THE MECHANICS 
 OF ELECTRICITY 
 
 . ' :".'. 
 
GIFT OF 
 Mrs* F.J.B. Gordeiro 
 
PUBLICATIONS BY THE AUTHOR 
 
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THE MECHANICS OF 
 ELECTRICITY 
 
 BY 
 
 F. J. B. CORDEIRO 
 
 AUTHOR OF 
 
 "THE GYROSCOPE," "THE ATMOSPHERE," "BAROMETRICAL 
 HEIGHTS," ETC. 
 
 NEW YORK: 
 SPON & CHAMBERLAIN, 123 LIBERTY STREET 
 
 LONDON: 
 
 E. & F. N. SPON, LIMITED, 57 HAYMARKET, S.W. 
 
 1915 
 
,!> 
 
 COPYRIGHT, 1915, 
 
 BY 
 
 c J. B. CORDEIRO 
 
 PINKHAM PRESS 
 BOSTON, U.S.A 
 

 PREFACE 
 
 When asked what electricity is, physicists a few years 
 ago would reply, "We do not know," and the inquirer was 
 made to feel that he had asked a foolish question. To 
 Maxwell, electricity itself seems to have been rather 
 an abstraction, and he occupied himself chiefly with 
 its effects, or the strains it produces in dielectrics. 
 To the ultra-Maxwellians who declare that "there is 
 no such thing as electricity," it is a disembodied spirit, 
 not necessarily connected with matter except in so far 
 as this is necessary to render its effects observable. 
 
 The general consensus of opinion at present is that 
 electricity is something. Lodge writes, "Electricity may 
 possibly be a form of matter it is not a form of energy. 
 We have nowhere asserted that electricity and the ether 
 are identical. If they are, we are bound to admit that 
 the ether, though fluid in the sense of enabling masses to 
 move freely through it, has a certain amount of rigidity 
 for enormously rapid and minute oscillatory disturbances. 
 Is the ether electricity then? I do not say so, neither do 
 I think that in that coarse statement lies the truth; but 
 that they are connected there can be no doubt." 
 
 Clausius surmised that electricity might be the ether, 
 and if we may judge from certain passages the surmise 
 amounted to a belief. This belief was, of course, not 
 based upon any direct proof, for that is hardly possible, 
 but was rather of the nature of an intuition. He seems 
 to have been alone in this opinion. 
 
 5 7 1 ; j 
 
vi PREFACE 
 
 The object of this book is to show that electricity and 
 the ether are identical. The ether is electricity and 
 electricity is the ether. It has been sought, through the 
 cumulative and corroborative evidence of the phenomena 
 to raise a presumption that amounts almost to a certainty. 
 
THE ETHER 
 
 Electricity not many years ago was classed as a force 
 of nature, of which there were a number of different 
 kinds, separate and distinct. These different natural 
 forces were given categorically as mechanical, electrical, 
 gravitational, magnetic, vital, cohesional, chemical, etc., 
 and, as the conception of force is intimately connected 
 with that of energy or work, there were as many different 
 kinds of energy. Heat was considered still another form 
 of energy, and light still another. 
 
 Eventually it was recognized that some, at least, of 
 these forms of energy were mutually convertible, and the 
 doctrine of the conservation of energy led to the view that 
 energy was a single entity, though capable of manifesta- 
 tion under a number of different forms. The next step 
 was that force under all circumstances was a single entity 
 essentially the same under whatsoever guise it might 
 present itself. It was recognized that in the universe 
 only two cardinal entities were observable, viz., matter 
 and force. The universe was seen to consist actually of 
 matter alone, albeit of many different kinds, and this 
 matter, or materies, was found to be indestructible and 
 non-reproducible. The doctrine of the conservation of 
 matter was founded by Lavoisier. 
 
