armature. If the coil were made to 
 rotate without the armature, currents would be induced in it 
 of the same kind as that induced by the armature, though of 
 feebler intensity, the maximum points of which would occur 
 when the coil was moving through the line joining the poles, 
 and the minimum points when it was at right angles to that 
 position. Now these are the converse of the maximum and 
 minimum induction points of the armature. In the position 
 in which the armature is placed in this machine, both 
 armature and coil contribute to the current, the one most 
 when the other gives least, and vice versa. The same 
 advantage is not secured by the ordinary construction. 
 
 We come now to describe the singular peculiarity and 
 merit of Wilde's machine. The current got from the 
 magneto-electric machine is not directly made use of, but is 
 
362 ELECTRICITY. 
 
 employed to generate an electro-magnet some hundreds of times 
 more powerful than the magnetic battery originally employed, 
 by means of which a corresponding increase of electricity 
 may be obtained. This electro-magnet, EE' (fig. 200), forms 
 the lower part of the figure, and by far the most bulky portion 
 of the entire machine. It is of the horseshoe form, E and E' 
 forming the two limbs of it. The core of each of these, 
 shewn by the dotted lines, is formed by a plate of rolled iron, 
 36 inches in height, 26 inches in length, and 1 inch in thick- 
 ness. Each is surrounded by a coil of insulated copper wire 
 (No. 10) 1650 feet long, wound round lengthwise in seven 
 layers. The current has thus, in passing from the insulated 
 binding-screw, r, to the similar screw, /, to make a circuit of 
 3300 feet. Each limb of the electro-magnet is thus a flat reel 
 of covered wire wrapped round a sheet of iron, the rounded 
 ends alone of which are seen in the figure. The upright iron 
 plates are joined above by a bridge, P, built up also of iron- 
 plate, and are fixed below the whole way, along with the 
 iron bars v, v, to the sides of a magnet-cylinder of precisely 
 the same construction as the one already described. The 
 iron framework of the electro-magnet is shewn by the dotted 
 lines. The depth of the bridge is the same as the breadth of 
 the bars, v', v', which are of the same size as the bars, v, v. 
 The various surfaces of juncture in the framework are 
 planed so as to insure perfect metallic contact. The upper 
 and lower machines are in action precisely alike, only the 
 upper magnet is a permanent magnet, and the lower one an 
 electro-magnet. We have the same magnet-cylinder, I, I, the 
 same armature, A, and springs, SS', and the same poles, ZZ' : 
 the size is, however, different ; the calibre of the magnet- 
 cylinder is 7 inches. The diameter of the lower armature 
 gives the name to the machine namely, a 7-inch machine. 
 Figs. 201 and 202 are on the scale of the lower machine (fig. 
 200). The length of wire on the lower armature is 350 feet. 
 It is 35 inches in length, and is made to rotate 1800 times a 
 minute. The cross framework attached at gg to the magnet- 
 cylinder, in which the front journal, /, of the armature rotates 
 (at Q), is shewn in the lower machine (fig. 200). When 
 the machine is in action, both armatures are driven simul- 
 
DYNAMO-MACHINES. 363 
 
 taneously by belts from the same countershaft. For the 
 electric light, the currents conveyed to the springs, S and 
 S', need not be sent in the same direction. In that case, the 
 separation between n and ri is vertical ; and each spring 
 presses against only one ring during the whole revolution, 
 receiving and transmitting each revolution two opposite 
 currents. Oil for the journal and commutator is supplied 
 from the cup C. 
 
 The machine here described is intended for a three-horse- 
 power steam-engine, but more power might be expended on it. 
 A larger engine could drive the smaller armature faster, and 
 thereby cause much more energy to be expended, and more 
 electricity to be induced in turning the lower armature than 
 with a power of three horses. The machine, when worked 
 with a power of three horses, will consume carbon sticks 
 three-eighths of an inch square, and evolve a light of sur- 
 passing brilliancy. With a machine that consumes carbons 
 half an inch square, a light of such intensity is got, that when 
 put on a lofty building it casts shadows from the flames of 
 street-lamps a quarter of a mile distant upon the neighbouring 
 walls. 
 
 It will be observed that one peculiarity t of all the 
 machines hitherto noticed is, that the currents produced 
 by them are alternately in opposite directions, and so 
 necessitate the use of commutators. It remained as a de- 
 sideratum to get a machine which would give continuous 
 currents always in one direction, This was first clearly 
 supplied, although only to a small extent, by the ring 
 armature or transversal electro-magnet of Pacinotti. Paci- 
 notti's machine was primarily intended to be an electro- 
 magnetic one, although it did give continuous currents in one 
 direction when driven the reverse way. 
 
 319. Gramme Machine. It was not, however, till the 
 appearance of the Gramme machine that we could be 
 said to have a really efficient machine for producing con- 
 tinuous currents in one direction without the aid of a 
 commutator. This machine is represented in fig. 203. 
 The peculiarity of this machine rests in its armature, 
 which somewhat resembles the transversal electro-magnet 
 
364 
 
 ELECTRICITY. 
 
 of Pacinotti. It consists of a flat ring of say six inches 
 or more in diameter, made of bundles of iron wire laid 
 side by side. Grasping these bundles are a series of flat 
 
 Fig. 203. 
 
 helices of insulated wire packed close together, sometimes as 
 many as 64 helices being put upon one ring. These helices 
 are all joined together so that a current can flow in the same 
 direction round them all. The junction of each helix with 
 its next neighbour is connected to a thin strip of copper, 
 which is inserted edgeways into a cylinder of insulating 
 material, which passes tightly through the ring. Passing 
 through the centre of this cylinder is the metal rod on which 
 the whole revolves. There are thus as many copper strips as 
 there are helices, and care is taken that none of the grooves 
 containing them communicate, either with each other or with 
 the central axis. The insulated cylinder with its copper 
 strips is turned accurately fair and smooth, so that it presents 
 the appearance of a shaft striped longitudinally, and is such 
 that springs pressing against it, as it revolves, come alternately 
 into contact with a copper strip and with an adjoining in- 
 sulated part. The whole is made to revolve close to, and 
 
DYNAMO-MACHINES. 365 
 
 between the poles of a powerful electro-magnet, these poles 
 being usually extended by having attached to them curved 
 pieces of iron forming parts of a cylinder which, if com- 
 plete, would closely envelop the ring armature. Two wire 
 brushes press against the striped shaft at points opposite to 
 each other, and in a line nearly at right angles to the line 
 joining the poles of the electro-magnet. Attached to these 
 wire brushes are the two terminals from which the current is 
 received when the machine is in action. 
 
 That we may see clearly how it is that the currents pro- 
 duced by this machine are always in one direction, let us 
 suppose that the iron wire core of the armature is fixed, and 
 that the helices are made to revolve around it. This will 
 evidently not alter in the least the actual action of the 
 machine. Manifestly, by induction the iron wire ring will 
 become magnetic, having its south and north poles respec- 
 tively opposite to the north and south poles of the inducing 
 electro-magnet, and having its neutral points at the ends of a 
 diameter at right angles to that joining the poles. Let us 
 also suppose that there is only one helix on the wire ring, and 
 that it can be carried round the ring from a starting position 
 opposite the north pole of the electro-magnet. Obviously, 
 at starting, the helix surrounds the south pole of the iron 
 ring, and in one half-revolution it passes from a south pole 
 through a neutral point to a north pole, while in the second 
 half-revolution it passes from a north pole through a neutral 
 point to a south pole. Its motion may thus be accurately 
 represented by supposing it to slide along a straight bar 
 magnet from its south pole to its north, then to be turned 
 round and sent back again, from the north pole to the south, 
 with the same side in front on the return journey as was fore- 
 most at first. A little consideration will shew that in these 
 circumstances the current induced in the helix always flows 
 in one direction through a circuit joining its ends. 
 
 In the Gramme machine, no extraneous source of electricity 
 is needed to sustain the current in the electro-magnet. This 
 is done by the produced current being made to circulate 
 through the coils of the electro-magnet. The small amount 
 of residual magnetism is sufficient to start a feeble current. 
 
366 ELECTRICITY. 
 
 This going round the electro-magnet, increases its inducing 
 power, which again induces a stronger current on the arma- 
 ture, and this, in its turn, strengthens the electro-magnets. 
 In this way the effect increases at each turn of the armature, 
 according to the compound interest law, and at a rate, when 
 the machine is going rapidly, which cannot be less than 600 
 or 700 per cent, per second. This explains why after a few 
 turns the machine becomes so difficult to drive, and why 
 there is hardly any limit to the strength of the current that 
 can be produced by it, other than the amount of driving- 
 power which can be employed. 
 
 Dynamo-machines for producing current electricity have 
 been largely applied to useful every-day purposes. We have 
 only to instance their application to produce the electric light 
 which has now become so extensive. Machines of this kind 
 have also been most successfully employed for purposes of 
 electro-metallurgy. 
 
 Many other forms of dynamo-machines are in use at the 
 present day, all depending essentially on the principles which 
 have already been explained. The chief of these are the 
 Siemens machine, the Brush machine, the Biirgin machine, 
 and the large machine recently invented by Edison. 
 
 Electro-magnetic Machines, or Electromotors. 
 
 320. The function of these machines is to convert current 
 electricity into mechanical work, and hence they may be 
 regarded as the converse of the magneto-electric machines. 
 In fact, almost all magneto- electric machines may be used as 
 electromotors, by sending a powerful current from an external 
 source through them. The forms in which they occur are 
 exceedingly various, but a description of the simple apparatus 
 illustrated in fig. 204, will suffice to explain their principle 
 of working. NS is a fixed permanent magnet (it would do 
 equally well an electro-magnet) ; the electro-magnet, ns, is 
 fixed to the axis ee, and the ends of the coil are soldered 
 to the ring c encircling a projection on the axis. The ring 
 has two slits in it, dividing it into two halves, and filled 
 with a non-conducting material, so that the halves are in- 
 sulated from each other. Pressing on this broken ring, on 
 
ELECTRO-MAGNETIC MACHINES. 
 
 367 
 
 opposite sides, are two springs, a and b, which proceed from 
 the two binding-screws into which the wires, + and -, 
 from the battery are fixed. In the position shewn in the 
 figure, the current is supposed to pass along a, to the half of 
 
 Fig. 204. 
 
 the ring in connection with the end /, of the coil, to go 
 through the coil, to pass by g to the other half of the ring, 
 and to pass along 6, in . its return to the battery. The 
 magnetism induced by the current in the electro-magnet, 
 makes s a south and n a north pole, by virtue of which N 
 attracts s, and S attracts n. By this double attraction, ns is 
 brought into a line with NS, where it would remain, did not 
 just then the springs pass to the other halves of the ring, 
 and reverse the current, making s a north, and n a south pole. 
 Repulsion between the like poles instantly ensues, and ns 
 is driven onwards through a quarter revolution, and then 
 attraction as before between unlike poles takes it through 
 another quarter, to place it once more axially. A perpetual 
 rotation is in this way kept up. The manner in which a 
 constant rotary motion may be obtained by electro-magnetism 
 
368 ELECTRICITY. 
 
 being understood, it is easy to conceive how it may be 
 adapted to the discharge of regular work. Powerful 
 machines of this kind have been made with a view to 
 supplant the steam-engine ; but such attempts, both in 
 respect of economy and constancy, have proved utter failures. 
 It has been found that zinc cannot compete with coal as a 
 source of mechanical action. 
 
 Jacobi was the first (1834)", to construct such machines. In 
 1838 he constructed a machine of f of a horse-power, by 
 means of which he propelled a small boat on the Neva. 
 
 When a large quantity of mechanical work is required, the 
 electromotors commonly used are the Gramme or Siemens 
 machines, which are found to be perfectly reversible. 
 