 Now this matter was found to be capable of changing 
 its position in space, both absolutely and relatively to 
 other matter: in other words it was capable of motion. 
 And to effect this motion it was found that force had to 
 be applied directly to the matter. Whatever influenced 
 the motion of matter, whether by originating the motion, 
 
 1 
 
ELECTRICAL 
 
 &r: changing a,cpf coexisting motion, or stopping the motion* 
 was force. It was found that all matter offered a resistance 
 to having its condition of motion, or no motion, changed, 
 and this resistance to such a change was called inertia. 
 It was further found that although matter at rest was 
 dead, yet while in motion it carried a store of energy which 
 could be abstracted from it and transferred elsewhere, 
 while from the principle of the conservation of energy, 
 since it possessed only a certain definite store, its energy 
 was necessarily lessened by the exact amount which had 
 been abstracted. 
 
 The universe, therefore, consists of matter, either dead 
 or living, i.e., either at rest or in motion. And we may 
 define force as that which influences the motion of matter, 
 and thereby stores up energy in it, or abstracts energy 
 from it. Force implies change of motion and energy, and 
 vice versa. We must further recognize that a force cannot 
 impart motion, and consequently store up energy, unless 
 it acts directly on matter. It cannot act at a distance, as 
 was until recently supposed. A body cannot exert a 
 gravitational force upon another body through empty 
 space, nor an electrical action, nor a magnetic action, nor 
 an action of any kind. But it can and does exert such 
 actions through intervening, closely connecting matter 
 in other words through a medium. It will be further seen 
 that any action of a force upon matter must be of the 
 nature of a push, and that a force cannot drag or pull 
 matter into motion. The action must be directly towards 
 the body acted upon, not away from it. To sum up the 
 universe consists only of matter, plus force or motion or 
 energy, as we please. There are only two factors matter 
 and the three cognate entities, force, motion or energy, 
 which are only different expressions for a single under- 
 lying entity.* 
 
 * Ostwald has proposed, instead of recognizing only matter and 
 force, to recognize only matter and energy. Such a contention 
 is purely metaphysical and of no value. 
 
MECHANICS 3 
 
 It follows that in studying the action of bodies on each 
 other at a distance, we must, if we wish to understand them, 
 examine particularly the medium connecting them. For 
 we have seen that there must be throughout a direct 
 material connection between such bodies: otherwise no 
 action can take place. When we hear a sound from a 
 distant point we know that the action is transferred through 
 the air. There is a continuous material chain between us 
 and the sounding body. If there were a single break, or 
 interruption of matter, at any point, by even an infinitesi- 
 mal thickness, we should be unable to hear the sound. 
 There was a time when the necessity of a continuous 
 material connection for sound was not recognized. It 
 was supposed to act at a distance through nothing. 
 And only very recently has the necessity of a continuous 
 material connection, or medium, been recognized for all 
 actions electrical, magnetic, gravitational, etc. The 
 medium, by, and through which, all the more important 
 actions at a distance are carried on, is the Ether, and we 
 shall now examine this chief medium of the universe. 
 
 The ether, both in volume and mass, constitutes over- 
 whelmingly the greater part of the material universe. 
 The amount of ordinary gross matter, or matter which is 
 not ether, is almost infinitesimal in proportion, and yet it 
 is only within a comparatively few years that man has 
 become conscious of its existence. So far as we at present 
 know, it has only three properties. It may have many 
 more, but these, at least, are the only ones we have been 
 able to recognize. It is a fluid, i.e., all bodies move freely 
 through it, and it moves freely through the interstices of 
 all bodies. It moves freely through intermolecular spaces, 
 and even through intramolecular spaces. It penetrates 
 through molecules, but not through atoms: so that it 
 occupies all space with the exception of that occupied by 
 the atoms of gross matter. It is always under a strain, 
 or tension, exerting a very heavy pressure. It is capable 
 