 321. Electrical Transmission of Power. Seeing that dynamo- 
 machines and electromotors are now in such a state of 
 efficiency, it becomes an important practical question how far 
 they can be utilised as a means of transmitting power to a 
 distance from one point to another. Such an idea must have 
 occurred to many minds, but perhaps the first public 
 expression of it as a practical application of electricity is 
 due to Professor Blyth, who in 1872 wrote as follows : 
 'Magneto-electric machines might be employed to utilise 
 the water power, at present running to waste, of mountain 
 torrents, by first employing these torrents to generate current 
 electricity by means of magneto-electric machines, and then 
 transmitting that current by means of wires to drive an 
 electro-magnetic engine wherever it was wanted.' The idea has 
 taken practical shape in the hands of Sir William Armstrong 
 and Siemens ; and the power of distant waterfalls has been 
 transmitted and made to drive sawmills, and do other useful 
 work. Quite recently also, Siemens has shewn a tramway- 
 car driven by one of his machines, the current being got 
 from a similar machine worked by a stationary steam- 
 engine in the neighbourhood of the tramway route. In 
 this case, the drawing current was conducted to the electro- 
 motor placed below the car, either by means of the rails, or by 
 means of conductors having sliding contact with two parallel 
 conductors placed along the route, to which the current from 
 the dynamo-machine was led, 
 
CHAPTEE XXV. 
 ELECTRIC TELEGRAPH. 
 
 322. The electric telegraph, like every other telegraph, aims 
 at producing intelligible signals at a distance. The etymology 
 of the word (tele, far off, and grapho, I write) implies that it 
 is an instrument for writing at a distance ; but it has come to 
 signify any means of conveying intelligence other than by 
 voice or writing. The idea of speed is also implied telegraphs 
 being seldom, if ever, employed where they cannot transmit 
 intelligence at a much quicker rate than can be done by the 
 ordinary means of transit. There are three agents, which, 
 from the rapidity of their propagation, are employed for 
 telegraphing sound, light, and electricity. Sounds, such as 
 those of bells, guns, &c., form a convenient means of sending 
 a single message through short distances. Light and electri- 
 city immeasurably exceed sound as ready, rapid, and certain 
 means of telegraphing through long distances. Light, though 
 an extremely rapid, is by no means a docile agent. It pro- 
 ceeds in straight lines, and will not bend round the ball of 
 the earth, or inequalities on its surface. The semaphore, 
 which was an ocular telegraph, and the only good one before 
 the electric telegraph, illustrated this. Towers had to be 
 erected in prominent positions, within sight of each other, 
 and the signals, which were made by arms on the top of them, 
 had to be retransmitted at every station. A large and well- 
 trained staff was necessary to observe and transmit, and 
 withal the work was slowly done. In foggy weather, more- 
 over, the semaphore was useless. Electricity, which rivals 
 light in speed, is most docile and trustworthy as a telegraphic 
 agent. It silently wends its way in all weathers, over plain 
 and mountain, across sea and land, and delivers its message 
 in the office or parlour almost at the precise instant it was sent. 
 
 The various forms of electric telegraphs in general use are 
 electro-magnetic. The signals are given by the deflection of 
 a needle to the right or left, or by mechanism connected with 
 the armature of an electro-magnet, which sways to and fro 
 under the action of the magnet and a counter spring, or 
 
370 ELECTRICITY. 
 
 between two opposite electro- magnets. Electro-chemical 
 telegraphs have also been designed, but they have never 
 come into permanent use. Electric telegraphs of all classes 
 are of two kinds those which merely give passing signals to 
 the observer or listener, and those which permanently record 
 their signals ; the former may be called signalling, the latter 
 recording telegraphs. The number of inventions connected 
 with the electric telegraph is almost endless, and would 
 engross a long series of volumes for their description. We 
 shall here content ourselves with giving a mere outline of the 
 working of the telegraph at present existing on most lines. 
 The forms most in use everywhere at present are Morse's 
 Telegraph and Cooke and Wheatstone's Needle Telegraph. 
 For private use, some form of the magneto-electric dial 
 telegraph is employed. In point of simplicity and certainty, 
 Morse's system can scarcely be exceeded, and even as regards 
 speed it stands equal, or nearly so, to the most rapid 
 recorders. We shall therefore give an account of the general 
 arrangements of a telegraph chiefly on Morse's system. 
 
 323. Morse's Recording Instrument, or as it is shortly called, 
 the ' Morse ' or ' Register,' is shewn in fig. 205. L is the line- 
 wire, and E the earth-wire, conveying the current from the 
 distant station. The current thus sent traverses the coils of 
 the electro-magnet, MM', the armature, A, of which is in 
 consequence drawn down. A is attached to the lever II', 
 moving round the axis k. By the attraction of A, the end V 
 is lowered, and brought against the stud n. The armature 
 must not touch the soft iron of the electro-magnet on being 
 drawn down, for if it did it would stick, and would not be 
 instantly released when the current ceases. When the end 
 V is lowered, the end I is raised ; IV t at its inner end, carries 
 a steel point or style, p, which by the upward motion is 
 brought against a strip of paper, PP', carried towards P / by 
 the rollers rr', set in motion by clock-work, C, quite inde- 
 pendently of electricity. The clock-work is liberated or 
 stopped by the switch S. The paper is supplied from a large 
 roll or bobbin, above the instrument, which turns round as 
 the rollers demand. So long as the style is elevated, the 
 paper strip is made by the clock-work to rub against it. A 
 
ELECTRIC TELEGRAPH. 
 
 371 
 
 line is thus embossed on its upper surface. To facilitate the 
 doing of this, there is a groove in the upper roller, opposite 
 the style. When the current from the distant station ceases, 
 the lever IV is pulled back to its original position by the 
 
 Fig. 205. 
 
 spring s, and the style falls away from the paper. To 
 prevent it falling too far, another stud, m, lies on the other 
 side of the axis. When the circuit is again closed, the style 
 once more marks the paper, and thus the lever keeps oscil- 
 lating under the opposing actions of the magnetism developed 
 by the transmitted current, and the elasticity of the spring s. 
 The time that the style remains elevated, determines the 
 kind of mark on the paper. If it is nearly momentary, a 
 dot is imprinted ; for a longer time, a dash. We have thus 
 the combinations of an alphabet in the combination of dots 
 and dashes. The following is the usual Morse Alphabet : 
 
 S 
 
 T 
 
 U 
 
 V 
 
 W 
 
 X 
 
 Y 
 
 Z 
 
 Thus A is a dot and a dash ; B, a dash and three dots, &c. 
 x 
 
372 ELECTRICITY. 
 
 The alphabet is so arranged that those letters occurring most 
 frequently are more easily signalled ; thus, E is one dot ; 
 T, one dash. An expert telegrapher can transmit from thirty 
 'to forty words a minute by this instrument on a land-line of 
 between 200 and 300 miles. Several modifications of Morse's 
 telegraph have been made, the principal of which is to 
 substitute ink marking for embossing. The beautiful instru- 
 ments of the Siemens and Halske are of this kind. 
 
 A clerk that has been well accustomed to a Morse telegraph, 
 in transcribing, seldom looks to the paper. The mere click- 
 ing of the lever becomes a language perfectly intelligible to 
 him. He need therefore only look to the record when he 
 may have heard indistinctly. Sir Charles Bright does away 
 with the recording instrument altogether, and substitutes two 
 bells, one muffled, the other clear, sounded by a hammer 
 oscillating between them. The bells speak a telegraphic lan- 
 guage as quick as the clerk can write. Recording instruments 
 are generally considered preferable to instruments which 
 merely signal, as they fix any fault of transmission or copy- 
 ing on the party at fault. Acoustic signalling, again, is pre- 
 ferable to ocular signalling, as a person can hear and write 
 much more easily than see and write. 
 
 324. Transmitting Key. Let us now transfer our attention 
 to the distant station, to see how the current is transmitted 
 from it. This is done by the transmitting key shewn in fig. 206. 
 A brass lever, II, moves round the axis A. On opposite sides 
 
 of the axis two 
 nipples of platinum, 
 m, n, are soldered to 
 its lower sides. The 
 nipple m is called 
 the hammer. Below 
 n is the stop anvil, fe, 
 /i cNs - tipped with platinum, 
 
 Fig. 206. which is in connec- 
 
 tion with the earth- 
 wire E. Below the hammer, m, lies the anvil a, the nipple 
 of which is likewise of platinum ; a is connected by the 
 wire C with one of the poles of the sending battery, gene- 
 
ELECTRIC TELEGRAPH. 373 
 
 rally the copper pole. When the lever is left to itself, n and 
 6 are in contact under the force of the spring s. When the 
 hand presses on the ebonite (insulating) handle H, contact is 
 broken at n and 6, and established at m and a. Three wires 
 are in connection with the key, E and C just named, and L, 
 the line-wire from the distant station, connected with the axis 
 pillar, and therefore with the lever. When the key is in the 
 receiving position, that shewn in the figure, the current from 
 the sending station takes the route L, A, I, n, &, E, the Morse, 
 then to earth. When H is pressed down, the key is in the 
 sending position, and transmits the battery current by C, a, 
 m, A, L, to the distant station. The play of the anvil and 
 hammer need not be more than T \th of an inch. This is 
 more than sufficient for completely breaking the current, and 
 it allows of speedy manipulation. 
 
 325. The Battery. The batteries employed are in this 
 country almost universally Daniell's. Constancy and certainty 
 of action is what is most wanted in the battery, and these 
 Daniell's battery yields. In Germany, Bunsen's battery is 
 also used, charged with diluted sulphuric acid, the carbon 
 being immersed in a mixture of 1 of acid to 10 of water, and 
 the zinc in one of 1 to 20. When batteries have to be moved 
 about much, sand is put in to keep the liquid from spilling. 
 The number of cells employed varies with the distance, the 
 insulation of the line, and the delicacy of the instruments. 
 The register, as afterwards mentioned, is seldom worked 
 directly by the transmitted current, but by relay. To work 
 a relay with good insulation, 60 Daniell's cells will suffice 
 for a distance of 300 miles. For less distances, less of course 
 will suffice. For short circuits, where the resistance is small 
 and current strong, small cells soon exhaust themselves ; 
 large cells therefore must be used to maintain the supply. 
 Magneto-electricity is also employed as a source of the 
 current. This answers well on short circuits, or for private 
 telegraphs, but experience has proved that the galvanic 
 battery is by far the most advantageous source of electricity 
 for extensive telegraphic work. 
 
 326. How Two Stations are connected together. The manner 
 in which two stations are 'joined up ' on Morse's system is 
 
374 
 
 ELECTRICITY. 
 
 shewn in fig. 207. B and Bj are the batteries at the stations 
 S, Sj ; k, tf are the transmitting keys ; n, ri, the registers ; 
 g, </, the galvanometers ; LL the line-wire insulated on posts ; 
 P, P 1? the earth-plates. When the key k, at the station S, 
 which is here represented as the sending station, is depressed, 
 the current from the battery B takes the following course. 
 From the copper pole C, of the battery B, it goes to the anvil 
 of Jc, passes through k to the galvanometer g, which having 
 
 Fig. 207. 
 
 traversed, it goes into the line LL to the receiving station S 1} 
 traverses the galvanometer, the key k', the coils of the 
 register n' ; thence it goes * to earth ' at the plate P ly returns 
 by the ground to P at the sending station, and thus finally 
 reaches the zinc pole Z of the battery B. At station S, 6 and 
 n are out of circuit ; and at S 1? 6' and battery Bj are out of 
 circuit ; n is thrown out of circuit, because its coil offers a 
 resistance equal to several miles of the line-wire, and it is 
 requisite to keep down the resistance to the minimum. If it 
 were in circuit, both registers could print simultaneously, but 
 that is not necessary, one record at the receiving station 
 being enough. The sender would thus have no idea as to 
 whether his message had told or not, did not the motions of 
 the needle of the galvanometer, g, reveal the currents put in 
 circuit. The galvanometer also shews the presence of earth- 
 currents on the line. If k were left to itself, and k' depressed, 
 the station Sj^ would then be the sending and S the receiving 
 station, and the connections would be exactly as shewn in the 
 figure, only at opposite stations. 
 
ELECTRIC TELEGRAPH. 375 
 
 Suppose the clerk at S wishes to telegraph to S 1} he 
 depresses the key k several times, so as to send a series of 
 dots and dashes giving the name of the station. The atten- 
 tion of S t is first arrested by the clinking of the armature of 
 the Morse. He thereupon turns the switch S (fig. 203), and 
 sets the clock-work in motion, and sends back to S that he is 
 ready, and the printing thereupon begins. When both keys 
 are depressed, the whole circuit is broken, so that when both 
 sender and receiver have their hands on their respective keys, 
 no message can be sent. One might fancy that confusion 
 would arise from cross messages, but clerks soon get over this 
 inconvenience, and communicate back and forward with 
 perfect facility. There is a code of working signals to indicate 
 the kind of message, 'repeat,' 'understand,' &c., besides 
 numerous recognised contractions. To arrest the attention of 
 attendants, the current is sometimes made to ring an alarum 
 bell. 
 
 327. The Line. Telegraphic stations must be united by one 
 insulated wire, carried over land, under ground, or under the 
 sea. The insulation of land-lines is insured by attaching the 
 wires to insulators fixed on posts some 20 feet high. The posts 
 are placed at distances corresponding to the number of wires 
 they have to carry. A distance of 80 yards is {he ordinary 
 distance for posts sustaining several wires, and 150 yards for 
 those only supporting one. Insulators are of all shapes. 
 Porcelain, though a better conductor than glass, is not so apt 
 to attract moisture, and is the substance generally employed 
 for them. The insulator known as Andrew's 
 Insulator, shewn in section (fig. 208), is said 
 to be very effectual. A bolt of iron, I, fixed 
 to the cross-beam, w, of the telegraphic pole, 
 is cemented into the ebonite cup or bell ee, 
 which in turn is cemented into the porcelain 
 bell pp. The porcelain bell acts as an umbrella 
 to keep the wood to which it is fixed dry and 
 insulating ; that failing, the inside of the two 
 cups is likely to remain dry and maintain Fig. 2os. 
 insulation. The line- wire is kept fixed by 
 binding wire into the groove a. The electricity has thus to 
 
376 ELECTRICITY. 
 
 travel over the outside and inside of both cups before it 
 reaches the iron bolt, which is also coated with ebonite. 
 Such insulators as the one described cannot be used in rail- 
 way tunnels, as they get coated over inside and out with 
 engine smoke, which, being conducting, quite impairs their 
 efficiency. The leakage in a long line, notwithstanding the 
 best insulation, is- considerable. The loss at each post is 
 insignificant, but when hundreds or thousands are taken into 
 account it becomes decided, so that merely a traction of the 
 total current that sets out reaches the earth at the distant 
 station. In rainy, and more especially in misty weather, the 
 insulation suffers much. 
 
 The wire most employed for telegraphic circuits is No. 8 
 (|th of an inch), but some companies are beginning to use 
 No. 4 wire on some of their long trunk lines. 
 
 328. A Submarine Line is made by a cable. The core of the 
 cable consists of one wire, or a strand of several wires of 
 copper, as pure as can be got in the market. One solid wire 
 is preferable to a strand of the same diameter in point of con- 
 ducting power ; but a strand is surer ; for when one wire is 
 broken at any point, the others still remain to conduct the 
 current ; there is no ' breach of continuity.' When the one 
 solid wire gets broken, which not unfrequently occurs with- 
 out being visible outside, the cable becomes useless. The 
 strand of wire is generally laid up in Chatterton's com- 
 pound, consisting of gutta-percha and resinous substances. 
 The interstices between the wires are thus filled up, and 
 this makes the cable solid throughout. It not unfrequently 
 happens, when this precaution is not taken, that water, under 
 the great pressure of ocean depths, becomes injected into 
 them. The strand thus laid up, is now included in one or 
 more coatings of gutta-percha, which acts as the insulating 
 protection for the wire. Chatterton's compound is generally 
 put between the layers of gutta-percha. The whole is 
 finally included in a sheathing of iron wire, laid on spirally, 
 to give the cable sufficient strength to withstand the strain 
 of paying out, or that to which it may be subjected by the 
 inequalities of the ocean bed. Between the iron sheathing 
 and the gutta-percha, a layer of tarred yarn is put, which acts 
 
ELECTRIC TELEGRAPH. 37? 
 
 as" a padding between the two, and improves the insulation 
 of the cable. Not unfrequently the iron wire of the sheath- 
 ing is also protected from corrosion by tarred hemp. Fig. 
 209 (full size) shews the con- 
 struction of the Malta and 
 Alexandria cable, which is 1330 
 nautical miles long. The differ- 
 ent layers are so far peeled off 
 to shew the construction. C is 
 a strand of seven copper wires, 
 laid in Chatterton's compound ; 
 G, three layers of gutta-percha, Fig. 209. 
 
 with Chatterton's compound 
 
 between each ; H, tarred yarn ; and I, the eighteen wires 
 constituting the sheathing. The diameter out in the sea is 
 0'85 of an inch. Near the shore, the sheathing is made 
 much stronger, to meet the danger of accident from the 
 dragging of anchors. 
 
 Considerable dispute has arisen as to the best material for 
 insulating marine cables. India-rubber and gutta-percha are 
 the two rival substances. It may be said in favour of gutta- 
 percha that not one yard of it, when laid, has decayed ; and 
 that, under ocean pressures, as proved by the Atlantic cable of 
 1865, its insulating power decidedly improves. In favour of 
 well masticated india-rubber, it is urged that cables, alike in 
 other respects, will, when coated with it instead of gutta- 
 percha, be capable of sending twice the number of words per 
 minute, the specific inductive capacity being so much greater 
 for the latter than for the former substance. On the other 
 hand, india-rubber is not so trustworthy in point of durability, 
 some specimens of it having become treacly after immersion 
 for some time in the sea. 
 
 329. The Earth. Two wires are not necessary to connect 
 two telegraphic stations, as might be supposed. One wire is 
 quite sufficient, provided its terminations be formed by large 
 plates sunk in the ground, or something equivalent. The 
 plates are generally of copper, and should not offer a surface 
 less than twenty square feet, and they must be buried so deep 
 that the earth about them never gets dry. The gas and 
 
378 ELECTRICITY. 
 
 water pipes in a town make an excellent 'earth' (earth 
 connection). The great object in an 'earth' is to put the 
 whole ground in the neighbourhood in connection with the 
 battery pole or line-wire, and much the same precautions 
 must be taken in making an earth for a telegraph as 
 for a lightning-conductor. If the earth is not good, the 
 current, instead of taking the ground as a passage to the 
 distant station, runs into other wires connected with the 
 plate and leading to where the ' earth ' is good. When the 
 'earths' are good, the current passes through the earth 
 between the two stations, no matter what be the nature of 
 the country it has to pass, plain or mountain, sea or land. 
 The earth resistance to the current, compared with that of a 
 long line, is next to nothing. The earth not only serves the 
 purpose of a second wire, but of one so thick that its 
 resistance may be left out of account, and thus halves the 
 resistance of the whole circuit. It is a question whether the 
 current actually travels between the two stations, or whether 
 an equal amount of opposite electricity becomes simultan- 
 eously lost at each. This question cannot be decided, as the 
 electric conditions in either case are identical. In conducting 
 power for equal dimensions, the earth stands much inferior 
 to the wire ; but then its thickness, so to speak, is indefinitely 
 greater, and hence its superior conducting power on the 
 whole. One good 'earth' serves for all the circuits of a 
 telegraphic station. 
 
 330. Return Current Inductive Embarrassment. When the 
 line- wire at a distant station is 'cut' (insulated or discon- 
 nected with the ground), and is placed in connection with 
 one of the poles of a battery, the other pole of which is to 
 earth, at the instant in which the connection is made, a 
 current flows into the wire, and if the insulation of the line 
 be perfect, almost instantly ceases. The needle of the 
 galvanometer makes a sudden deflection, and then returns 
 to its position of rest. If now, at one turn of a commutator, 
 the battery connection be cut off, and the line be put to 
 earth, the needle deflects momentarily in the opposite way, 
 and the charge given to the wire returns and goes to earth. 
 This flowing back again of the charge is called the return 
 
ELECTRIC TELEGRAPH. 379 
 
 current. In land-lines the return current is very slight, in 
 submarine cables it is very marked. The return current 
 shews that a telegraphic line may be charged statically, just 
 like the insulated balls, cylinders, &c., illustrating frictional 
 electricity. A line of telegraph may be looked upon as a 
 Leyden jar, the wire as the inner coating, the air or gutta- 
 percha as the glass or dielectric, and the earth or sea as the 
 outer coating. A coil of submarine cable, immersed in a 
 trough of water when the core is insulated, may be charged 
 and discharged exactly as a Leyden jar, the water being the 
 outer coating. The return current is most marked in long 
 lines. In such it is not necessary to ' cut ' the wire, the 
 great resistance of the long wire being equivalent to partial 
 insulation ; the return current being, however, much smaller 
 in extent. 
 
 The statical charge, of which a line of telegraph is thus 
 capable, shews that the electric force not only tends to pro- 
 pagate itself longitudinally, but laterally. The effect of 
 lateral induction is to retard the time of delivery of a signal, 
 and to prolong it, so that, although it is a momentary signal 
 at starting, it becomes a prolonged signal at its destination. 
 Wheatstone's calculation gives a velocity of 288,000 miles 
 per second for electric discharge. If signals were propa- 
 gated at this rate, the time elapsing between the sending and 
 delivering of a current, even on a line extending over one- 
 half the circumference of the globe, would be inappreciable. 
 But in aerial lines of land telegraphs, even only a few 
 hundred miles in length, there is evidence that electricity 
 does not propagate itself at anything like that speed, and in 
 submarine cables the velocity scarcely reaches thousands of 
 miles per second. The mere slowing of the message would 
 not matter so much, provided the signals, when they reached 
 their destination, were told out as they were sent. But they 
 are not. Each signal at the receiving station takes a longer 
 time to leave the line than it did to enter it. Hence, in a 
 very long land-line, or in a cable, if the sender transmitted 
 at the same rate as he does in short circuits, the signals 
 would run into each other at the receiving station, and be 
 undistinguishable. Time must be given to allow each signal 
 
380 ELECTRICITY. 
 
 to ooze out of the cable before another is sent. The effects 
 of lateral induction on the transmission of telegraphic 
 currents constitute what is termed inductive embarrass- 
 ment. 
 
 According to Sir William Thomson, the maximum speed 
 attainable on an aerial land-line of 2000 nautical miles in 
 length, and consisting of an iron wire one-fourth of an inch 
 in diameter, would be 20 words per minute. The same 
 authority has established that the retardation increases with 
 the square of the length of the line. Accordingly, on a line 
 1000 miles in length, the number of words would be 80 ; on 
 one 500 miles, 320 ; and so on. Direct lines are not worked 
 for distances greater than 1000 miles, and very seldom even 
 for the half of that distance. The maximum speed of tele- 
 graphing on short circuits has been 50 words ; so that on a 
 line 1000 miles in length and one-fourth of an inch thick, 
 there is still a wide margin before the lateral induction 
 would interfere. Most land-lines, however, are not more 
 than one-eighth of an inch thick, and in them the embarrass- 
 ment would be felt nearly four times as much as in the line 
 just mentioned. On a line 1000 miles in extent of No. 8 
 wire, it would be advisable to break the circuit half-way, and 
 re- send at the mid- station by translation. The whole would 
 thus be worked as two circuits of 500 miles, and the speed 
 of signalling could be four times increased. The maximum 
 speed of signalling through the 2000 miles of the Atlantic 
 telegraph of 1858 was two and a half words a minute. The 
 copper core had a conducting power somewhat higher than 
 a No. 4 iron wire. According to the law of squares, if the 
 cable had been 1000 miles, the rate of signalling might have 
 been increased to 10 words ; if 500 miles, 40 words ; and so 
 on. If the ratio of the thickness of the core to that of the 
 insulating coating be kept the same, the number of words 
 that can be sent varies as the amount of material employed, 
 or as the square of the diameter of the cable. Thus, if a 
 cable be of the same make and of equal length as another, 
 but twice as thick, four times as many words may be sent 
 by it. The thickening of the core alone is not all gain in 
 the way of lessening embarrassment, for while the conduct- 
 
ELECTRIC TELEGRAPH. 38l 
 
 ing power of the core increases with, its section, the lateral 
 induction increases with its circumference. 
 
 Numerous explanations have been given of inductive 
 embarrassment. We may suppose the charge at starting to 
 have two inductive channels to reach the ground, one through 
 the core to the further end of the cable, and the other through 
 the gutta-percha. Electricity, when it has two channels, acts 
 through each in the proportion of the facility offered it. If 
 the gutta-percha were thick and the core short, the facility 
 offered by the latter would be indefinitely greater than that 
 offered by the former. There would be then no lateral in- 
 duction, for the electricity would keep to the core. But when, 
 as in long cables, it has some hundreds of miles of core and a 
 quarter of an inch of gutta-percha to work through, the rival 
 channels stand more nearly on a par. At each point the 
 part of the electricity sent in to the cable acts inductively 
 through the gutta-percha, and the rest acts in the line of the 
 core. This last is subject to this diversion as it moves along ; 
 hence, if the cable be long, the whole is for the instant 
 absorbed in charging the cable statically, and possibly only 
 a part at a time. Such being the case, the further progress 
 of discharge is effected not immediately by the force of the 
 transmitting battery, but by the polarity induced* by it in the 
 particles of the dielectric gutta-percha. The effect is some- 
 what the same as would be experienced in sending a charge 
 of water through a pipe filled with the same, whose sides, 
 though water-tight, were elastic. If the pipe be long and 
 narrow, and the friction of the water against the sides con- 
 sequently great, on the charge being injected, the pipe on the 
 sending side yields, and the further transmission of the charge 
 is effected by the elastic force of the sides. The charge travels 
 as a wave to the other end, and its delivery is thereby retarded 
 and modified. This temporary yielding resembles the 
 inductive diversion of the charge to the gutta-percha. 
 
 In aerial lines the lateral channel, the air, which is some 
 twenty feet thick between the wire and the ground, offers 
 much less facility for inductive action than in gutta-percha 
 cables. The lateral induction is consequently very much less. 
 In insulated subterranean lines it is nearly as much as in 
 
382 ELECTRICITY. 
 
 submarine cables. They are consequently never used except 
 for short distances, where they are unavoidable. 
 
 There is as yet no way of obviating lateral induction in 
 telegraphic cables, except a thick core and a thick layer of 
 insulating material. This is tantamount to saying there is 
 no cure at all ; for in very long lines, where it is most felt, 
 a thick cable cannot, from mechanical difficulties, be laid. 
 There are several ways, however, of diminishing it. A 
 material, such as india-rubber, whose specific inductive 
 capacity is low, lessens the evil considerably. The tarred 
 hemp used in cables also reduces the lateral induction. 
 Some have suggested the use of a double wire in the cable, 
 the second wire supplying the place of the earth. This has, 
 however, been found to aggravate instead of lessening the evil. 
 The use of electricity of high tension, such as that of induction 
 coils, has also been tried. That such passes with greater 
 despatch may be open to doubt, and that it is dangerous in 
 causing the charge to puncture the gutta-percha, and thereby 
 destroy the cable, is highly probable. A transmitting key 
 was used in the Atlantic expedition of 1865, which had a 
 double action. It first placed the cable in connection with 
 one of the poles of the battery, and then with the ground. 
 The first connection charged the cable, the second allowed 
 discharge to take place at both ends of it. By this key the 
 number of words was increased by one-half. 
 
 The insulation of submarine cables is almost perfect, so 
 that inductive embarrassment must not be confounded with 
 leakage. The insulation of the Atlantic cable of 1865 was so 
 perfect, that when ' cut' and charged, it took 15 minutes to 
 fall from charge to half-charge. 
 
 331. Earth Currents. These are very unwelcome visitors in 
 telegraphic oflices. They arise from different parts of the 
 earth, being, from some unknown cause, at different poten- 
 tials. They flow sometimes in one direction, sometimes in 
 another, change rapidly, and are frequently so strong as to 
 render the line for the time quite useless. They occur 
 simultaneously with magnetic storms. The famous magnetic 
 storm that raged on August 2, 1865, at the same time that the 
 Atlantic cable ceased to act, was accompanied by earth currents 
 
ELECTRIC TELEGRAPH. 383 
 
 so strong that the Astronomer-royal considered it impossible, 
 even if the cable had been perfect, to have signalled through 
 it. One remedy for earth currents is to do away with 
 the earth circuit, and put two wires to the same place in one 
 circuit. Although the earth current runs equally strong in 
 both, the two wires bring it to opposite ends of the instru- 
 ments at the stations, and its effect is thereby neutralised. 
 This, of course, can only be done where two wires exist. 
 Another remedy is to use condensers, and work with an 
 interrupted circuit. Little or nothing is as yet known of the 
 laws regulating such currents. 
 
 332. Relay. Hitherto we have supposed that the record- 
 ing instrument of Morse is worked directly by the line 
 current. This is only done on short circuits, generally 
 less than 50 miles. On long circuits, direct working could 
 only be accomplished by an enormous sending battery. The 
 loss by leakage on the way is very considerable, so that a 
 current strong at starting loses greatly before it reaches the 
 station intended ; besides, the leakage becomes all the greater 
 the greater the number of cells employed, or the greater the 
 tension of the battery. It is found a much better arrangement 
 to get the ' Morse' worked by a local current, which may be 
 made as strong as requisite without any loss, and'to include a 
 very delicate instrument in the line circuit, which has only to 
 make or break the local circuit. Such an instrument is 
 called a relay, the principle of the action of which is shewn 
 in fig. 210. Instead of the electro-magnet of the register 
 being in the line circuit, the electro-magnet, E, of the relay 
 is included. The coil is long, and of thin wire, and a very 
 faint current is sufficient to develop magnetism in the core. 
 The line current passes through the coils of E just as it 
 is represented doing through that of the Morse in fig. 205. 
 The armature of the relay, A, is attached to a lever, ee', 
 moving round the axis a. When a current is sent through 
 the coil, the lever is drawn down, and the end e' rests on the 
 screw S. When there is no current, the elasticity of the 
 spring s brings it back against the screw S'. The spring, s, 
 is so adjusted that the play of ee' may be made as easy or 
 stiff as the strength of the line current requires. The 
 
384 
 
 ELECTRICITY. 
 
 Fig. 210. 
 
 pillars N and P are connected with the poles of the local 
 battery. The metal spring s places the lever ee r in conducting 
 connection with P. The poles of the battery may therefore 
 
 be taken to be the 
 screw S, and the end 
 e' of the lever. When 
 these are in contact, 
 the local current flows, 
 and it stops when e' is 
 brought back against 
 the insulated screw S'. 
 The Morse is included 
 in the local circuit. 
 When a current comes 
 from the sending sta- 
 tion, the armature, A, 
 
 is attracted, e! falls on S, the local circuit is closed, and the 
 Morse begins to print. When the current ceases, e' falls on 
 S', and the style of the Morse is withdrawn from the paper. 
 The effect is thus the same as if the line current printed, and 
 not the local current. By this means, a current that would 
 have no effect on the Morse, can complete the local circuit, 
 and print most legibly. 
 
 333. How several Stations are connected in one Circuit. - 
 This is effected in three ways by an open circuit, by a closed 
 circuit, and by translation. In all of these, each station may 
 telegraph simultaneously to all the stations in the circuit, and 
 if the message concerns them all, a record may be printed at 
 each station. When a station wishes to telegraph to another, 
 it keeps signalling the name till the station in question signals 
 back that he is ready. The others, rinding that the message 
 does not concern them, leave the two concerned in possession 
 of the circuit. 
 
 The arrangement of an intermediate station in an open 
 circuit is shewn in fig. 211. L^ and L 2 are the wires from 
 the terminal stations ; E is the relay ; the rest mean the 
 same as in fig. 207. The station is represented as receiving. 
 The line current passes through the key, the relay R, and 
 on to L 2 . The relay sets the local battery and the 
 
ELECTRIC TELEGRAPH. 
 
 385 
 
 register in operation. The line current is brought into the 
 station, and led out without being affected. Electrically, it 
 is the same as if it had gone on in the air direct from L 
 to L 2 . When the station sends, 
 the key is depressed. The cur- 
 rent goes from into the line 
 L 1? is earthed at the one ter- 
 minal station, leaves the earth 
 at the other, and returns by Z 
 to L 2 . The battery here has 
 no 'earth/ as at the terminal 
 stations, the arrangement of Fig. 211. 
 
 which is as in fig. 207. An 
 
 'earth,' however, is generally put at each station, so that 
 it may be worked as a terminal station if required. R at 
 sending is out of circuit. According to this plan, every 
 station must have a battery as strong as the terminal 
 stations. In the closed circuit, no battery is needed at 
 the intermediate station. If the battery and its connections 
 be removed, fig. 211 gives the arrangement in a closed cir- 
 cuit. The battery may be placed only at one terminal 
 station, or it may be divided into two, and a half put at each 
 end both, however, being joined up to act with, not against 
 each other. The circuit is closed when no one operates, 
 so that a current constantly flows. The keys breaking the 
 connections stop it for the time. The relays act negatively, 
 making the Morse print when there is no line current, and be 
 at rest when it flows. If S' in the relay (fig. 210) were unin- 
 sulated, and S insulated, it would act in a closed circuit. The 
 advantage of the closed circuit is, that the batteries which 
 require considerable attention are confined to the terminal 
 stations, where they can be best cared for. Besides, little or 
 no adjustment is needed for the relays. In the closed circuit, 
 all the relays are in circuit at once. Open and closed circuits 
 are used in lines where a number of smaller towns are joined 
 together, the business of all of them being no more than 
 sufficient to keep the line working. They are for short 
 distances, seldom more than 200 or 300 miles. 
 
 When two stations, say 500 miles apart, are to be connected 
 
386 
 
 ELECTRICITY. 
 
 by telegraph, it is seldom done by a direct line, it being 
 found more efficient to transmit to a half-way station, and 
 thence to retransmit to the end one. The retransmission is 
 effected not by manipulative skill, but by mechanical contriv- 
 ance, so that, while the half-way station may read the message 
 sent, no time is lost in the transmission, and the two end 
 stations and the intermediate station communicate with each 
 other as readily as if they were iri an open or closed circuit. 
 This mechanical retransmission is called translation. It is 
 effected by making the lever of the register act as a relay in 
 transmitting a message to the next station. The system, to be 
 fully explained, would require more detail than we can here 
 give to it. We shall only shew how translation can be effected, 
 
 leaving out of account how 
 all the stations can communi- 
 cate as in one circuit. We 
 also suppose, for the sake of 
 simplicity, that no relay is 
 needed, and that we are deal- 
 ing with a direct working 
 register. The current, Cj (fig. 
 212), from the sending station 
 enters the coil of the register 
 M, and goes thence to earth 
 P, and returns as shewn by arrow C r The register may 
 record or not, according to the message, but its doing so 
 or not in no way interferes with translation. The copper 
 pole, C, of the battery is connected with the lever IV of 
 the register, and the zinc pole is to earth. When the lever 
 is drawn down by the current, C 1 , it strikes against the point 
 at the top of the pillar p, that checks its motion. The pillar 
 p is joined to line L 2 , running to the further station, and 
 when the lever falls, a second circuit namely, that of the 
 battery is closed, in which C, the lever, the pillar, L 2 , the 
 further station, the earth, P, and Z are all included. Thus, as 
 ll f prints at the intermediate^station, it at the.'same time sends 
 a new printing current to the next. When it ceases to print, 
 so does the register at the distant station. It is in this way 
 that parliamentary news is transmitted simultaneously to all 
 
ELECTRIC TELEGRAPH. 
 
 387 
 
 the important towns lying between London and Aberdeen. 
 At the shore ends of submarine cables there is always a 
 translating apparatus. This allows the cable to be worked 
 by a battery suited to it, without loss of time in making it 
 a special circuit. As an example of translation, it may be 
 mentioned that the Indo-European line from London to 
 Teheran, a distance of 3800 miles, is worked by five repeaters 
 without any retransmission by hand. 
 
 334. CooJce and Wheatstone's Needle Telegraph. This con- 
 sists of an upright galvanometer, with the astatic needles 
 loaded at the lower end 
 to keep them, when 
 not acted on, in a verti- 
 cal position. A front 
 view of the single- 
 needle instrument is 
 given in fig. 213, and a 
 back or interior view 
 in fig. 214. One needle 
 moves within the coil 
 00, and the other on 
 the face of the dial. It 
 is the dial needle which 
 acts as the indicator. 
 The alphabetical code 
 is made up by com- 
 binations of the right 
 and left deflections of 
 the needle. The old 
 alphabet is given in 
 fig. 213. A is made 
 by two left deflections, Fig. 213. 
 
 M by one right ; D by 
 
 one right, then one left ; R by one left, then one right ; 
 G by two right, and one left; and so on. The short 
 arm indicates which beat is made first, and the long that 
 made second. The telegraph companies now adopt an 
 alphabet corresponding to Morse's code, a right-hand deflec-- 
 tion corresponding to a dash, and a left-hand deflection to a 
 
388 
 
 ELECTRICITY. 
 
 dot. The instrument is so arranged, that when the handle, 
 H, stands erect, the whole is in the receiving state. When 
 the handle turns to the right or left, the instrument sends, 
 and the needle deflects accordingly to the left or right at both 
 the sending and receiving stations. The instrument (fig. 214) 
 
 has four connections : 
 L, the line wire ; E, 
 the earth wire ; C, the 
 copper pole of the 
 sending battery ; and 
 Z, the zinc pole. It 
 is represented in the 
 receiving position. 
 The current takes the 
 course L, a, the coil 
 T, the spring cd, the 
 metal points in the 
 pin 2?, the metal spring 
 ef, thence by g to 
 earth. The handle 
 in front works the 
 cylinder PIN, which 
 turns on the axis n. 
 It is divided into 
 three parts : those 
 marked P and N are 
 covered with copper, 
 and are insulated 
 from each other by 
 
 the intermediate part, I, which is of ivory. By the spring st, 
 which presses against it, P becomes the + pole of the battery, 
 and by the spring mi, through the axis n, N becomes the 
 pole. A metal tooth, k, is fixed to P, and another, h, to N. 
 These stand vertical, and are out of circuit when the instru- 
 ment is in the receiving position. When a zinc (reverse, or 
 negative) current is put to line, the handle, H, is so turned 
 that h presses against the spring dc, and removes it from 
 the point at d, thus breaking the receiving circuit. At the 
 same time that h presses on dc, Jc presses on or. The reverse 
 
 Fig. 2U. 
 
ELECTRIC TELEGRAPH. 389 
 
 current takes the following course : Z, i, n, N, h, c, coil, a, 
 L, distant station, earth, E, g, r, o, Jc, P, s, t, C. When the 
 handle is turned the opposite way, h presses against ef, and k 
 against another spring similar to or, on the other side of P, 
 which is not shewn in the figure, and which is connected with 
 the strip of metal c, and thereby with 00, and the copper (or 
 positive) current is put to line. The cylinder PN acts as a 
 commutator, sending a copper or zinc current, according to 
 the side towards which it is turned. Sometimes two needles 
 are placed in the same box, each having a separate line- 
 wire to work it. The telegraphing can be much more 
 expeditiously done with two needles than with one, as two 
 deflections can be made at once, one on each instrument. The 
 rate of signalling with a double needle is rather above what 
 can be done by a Morse. Seeing that two wires are necessary 
 for a double-needle instrument, and that only one is necessary 
 for a Morse, it is a much more expensive instrument. Single- 
 needle lines are much used for working railways, and for 
 circuits with little traffic, but not for main telegraphic lines. 
 The needle instrument is delicate enough to be worked direct 
 without a relay. The dial of these instruments is movable, so 
 that when earth currents deflect the needle to a position from 
 the vertical, the stopping pins still stand at an equal distance 
 on each side of it. When several stations are joined on the 
 needle system, the open circuit arrangement is employed. 
 
 335. Reflecting Galvanometer and Siphon Recorder. For 
 signalling through long submarine circuits such as the 
 Atlantic cable, the reflecting galvanometer (sect. 270) is the 
 only instrument which has as yet been found practically 
 successful. When so used, it really becomes a single-needle 
 instrument whose index is a spot of light. By the right and 
 left movements of this spot of light across a paper scale, the 
 signals are made out ; and the instrument is of such delicacy, 
 that even a feeble working current, notwithstanding the 
 length of the circuit, can make these movements quite 
 distinct. Condensers are employed to annul the effects of 
 earth currents. 
 
 For recording messages through long submarine circuits, 
 Sir William Thomson has also invented a very delicate 
 
390 ELECTRICITY. 
 
 instrument called the Siphon Kecorder. It is so called from 
 one of its essential parts, which consists of a fine light glass 
 siphon, so hung that its shorter leg dips into a cistern of ink, 
 while its longer leg comes close to, but without touching, a 
 strip of paper, paid out by clock-work at a uniform rate. 
 When a message is being sent, the point of the siphon tube is 
 made to vibrate backwards and forwards in a direction trans- 
 verse to that in which the paper is moving. This motion is 
 given to it by means of a delicately suspended rectangle of 
 wire with which it is in connection, and which hangs, when 
 at rest, with its plane axially between the poles of a strong 
 permanent or electro-magnet. The working current passes 
 through this rectangle, and according to its direction causes 
 it to rotate through a small angle to the one side or the other. 
 In order that the point of the siphon may move across the 
 paper without friction, and yet leave an ink trace, the follow- 
 ing ingenious arrangement is adopted. The cistern of ink in 
 which its shorter leg dips, is kept constantly electrified by 
 means of a small electro- static induction machine, and in this 
 way the electrified ink is constantly spurted out upon the 
 paper in a fine stream. The letters of the message are made 
 out from the ink trace/which consists of a series of connected 
 angular-hand strokes 'extending to greater and less distances 
 on one side or the other of the middle line of the paper, 
 according to the direction and duration of the currents sent 
 to line at the transmitting station. 
 
 For a full description of this instrument, as well as for the 
 methods of automatic, duplex, and quadruplex telegraphy, 
 we must refer to treatises on Practical Telegraphy. 
 
 CHAPTER XXVI. 
 TELEPHONE. 
 
 336. The telephone may be defined to be an instrument 
 for transmitting musical sounds and articulate speech from 
 one point to another. 
 
 In all telephonic arrangements worked by electricity, we 
 
TELEPHONE. 391 
 
 have essentially three things a transmitter, a receiver, and 
 a closed circuit which includes both transmitter and receiver, 
 and which may or may not also include some form of 
 battery. The function of the transmitter is to produce 
 variations of the current-strength in the circuit when under 
 the influence of sonorous vibrations ; and the function of 
 the receiver is to translate these variations into sound, and 
 so reproduce, at the distant station, the sounds which were 
 uttered into the transmitter. 
 
 According to Ohm's law, if C be the current-strength, E 
 the electro-motive force, and E, the resistance in any electrical 
 
 TT 
 
 circuit, we have C = ^, and, hence, we see that the current 
 
 XV 
 
 strength in any circuit can be varied in two distinct ways, 
 either, first, by varying the resistance and keeping the 
 electro-motive force constant, or, secondly, by varying the 
 electro-motive force and keeping the resistance constant. 
 These two ways of varying the current-strength give rise 
 to two distinct classes of telephone, of which we shall now 
 give examples, although it will be impossible for us even 
 to allude to many of the forms of telephone which have 
 either been proposed or are in actual use. 
 
 337. Reiss's Telephone. This is an example of a telephone 
 which is worked by varying the resistance in the circuit, 
 the electro-motive force being constant. It was invented 
 by Philip Keiss in 1861, and is represented in fig. 215. 
 AA is a hollow wooden box, with two round holes in 
 it, one on the top, the other in front. The hole at the 
 top is closed by a piece of bladder, S, tightly stretched on 
 a circular frame ; a mouth-piece, M, is attached to the front 
 opening. When a person sings in at the mouth-piece, the 
 whole force of his voice is concentrated on the tight mem- 
 brane, which in consequence vibrates with the voice. A 
 thin strip of platinum is glued to the membrane, and con- 
 nected with the binding screw a, in which a wire from the 
 battery, B, is fixed. A tripod, efg, rests on the skin. The 
 feet e and / lie in [metal cups on the circular frame over 
 which the skin is stretched. One of them, /, rests in a cup 
 containing mercury, and is connected with the binding screw 
 
392 
 
 ELECTRICITY. 
 
 6. The third foot, g, consisting of a platinum point, lies on 
 the circular end of the strip of platinum just mentioned. 
 This point being placed on the centre of the oscillating 
 membrane, acts like a hopper, and hops up and down with 
 it. It is easy to understand how, for every vibration of 
 
 Fig. 215. 
 
 the membrane, the hopper will be thrown up for the instant 
 from connection with its support, and how the close circuit 
 is thus broken at every vibration. The receiving apparatus, 
 R, consists of a coil of wire placed in circuit, inclosing an 
 iron wire, both being fixed on a sounding-box. The con- 
 nections of the various parts of the circuit are easily learned 
 from the figure. Suppose a person to sing a note at the 
 mouth-piece which produces 300 vibrations a second, the 
 circuit is broken at the bladder 300 times, and the iron 
 wire ticking at this rate gives out a note of the same pitch. 
 The note is weak, and in quality resembles the sound of a 
 toy trumpet. Dr Wright devised a receiving apparatus of the 
 following kind. The line current is made to pass through 
 the primary coil of a small induction coil. In the secondary 
 circuit he places two sheets of paper, silvered on one side, 
 back to back, so as to act as a condenser. Each current that 
 comes from the sending apparatus produces a current in the 
 secondary circuit, which charges and discharges the condenser, 
 each discharge being accompanied by a sound like the sharp 
 tap of a small hammer. The musical notes are rendered 
 
TELEPHONES. 393 
 
 by these electric discharges, and are loud enough to be heard 
 in a large hall. 
 
 338. Bell Telephone. The Bell Telephone, so called from 
 its inventor, Professor Graham Bell, is an example of a tele- 
 phone which is worked by varying the electro-motive force 
 and keeping the resistance constant. In this form the trans- 
 mitter and receiver are identical ; and no battery is included 
 in the circuit, the working current being an induced current 
 due to the variation of the magnetic intensity within a helix 
 of wire. Fig. 216 shews a sectional sketch of two Bell tele- 
 phones arranged in circuit so as to transmit articulate speech. 
 
 Fig. 216. 
 
 Let A denote the transmitter and B the receiver, I being the 
 connecting line wire ; a and a! are two cylindrical steel 
 magnets, each about six inches long, and a quarter of an inch 
 in diameter ; 6 and V are two small wooden bobbins sur- 
 rounding the north poles of the magnets, and filled with a 
 good many turns of fine insulated copper wire, the ends of 
 wire being put into connection with the line wires ; c and c' 
 are two thin circular discs of iron (usually ferrotype plate) 
 fixed close to, but not touching, the poles of the magnets ; 
 d and d' are two conical wooden pieces for applying the 
 mouth to in the one case, and the ear in the other. 
 
 Suppose now that a person speaks into the transmitter 
 at A. The sound-waves striking against the disc c, set it 
 into vibration, and hence c may be regarded as an armature 
 moving rapidly in front of the pole of the magnet a. These 
 vibratory motions produce corresponding variations in the 
 magnetism of a, and these again cause corresponding induced 
 currents in the wire of bobbin b. These induced currents 
 flow along the line wires to the receiver, B, and passing 
 
394 
 
 ELECTRICITY. 
 
 through the bobbin &', produce corresponding changes in 
 the magnet a'. These changes of magnetism affect the iron 
 disc c', and put it into vibrations which are sympathetic with 
 those of c. Hence c' gives out 
 sounds precisely corresponding to, 
 but less loud, than those directed 
 against c, and hence an ear applied 
 at d r hears the words uttered by 
 the mouth at d. The speech pro- 
 duced by the Bell telephone, 
 although not very loud, is exceed- 
 ingly distinct; so much so, that 
 one has no difficulty in recognising 
 the voice of the speaker. But 
 perhaps the greatest marvel of this 
 ingenious instrument is its extreme 
 delicacy in detecting variations in 
 even the most feeble current, pro- 
 vided these variations are rapid 
 enough. Professor Tait has calcu- 
 lated that the current from a single 
 Grove's cell, acting through a re- 
 
 Fig. 217. 
 
 sistance of a billion B.A. units, is 
 
 sufficient to work a telephone, pro- 
 vided the current is varied five hundred times per second. 
 Hence the telephone is by far the most delicate instrument 
 yet invented for detecting minute and sudden variations in 
 the strength of a current. 
 
 The Bell telephone in its usual complete form is repre- 
 sented in fig. 217. 
 
 339. Microphone. The microphone, invented by Professor 
 Hughes, is an instrument which produces rapid variations 
 in the resistance of an electrical circuit when acted upon by 
 any kind of vibratory or tremulous motion. It consists 
 essentially of two or more conductors in loose contact, such 
 as is produced by letting the conductors rest lightly the one 
 against the other. When the loose contact is placed in 
 circuit with a cell and a Bell telephone, any tremor acting 
 upon the loose contact varies the resistance at the surfaces in 
 
TELEPHONE. 
 
 395 
 
 contact, and is announced by a loud sound in the telephone. 
 It is for this reason that it is called the microphone, inas- 
 much as it makes audible, in the telephone, such faint 
 tremors as those produced by the ticking of a watch, or 
 even the tread of a fly across a wooden board. Almost any 
 two conductors in loose contact, whether of the same or 
 different materials, will produce the microphone effect ; but 
 it has been found that the best effect is produced by a loose 
 contact between two pieces of gas-carbon. No doubt, the 
 peculiar excellence of carbon in this respect is due to its 
 more or less gritty nature, and also to the fact that it does 
 not readily oxidise by exposure to the atmosphere. The 
 usual form of microphone, when arranged so as to be acted 
 upon by faint tremors, is represented in fig. 218. A and B 
 are two small blocks of 
 carbon attached to a ver- 
 tical piece of wood which 
 is supported on a hori- 
 zontal sole-plate, also 
 of wood. C is a small 
 stick of carbon, pivoted 
 at both ends, and sup- 
 ported vertically in coni- 
 cal holes between the 
 two carbon blocks. The 
 carbon stick is thus in a 
 position of extreme in- 
 stability, and any tremor 
 communicated to the 
 wooden supports will 
 cause it to oscillate. The 
 current from a small battery is led through the carbons and 
 a Bell telephone, and the arrangement is complete. When a 
 watch is placed on the sole-plate of the instrument, every tick 
 is distinctly heard in the telephone ; and when a fly is allowed 
 to creep over any part of the instrument, every tread is also 
 revealed in the telephone. Further, if a person sing or speak 
 in the neighbourhood of the instrument, the sonorous vibra- 
 tions are communicated to the support of the carbon blocks, 
 
 Fig. 218. 
 
396 ELECTRICITY. 
 
 and thence to the carbon stick, which is thus thrown into a 
 corresponding state of vibratory motion. The resistance of 
 the circuit is in this way varied, and every sound is faithfully 
 reproduced in the telephone. 
 
 A difference of opinion prevails among physicists regarding 
 the real cause of the microphone action. Some, and these 
 of the highest authority, hold that the action is due merely 
 to the variations of resistance due to variations of pressure 
 at the surfaces of contact of the carbons. It is difficult, 
 however, to see how this can be the whole, or even the 
 main cause of the action ; for we must remember that the 
 surfaces of the carbon in contact are continually changing 
 in virtue of the minute electric arcs which must take place 
 between the points of carbon which are just clear, and no 
 more, of contact. And if the surfaces in contact are thus 
 perpetually changing, it is hardly possible that the pressure 
 between them could vary according to any law sufficiently 
 regular to account for the transmission of articulate speech. 
 It seems highly probable that the microphone is more of 
 the nature of a very refined make-and-break, and thus 
 analogous to the Reiss transmitter, but only immensely more 
 delicate. As a matter of fact, we know that when the 
 microphone is used to transmit musical sounds of a definite 
 pitch, it does act as a make-and-break, for sparks can be 
 seen between the carbon points ; and there does not seem 
 to be any good reason for supposing that this make-and- 
 break action entirely ceases, and a perfectly different action 
 comes into play, when the instrument is used to transmit 
 articulate speech. 
 
 340. Microphone Transmitters. The chief practical appli- 
 cation of the microphone is its employment as a transmitter 
 to a Bell telephone as receiver. For this purpose it has 
 been found very effective, and is now almost universally 
 adopted. The forms of microphone transmitter are very 
 various, all depending upon the same principle, and differing 
 only in matters of detail. A common form is represented in 
 fig. 219, which shews the arrangement of telephone and trans- 
 mitter at one end of the line as used for carrying on a 
 conversation. The sloping lid of the box is made of a thin 
 
TELEPHONE. 397 
 
 deal board, to the under side of which the microphone is 
 attached. In this form the microphone usually consists of 
 several sticks of carbon radiating from a central carbon block, 
 and supported, at the outside, by a suitable number of other 
 blocks placed equally distant round the central block. The 
 
 Fig. 219. 
 
 sticks rest loosely in pivot holes in both of their supporting 
 blocks. The current is led from the central block through 
 each of the carbon sticks and away to the line wire. The 
 speaker simply holds his head over the sloping lid at a 
 convenient distance, and speaks not loudly but distinctly. 
 Excessive loudness is a mistake, as it produces roaring in the 
 telephone. 
 
 341. Telephone Exchange. In most large towns a system 
 of telephone exchanges has recently sprung up. The object 
 of these exchanges is to enable business and professional men 
 to converse directly with each other at any moment. For 
 this purpose a convenient central station is chosen from 
 which wires are led to the houses or business places of all 
 the individuals who subscribe to the exchange. At the 
 central station a staff of attendants, usually girls, are always 
 present, and a system of switches is arranged whereby an 
 
398 ELECTRICITY. 
 
 attendant can, at a moment's notice, place any one member 
 of the exchange in direct communication with any other. 
 This is accomplished by merely inserting a plug which 
 completes the electrical circuit between the one and the 
 other. Suppose A wishes to communicate with B. A first 
 rings up the attendant, and tells him to join him on to B, 
 all the members being known to the attendant and to each 
 other by each having a separate number. The attendant 
 then inserts the requisite plug, and A and B are ready to 
 converse directly with each other, without the attendant or 
 any one else knowing what is said. When the conversation 
 is ended, a signal is sent to the attendant, and the plug is 
 withdrawn. 
 
 342. The Microphone as a Receiver. The curious fact has 
 been discovered that the microphone can act as a receiver 
 as well as transmitter, although imperfectly. This can 
 be readily shewn by the following experiment due to 
 Professor Blyth. Two ordinary porcelain jam-pots, of 
 convenient size, are taken, and half filled with cinders or 
 gas carbon in small lumps. Down the sides of each pot 
 two strips of copper are inserted, facing each other, to serve 
 as electrodes. The two jam-pots are then placed in circuit 
 with a battery of four or five Grove's cells. If a song be 
 sung into one of the jam-pots, a listener can hear it quite 
 distinctly proceeding from the other, on applying it to his 
 ear. Articulate speech can also be transmitted in this way 
 so as to be quite recognisable, although it comes out rather 
 squeaky. 
 
 343. Edison's Telephones. Mr Edison of New York has 
 invented a variety of ingenious forms of telephone, the 
 most interesting of which, perhaps, are his carbon button 
 transmitter and his slipping receiver. The carbon button 
 consists of a small thin cylinder made from compressed 
 paraffin smoke mixed with gum water. This button is 
 placed between two pieces of platinum foil, which serve 
 as electrodes for sending a current through it. The button 
 with the foil is placed between a rigid support at the one 
 end and a flexible ferrotype disc at the other. Usually, a 
 small pad of india-rubber is inserted between the button 
 
TELEPHONE. 399 
 
 and the flexible disc. When sonorous vibrations are sent 
 against the disc, its to-aiid-fro vibrations cause more or 
 less compression throughout the mass of the carbon button, 
 and so vary its resistance. In this way, when in circuit with 
 a battery, it is made to act as a transmitter to any suitable 
 form of receiver. 
 
 The action of the slipping receiver depends upon the fact, 
 discovered by Mr Edison, that the friction between a metallic 
 spring and a revolving cylinder of prepared chalk soaked in an 
 electrolytic liquid, varies when a current passes between the 
 surfaces in contact. When the current passes, the friction is 
 diminished, as if the chalk were oiled ; and when the current 
 ceases, or is weakened, the friction is increased. In the 
 actual instrument the small chalk cylinder is driven slowly 
 round by hand. One end of a steel spring presses against 
 the surface of the chalk, the pressure being regulated by 
 a pad of india-rubber. The other end of the spring is 
 attached to the centre of a mica disc. Now, when the 
 current through the spring and chalk cylinder is made to 
 vary by the action of the transmitter, the friction is 
 alternately increased and diminished ; and this gives a series 
 of rhythmical jerks to the mica disc, which make it speak 
 out loudly and distinctly the words uttered int6 the trans- 
 mitter. This instrument, notwithstanding its ingenuity and 
 scientific interest, is apt to get out of order, and has not 
 come as yet into very general use. 
 
 344. Photophone. This is the name given to a form of 
 telephone transmitter which is acted upon by light instead of 
 sound. It was introduced by Professor Graham Bell. Its 
 action depends upon the fact, first discovered by Willoughby 
 Smith, that crystalline selenium has its electrical resistance 
 altered on exposure to light. To construct a photophone, or, 
 as it is sometimes called, a selenium cell, we may proceed as 
 follows : Procure two small brass combs with fine long teeth. 
 From each knock out every alternate tooth, and then place the 
 two combs on a flat mahogany board, with the teeth inter- 
 lacing but not touching at any point. In this position screw 
 them firmly to the board, and solder a wire to each comb to 
 serve as electrodes, Next procure a stick of good selenium, 
 
400 ELECTRICITY. 
 
 and having warmed the combs sufficiently to melt the 
 selenium, rub it in carefully between the teeth. In this con- 
 dition the selenium is in the amorphous state, and must be 
 rendered crystalline by heating the whole cell in an air-bath 
 to about 240 C., and then allowing it gradually to cool. If 
 the cell be now included in circuit with a galvanometer and 
 a battery of 15 Grove's cells, its resistance will be found to 
 alter when exposed to light. 
 
 When the cell is put in circuit with the battery and tele- 
 phone, and an intermittent light thrown upon it, correspond- 
 ing sounds are heard in the telephone. This can be prettily 
 illustrated by placing the flame of a Koenig's capsule, provided 
 with a mouthpiece, in front of the cell, and singing or speaking 
 into the mouthpiece. The alterations in the, flame so affect 
 the resistance of the selenium as to make the singing and 
 speaking quite recognisable in the distant telephone. If a 
 singing flame be put in front of the cell, the music of the 
 flame is beautifully reproduced in the telephone. 
 
 Electrical Storage of Energy. 
 
 345. The simplest example of the storage of energy by 
 means of electricity is perhaps a charged Leyden jar. In this 
 we have energy stored in the potential form of electrical sepa- 
 ration ; the inside coating having usually a positive charge, and 
 the outside coating the corresponding negative charge. When 
 the knob and outside are joined by the discharging tongs, we 
 have the stored energy recovered in the form of the sound, 
 heat, and light of the spark. Another simple example of the 
 same thing is the counter electro- motive force of polarisation 
 always set up in an ordinary voltameter when a current is 
 sent through it. When the current flows, it carries hydrogen 
 with it, and sends oxygen in the opposite direction. In this 
 way, a layer of oxygen is formed on the one platinum plate, 
 and a layer of hydrogen on the other. When the battery is 
 removed from the circuit, and the platinum plates are joined 
 by a wire, a momentary current passes through the wire in 
 the opposite direction to that of the charging current. This 
 can easily be tested by a galvanometer. 
 
 346, Planters Secondary Battery. -A Plante's cell is in 
 
TELEPHONE. 401 
 
 reality a huge voltameter, in which the platinum plates are 
 replaced by plates of lead. In order to get a large surface in 
 a convenient space, it is usually constructed as follows : 
 Two large sheets of lead are placed the one on the top of the 
 other, with narrow strips of india-rubber between them. 
 The two sheets are then rolled up together, so that the one 
 forms a spiral coil insulated within the other. The whole is 
 then placed in a deep glass jar with acidulated water. 
 Wires are soldered to each plate to serve as electrodes. 
 When the current from two or three Bunsen's or Grove's 
 cells is sent through the secondary cell for a considerable 
 time, layers of oxygen and hydrogen are gradually formed 
 on the respective lead plates, and this process goes on till the 
 electro-motive force of polarisation is equal to that of the 
 charging battery. In this state the action ceases, and we 
 have the energy of the battery stored in the cell. When the 
 battery is now removed, and the electrodes of the cell are joined 
 by a wire, a powerful current passes through the wire for a 
 short time. The duration of the discharging current depends 
 upon the resistance of the wire through which it has to pass. 
 Thus, a cell which will keep a thick wire red-hot for only a 
 few minutes, will keep a fine platinum wire in a state of 
 incandescence for nearly an hour. 
 
 Plante has found that the action of his cell is greatly 
 improved by the process of what he calls 'forming' the 
 plates. This is performed by charging the cell alternately 
 in opposite directions for stated times, and discharging it 
 between each reversal of the charging battery current. 
 
 In order to get great effects, Plante has constructed secondary 
 batteries consisting of a great number of cells ; and he has 
 also adopted an ingenious device for charging a number of 
 cells side by side, and then discharging them in series. In 
 this way he gets an enormous electro-motive force, sufficient 
 to produce sparks in air resembling those of an induction 
 coil. 
 
 347. Faure Cell.-- This cell, invented by M. Faure in 1880, 
 is the most recent improvement in secondary batteries. It 
 is constructed as follows : Two thin lead plates of convenient 
 length and width are taken. Each of these is first coated 
 
402 ELECTRICITY. 
 
 with a layer of red lead about inch thick. The red 
 lead is made into a thick paste with dilute sulphuric acid, 
 and spread evenly over the surface of each plate. The 
 plates thus coated are next covered with a layer of felt or 
 flannel, or, what answers very well, three or four folds of 
 filter paper. The two plates may then be either rolled 
 together, as in the Plante cell, or folded backwards and for- 
 wards so as to be put into a rectangular box lined with lead. 
 The liquid used is dilute sulphuric acid, in which the plates 
 are immersed. The great advantage of this cell over the 
 Plante is, that it takes very short time to ' form/ and the 
 discharging current does not run down so quickly. When a 
 battery of a number of Faure cells is charged with a dynamo- 
 machine, it will give out a current sufficient to work a number 
 of incandescent lamps for a whole evening, and in this way it 
 is employed for household electric lighting. The Faure 
 battery has also been successfully employed in lighting up 
 the carriages in underground railways, the charging current 
 being got from a dynamo-machine driven by the train when 
 in motion. 
 
 The chemistry of the Faure cell can hardly as yet be said 
 to be fully understood ; but there seems no doubt that when 
 the charging current passes, spongy lead is formed on the one 
 plate, and peroxide of lead at the other. 
 
 CHAPTER XXVII. 
 
 ELECTRO-OPTICS, OE THE CONNECTION BETWEEN LIGHT 
 AND ELECTRICITY AND MAGNETISM. 
 
 348. According to the undulatory theory of light, now uni- 
 versally adopted, light is supposed to consist of undulations 
 propagated from the luminous source through a very subtle 
 elastic medium called the luminiferous ether. The vibrations of 
 the ether particles, which produce these undulations, are also 
 supposed to take place in all directions in planes perpendicu- 
 lar to the direction in which the ray of light is going. This 
 latter assumption is rendered necessary in order to explain 
 
ELECTRO-OPTICS. 403 
 
 the observed facts of the polarisation of light, for an account 
 of which we must refer the student to some work on Physical 
 Optics. 
 
 349. Electro-magnetic Theory of Light. According to this 
 theory, for which we are indebted to Clerk Maxwell, both 
 light and electro-magnetic induction are supposed to be influ- 
 ences propagated through the same medium the luminiferous 
 ether and in fact light itself is supposed to be only a par- 
 ticular form of electro-magnetic disturbance. If the theory 
 be true, we ought to expect to find some relations subsisting 
 between the phenomena of the propagation of light through 
 any medium, and the phenomena of the propagation of 
 electro-magnetic induction through the same medium. Several 
 such relations have been pointed out by Clerk Maxwell, which 
 tend to confirm the theory. 
 
 If V be the velocity of electro-magnetic induction in any 
 medium, K its specific inductive capacity in electro-static 
 units, and m its coefficient of magnetic induction, then Clerk 
 Maxwell has shewn by a mathematical analysis that we have 
 the equation 
 
 If we take air as the medium, and use electro-magnetic 
 units, we have m = 1, and K = -^-, where v is the number of 
 
 electro-static units in one electro-magnetic unit. Substituting 
 in (1), we have V= v. Now, the value of v has been found 
 by several independent experiments, the mean of which 
 gives 
 
 v = 2-9857 X 10 10 centimetres per second, 
 or v = 185,521 miles per second. 
 
 The velocity of light has also been found by various inde- 
 pendent methods, the most satisfactory of which are the 
 determinations by Cornu in 1874, and by Young and Forbes 
 in 1881. Calling the velocity of light in air L, we get from 
 these experiments L = 2*9857 X 10 10 centimetres per second. 
 
 Comparing the values of L and V, we see that the velocities 
 z 
 
404 
 
 ELECTRICITY. 
 
 of light and electro-magnetic induction in air are exactly 
 identical. 
 
 Assuming the same to be true for any other transparent 
 non-conducting medium, we can find a relation between the 
 index of refraction of the medium and its specific inductive 
 capacity. Let ^ be the index of refraction from air into the 
 medium, K its specific inductive capacity, and m its co- 
 efficient of magnetic induction. Then if V^ denote the 
 common velocity of light and electro-magnetic induction in 
 the medium, we have from the principles of optics, 
 
 Also from (1), since m is nearly unity for all transparent 
 media, we have 
 
 V* 
 
 in electro-magnetic measure. 
 Hence we have 
 
 But we have already seen that L = v, and therefore /* = 
 that is to say, if the electro-magnetic theory of light be true, 
 the index of refraction of a medium should be equal to the 
 square root of its specific inductive capacity. We have thus 
 a test of the theory by comparing a table of refractive indices 
 with a table of specific inductive capacities, it being remem- 
 bered, however, that we must take the refractive index for 
 waves of infinite wave length. The following table shews 
 the comparison according to Gordon : 
 
 Dielectric. 
 
 VK. 
 
 MX = 00). 
 
 Double flint-glass, extra dense,. 
 Extra dense flint-glass 
 
 1-778 
 1747 
 
 1-672 
 1*620 
 
 Hard cvown-glass 
 
 1-763 
 
 1-504 
 
 Paraffin 
 
 1-412 
 
 1-422 
 
 
 
 
 350. Action of Magnetism on Light. The first clear con- 
 nection between magnetism and light was pointed out by 
 
ELECTRO-OPTICS. 405 
 
 Faraday in 1845. He experimented first with a particular 
 kind of glass called ' heavy glass,' which is a silicated borate 
 of lead, but he afterwards found that many other substances 
 could produce the same effect. His experimental arrange- 
 ments were as follows : A piece of heavy glass, about two 
 inches square and half an inch thick, was placed lengthwise 
 between the poles of a powerful electro-magnet, in such a 
 position that a pencil of light could be sent through it in a 
 direction as nearly as possible parallel to the line of magnetic 
 force. The light from an Argand lamp was polarised in a 
 horizontal plane by reflection from a piece of glass placed at 
 the proper polarising angle. The polarised beam was passed 
 through the heavy glass, and after emergence, was led 
 through a Nicol's prism, so placed that it could rotate round 
 an axis parallel to the direction of the ray. This Nicol acted 
 as the analyser. Before the current was sent through the 
 electro-magnet coils, the analysing Nicol was placed at the 
 proper angle for extinguishing the light of the lamp. When 
 the current was now turned on, the light instantly reappeared, 
 and continued to come through so long as the current flowed, 
 but immediately disappeared when the current was turned 
 off. When the current was on, and the light coming through 
 the Nicol, Faraday found that the Nicol had to be rotated 
 through a definite angle in a definite direction before the 
 light was again extinguished ; and that the direction of rota- 
 tion was reversed when the poles of the magnet were reversed 
 by reversing the current. He also found that the amount of 
 rotation required to produce extinction of the light was pro- 
 portional to the strength of the magnetic field, and to the 
 length of glass through which the light had to pass. 
 
 This shewed that the magnetic action had the power of 
 rotating the plane of polarisation, and that the angle of 
 rotation varied continuously from point to point through the 
 glass, and that the amount of rotation was proportional to the 
 difference of magnetic potential between the point where the 
 light entered, and the point where it left the glass. 
 
 The direction of rotation is related to the direction of the 
 lines of force, in the same way as the rotation and longitu- 
 dinal motion of an ordinary cork-screw. 
 
406 ELECTRICITY. 
 
 Since Faraday's time this subject has been carefully 
 examined by Verdet, Becquerel, Rontgen, and others, who 
 have found the effect to be produced not only by solid, but 
 also by liquid and gaseous dielectrics. They have also 
 tabulated the magnetic rotative powers of the various sub- 
 stances for light of different colours. 
 
 Another remarkable action of magnetism upon polarised 
 light has recently been discovered by Dr Kerr of Glasgow. 
 He reflects a beam of polarised light from the highly polished 
 pole of a powerful electro-magnet. In the path of the 
 reflected light, a Nicol's prism i3 placed in such a position as 
 to produce extinction of the light when no current goes 
 through the magnet. Directly the current is turned on, 
 the light reappears, and continues so long as the current 
 flows, shewing that the plane of polarisation has been rotated 
 by the magnetic action. 
 
INDEX. 
 
 PAGE 
 
 Abel's fuses 342 
 
 Absolute electrical measurements.. .324 
 
 Acceleration 75, 170 
 
 Accumulators 129-143 
 
 Air-spark, the 318 
 
 Amalgam 118 
 
 Amalgamated zinc 175, 190 
 
 Ampere's theory of magnetism 268 
 
 Anions and Anodes 222 
 
 Arago's magnetism of rotation 321 
 
 Armatures 24, 357 
 
 Armstrong's hydro-electric machine 72 
 
 Astatic galvanometer 276 
 
 Atmospheric electricity 157 
 
 Aureole 308 
 
 Back-stroke 162, 164 
 
 Bain's electric pendulum 343 
 
 Ball-lightning 159 
 
 Barlow's wheel > . 262 
 
 Battery Bunsen's 182, 186 
 
 constant . . , 181 
 
 Daniell's 182, 373 
 
 earth 344 
 
 electric 138 
 
 galvanic, tension and 
 
 quantity arrangements of. . . 178, 217 
 
 Battery, gas 180 
 
 Grove's 182, 184 
 
 iron 187 
 
 magnetic 23 
 
 Plante's secondary 400 
 
 sand 373 
 
 Smee's 179 
 
 thermo-electric 238 
 
 Wollaston's 179 
 
 ; see also Cell. 
 
 Bell telephone 393 
 
 Bertsch machine, the 348 
 
 Bohnenberger's electrometer. 178 
 
 Breaks 283, 302 
 
 Brush, electric 124 
 
 Bunsen's battery 182, 186 
 
 Carbon button transmitter 398 
 
 Cations < and cathode 222 
 
 Cell, Bichromate of potash 187 
 
 , Daniell's 182 
 
 PAGE 
 
 Cell, Tray 184 
 
 , Leclanche 188 
 
 , Meidinger's 190 
 
 ; see also Battery. 
 
 Charge by cascade 139 
 
 , conductive 67 
 
 , inductive 66 
 
 , residual 135 
 
 , secondary 135 
 
 Charts, magnetic 46 
 
 Chatterton's compound 376 
 
 Circuit, closed 294, 384 
 
 , compound voltaic 177 
 
 , galvanic, homogeneity and 
 
 polarity of. 181 
 
 Circuit, open 384, 385 
 
 Cleavage, electricity of. 71 
 
 Coercive force 18 
 
 Coil, induction 301 
 
 , primary 281, 301, 309 
 
 , secondary 281, 301, 309 
 
 Commutators . , .* 304 
 
 Compass, mariner's 40 
 
 , Sir W. Thom- 
 son's 42 
 
 Condensed spark 309 
 
 Condenser 172, 304 
 
 Conducting power of metals 67, 200 
 
 Conductor, negative 118 
 
 -, prime 117 
 
 Conductors and non-conductors 
 
 66, 67, 68 
 
 Conservation of energy 82 
 
 Contact force 229 
 
 Coulomb's torsion balance 28, 29 
 
 Crown of cups, Volta's 178 
 
 Current electricity 164-175 
 
 electrolytic action 221, 222 
 
 electro-magnetic units 168 
 
 , heating effects of. 128 
 
 induction 280-301 
 
 , physiological effects of 
 
 129, 218 
 
 Current resistance 192-204 
 
 , strength or quantity of 
 
 1 66, 167 
 
 Currents, action of the earth on.. . .263 
 , action on magnets 257 
 
408 
 
 ELECTRICITY. 
 
 PAGE 
 
 Currents, attraction and repulsion 
 
 of 254 
 
 Currents, circular 260 
 
 , earth 263, 378, 382 
 
 , extra 285, 294 
 
 , induced 291, 319, 321 
 
 , parallel 253 
 
 Cylinder-machines 121 
 
 Daniell's battery 182, 373 
 
 Declination 34 
 
 needles or declino- 
 meters 36, 268 
 
 Decomposition of water 223, 226 
 
 Diamagnetic bodies 19, 20, 22 
 
 Dielectrics 66, 311 
 
 Dip, magnetic 34 
 
 Dipping needle 42 
 
 Directive action of the earth 33 
 
 Discharge by alternate contacts... 136 
 
 - by points and flames. . .127 
 
 , convective 123 
 
 , disruptive 121 
 
 , effects of 123 
 
 Discharging tongs 134 
 
 Diurnal variation of the needle .... 54 
 
 Divided touch 26 
 
 Double touch 26 
 
 Dynamical principles 74-83 
 
 Dynamo-machines 353, 359 
 
 Earth, action of, on currents .. 263, 378 
 
 , as a magnet 15 
 
 , electrification of the. ..no, 156 
 
 Ebonite, as an insulator 68 
 
 Edison's incandescent lamp 340 
 
 telephones 398 
 
 Electric brush, the 124 
 
 clocks 343 
 
 discharge, velocity of. .... 141 
 
 egg... ....313 
 
 elasticity 101 
 
 " DW discharge 127 
 
 lamps 337 
 
 light ._ 221, 334-340 
 
 machines 117-129 
 
 -< mortar 140 
 
 pendulum 61, 343 
 
 polarity 71, 72, 93 
 
 spider 137 
 
 telegraph 369-390 
 
 tramway car 368 
 
 Electrical measurements _ 324 
 
 quantity and density... . 83 
 
 storage of energy. .... . . 400 
 
 transmission of power. . .368 
 
 Electricity, atmospheric 155-163 
 
 , distribution of 62 
 
 , frictional 61-73 
 
 generated by steam 72 
 
 , positive and negative . . 62 
 
 , terrestrial 155-163 
 
 -, theories of 63, 64 
 
 glov 
 
 lami 
 
 PAGE 
 Electricity, velocity of ........ 141, 379 
 
 Electrics and non-electrics ........ 68 
 
 Electrification, processes of. ....... 70 
 
 Electro-chemical order of the 
 
 metals .................... 67, 68, 71 
 
 Electrodes ................... 155, 311 
 
 Electro-kinetics ................... 164 
 
 Electrolysis ...................... 221 
 
 Electrolytes ...................... 222 
 
 Electro-magnetic induction appar- 
 
 atus ............................ 301 
 
 Electro-magnetic machines ____ 262, 366 
 
 -- rotations.26i, 262, 327 
 
 - units ............ 327 
 
 Electro-magnetism ............ 264-272 
 
 Electro-magnets .............. 27, 270 
 
 Electro-metallurgy ........... 229, 331 
 
 Electrometers and electroscopes 
 
 143-155 
 Electro-motive force.. no, 165, 172, 191 
 
 - , unit ofl.i68, 169 
 Electromotors .................... 366 
 
 Electro-optics .................... 402 
 
 Electrophorus ................ 122, 348 
 
 Electro-plating .................... 333 
 
 Electroscope .............. 64, 143-155 
 
 -- , heterostatic ......... 144 
 
 , idiostatic ............ 144 
 
 Electro-static machines ............ 125 
 
 Electro-tonic state ................ 281 
 
 Electrotype ...................... 331 
 
 Energy definition of .............. 80 
 
 kinetic .................. 81 
 
 law of the conservation of. 82 
 
 mutual potential, 
 potential.. . 
 
 Si 
 
 Equi-potential surface 107 
 
 Evaporation and electrification 72 
 
 Exploding gunpowder at a distance. 340 
 
 Faraday's Law 222 
 
 Faure cell 401 
 
 Ferromagnetic bodies 19 
 
 Flames, magnetic nature of 22 
 
 Force 76, 171 
 
 Forked lightning 159 
 
 Friction machines 117-129 
 
 Frictional electricity 61-73 
 
 Galvanic current 218-229 
 
 trough 179 
 
 Galvanism 164 
 
 Galvanometers, 209, 273-280; re- 
 flecting, 389 ; tangent, 273 ; sine, 
 
 275 ; astatic. 276 
 
 Gases, dielectric strength of 312 
 
 , magnetic nature of 22 
 
 Gauss's magnetometer 45 
 
 Glass, insulating power of 68 
 
 Glow 127 
 
 Gramme machine 363 
 
 Grove's battery, 184 ; gas battery. .180 
 
 Heat, effects of, on magnetism .... 32 
 
INDEX. 
 
 409 
 
 Holtz electric machine . 
 Hydro-electric machine. 
 
 PAGE 
 ...125 
 ...72 
 
 Incandescent lamps 339 
 
 Inclination 34 
 
 Induction 66, 92-103 
 
 induced by the magnet- 
 ism of the earth 297 
 
 Induction coil, 301 ; Ladd's, 304 ; 
 
 experiments with 308 
 
 Induction machines, 125 ; magneto- 
 electric 245-264 
 
 , mutual and self 284 
 
 , statical 192 
 
 Inductive capacity 137 
 
 embarrassment 378 
 
 Insulating stool 128 
 
 Insulation 68 
 
 Insulators 375 
 
 Intensity 44 
 
 Iron, passivity of 187 
 
 Isoclinic lines 49 
 
 Isodynamic lines 46 
 
 Isogonic lines 46 
 
 Jablochkoff lamp, the 338 
 
 Joule's law 241 
 
 Kinetic energy. 81 
 
 Lane's jar 312 
 
 Leclanche cell 188 
 
 Lenz's law of current induction 292 
 
 Leyden jar 132, 152, 309 
 
 , experiments with. . 140, 308 
 
 Light, action of magnetism on. 404, 406 
 
 , electro-magnetic theory of. . 403 
 
 Lightning 158-160 
 
 . conductor 161 
 
 Linear conductors 194-196 
 
 Liquids, effect of the magnet on. ... 21 
 
 Loadstone n 
 
 Local action 191 
 
 Luminiferous ether 402 
 
 Luminous rain 160 
 
 Magnet, effect of current on 168 
 
 equivalent 245 
 
 Magnetic armatures 24 
 
 attraction 29 
 
 axis 12 
 
 charts 46 
 
 curves 12 
 
 elements 34 
 
 equator 49 
 
 field... 13, 14 
 
 force, line of 13 
 
 hammer 283 
 
 induction 17 
 
 intensity 34 
 
 magazine 23 
 
 meridian 34 
 
 needle, 15 ; variations of. 52 
 
 Magnetic parallels 49 
 
 polarity n 
 
 poles of the earth 48 
 
 storms 57 
 
 tick. . . 272 
 
 variations 37 
 
 Magnetisation by magnets 25 
 
 by the galvanic 
 
 current 27 
 
 Magnetism 11-60 
 
 Ampere's theory of 268 
 
 chronology of. 59 
 
 effects of heat on 32 
 
 of rotation 321 
 
 terrestrial 33-58 
 
 theories of 57 
 
 Magneto-electric induction. .. .245-264 
 machine 
 
 3i. 353, 354, 359 
 Magneto-electricity ............... 319 
 
 Magnetometers, Gauss's ........... 45 
 
 Magnetoscope .................... 15 
 
 Magnets, action upon each other, 
 14 ; on soft iron by induction ____ 31 
 
 Magnets, affected by heat ......... 32 
 
 - , induction of currents by.. 319 
 Magnets, forms of ................ 23 
 
 - , horseshoe ............... 24 
 
 - , kinds of ................. n 
 
 - , natural ................. 24 
 
 - ; - , power of ................ ii 
 
 Mariner's compass ................ 40 
 
 -- : - , Thomson's ...... 42 
 
 Mass ................ '. ............ 75 
 
 Meidinger's cell ........ t .......... 190 
 
 Microphone ...................... 394 
 
 Morse's instrument ............... 370 
 
 Needle, variations of the .......... 52 
 
 Negative conductor ............ . . .118 
 
 - electricity ............... 62 
 
 -- potential ................ no 
 
 Neumann's theory of induction .... 292 
 
 Ohm's law ........................ 192 
 
 Paramagnetic bodies ........ 19, 20, 22 
 
 Pendulum, the electric ........ 61, 343 
 
 Photophone ...................... 399 
 
 Pile, Volta's ...................... 178 
 
 - , Zamboni's dry .............. 178 
 
 Plante's cell ...................... 400 
 
 Plate machine .................... 118 
 
 Points, effect of, in electric dis- 
 
 charge ......................... 127 
 
 Polarisation, electro-static ......... 93 
 
 181 
 
 -, galvanic, 
 magnetic . 
 
 n, 15 
 
 Polarised light, action of magnet- 
 ism on 406 
 
 Pole unit ; 45, 169 
 
 Poles, galvanic 181 
 
 , magnetic n, 15 
 
410 
 
 ELECTRICITY. 
 
 PAGE 
 
 Positive electricity 62 
 
 potential no 
 
 Potential 103-117 
 
 Prime conductor 117 
 
 Proof-plane 88 
 
 Pyro-electricity 72 
 
 Quantity, electric 83-91 
 
 Reiss's telephone 391 
 
 Relay 383 
 
 Replenisher 351 
 
 Residual charge 135 
 
 Resinous electricity 62 
 
 Resistance 
 
 165, 172, 173, 198, 200, 201, 202 
 
 Resistance box 213 
 
 coils 206 
 
 measurement of.. . .204-218 
 
 unit of 168 
 
 Resultant force 77 
 
 Return current 379 
 
 Rheostat 206 
 
 Roberts's cartridge 341 
 
 Sabine, Sir Edward, chart by 46 
 
 Saturation point 27 
 
 Selenium cell 399 
 
 Self-induction 284, 292 
 
 Semaphore 369 
 
 Sensitive state 318 
 
 Sheet-lightning 159 
 
 Siemens' armature 357 
 
 Single touch 25 
 
 Siphon recorder 389 
 
 Slipping receiver 398 
 
 Smee's battery 179 
 
 Solenoids 264, 295 
 
 Spark, electric 159, 309, 313 
 
 , photograph of.. 124, 159 
 
 St Elmo's fire 161 
 
 Statical electricity 61-73 
 
 system of units 76 
 
 Storage of energy 400 
 
 Telegraph, Cooke and Wheat- 
 stone's 387 
 
 Telegraph, electric 369-390 
 
 , Morse's 370 
 
 , submarine 376, 377 
 
 Telephone 390-398 
 
 exchange 397 
 
 Terrestrial electricity 155-163 
 
 magnetism 33-58 
 
 PAGE 
 
 Thermal current 236 
 
 Thermo-electric battery 238 
 
 diagram 243 
 
 pair 238 
 
 pile 241 
 
 Thermo-electricity 236-245 
 
 Thomson, Sir William, his com- 
 ! pass, 42 ; reflecting galvanom- 
 eter, 279 ; sawdust Daniell and 
 tray cell, 183; his replenish er... .351 
 
 Thunder >. 162 
 
 Topler's Holtz machine 352 
 
 Torsion balance 28, 84 
 
 Tourmaline, electrifications of. 71 
 
 Translation 386 
 
 Transmitting key 372 
 
 Tray cell 183, 184 
 
 Unipolar induction 299 
 
 Unit, absolute electrical 167 
 
 capacity 168 
 
 current 168 
 
 electro-motive force 168 
 
 , gravitation, of work 78 
 
 quantity 167 
 
 resistance 168 
 
 Units 74, 167-175 
 
 , electro-static system of 167 
 
 , electro-magnetic system of. . 169 
 
 of measurement 74 
 
 Vacuum tubes 314 
 
 Velocity 74, 141, 170 
 
 Vitreous electricity 62 
 
 Volta's electrophorus 122, 348 
 
 law of contact force 230 
 
 pile 178 
 
 Voltaic batteries 175-191 
 
 cell 175 
 
 electricity 175-191 
 
 P^r 175 
 
 Voltameter 224 
 
 Wallace- Farmer lamp 339 
 
 Water, decomposition of 223, 226 
 
 Wheatstone bridge 211 
 
 electric needle tele- 
 graph 387 
 
 Wilde's magneto-electric machine. .359 
 
 Wollaston's battery 179 
 
 Work, gravitation unit of. 78 
 
 Zamboni's dry pile 178 
 
 Zero potential no 
 
 THE END. 
 
 Edinburgh : Printed by W. & R. Chambers. 
 

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