4 ELECTRICAL 
 
 of compression and expansion, thereby varying its density. 
 It is therefore elastic. It possesses enertia, and is there- 
 fore matter. It is capable of propagating a disturbance, 
 thereby exhibiting in a combined form its two properties 
 of elasticity and inertia, since these two qualities are 
 necessary and sufficient for the transference of a dis- 
 turbance. It should be stated that it has been held, and 
 is even now held in some quarters, that the ether is devoid 
 of elasticity, i.e., incompressible. This was to explain 
 the seeming existence of transverse vibrations in this 
 medium. But such an explanation is self -contradictory. 
 If it were incompressible it could propagate no waves at 
 all. Further a fluid cannot execute transverse vibrations, 
 that being a property of solids. To meet this, it was 
 stated that it was not a fluid, but a kind of solid. Thus 
 its two manifest properties of fluidity and elasticity were 
 denied to explain a supposed property of transmitting 
 transverse vibrations a property which it has never 
 possessed and cannot possess. Even then the object is 
 defeated, for, by removing its elasticity, all possibility of 
 wave propagation is cut off. We shall see later on that the 
 ether is capable of simulating transverse vibrations, but 
 no true transverse vibrations are possible. 
 
 We have said that the ether is matter, but it differs 
 most extraordinarily from ordinary gross matter. While 
 ordinary matter is built up of discrete units molecules 
 and atoms the ether seems to be a continuum. It is 
 matter, but of a very simple kind; or matter reduced to 
 its simplest terms. Its fluidity and continuity are not 
 so much properties as negations of properties, since the 
 discrete and solid and liquid properties of ordinary matter 
 are highly differentiated conditions from a simple, ele- 
 mentary condition. Its elasticity may possibly be a con- 
 comitant and necessary adjunct of its inertia, so that 
 these two properties may possibly represent a single 
 fundamental and underlying property. Hence the ether 
 
MECHANICS 5 
 
 may be matter in its simplest form, from which all gross 
 matter has been differentiated, and the single fundamental 
 property of all matter may be simply inertia. 
 
 The ether has no internal friction, or viscosity, or any 
 friction at all, a property which all gases possess; but since 
 this property in gross matter is due to its molecular 
 structure, it is naturally wanting in a continuum. A fluid 
 without any friction or viscosity is called a perfect fluid, 
 and hence the ether is the only perfect fluid. Differing so 
 extraordinarily from gross matter, we may expect that 
 its elasticity and inertia will differ extraordinarily from 
 the corresponding properties in gross matter. And we 
 find that such is the case. It is impossible to measure 
 these quantities directly, but we may judge indirectly 
 from their effects what the amount must be. The ratio 
 of the elasticity to the density, or inertia, has been de- 
 termined with some degree of exactness. In any medium, 
 longitudinal waves, which are waves of a peculiar type, 
 are propagated with a velocity which is equal to the square 
 
 root of the elasticity divided by the density, or V = +l (1). 
 
 Now it is possible for a fluid medium to tra n smit dis- 
 turbances of two totally different types, viz., waves with 
 longitudinal vibrations, and what are known as electro- 
 magnetic waves, with which we shall later on become famil- 
 
 E 
 iar. The ratio ~ has been determined by measuring the 
 
 velocity of electro-magnetic disturbances in the ether, on 
 the assumption that Equation (1) holds for such dis- 
 turbances. Since the intimate mechanism of such waves 
 was not then known, such an assumption was hardly 
 warranted. There was no doubt that Equation (1) held 
 for longitudinal waves, but it was not at all certain that 
 electro-magnetic waves might not be propagated with a 
 totally different velocity. However, it turns out, as we 
 shall see, that all disturbances are propagated with prac- 
 
6 ELECTRICAL 
 
 tically the same velocity in an isotropic fluid medium. 
 The square root of our ratio is something like 3 X 10 10 centi- 
 meters per second, or about 186,000 miles per second. This 
 shows that the pressure, or elasticity, of the ether must 
 be extraordinarily high. What the actual values of the 
 two quantities are, we do not yet certainly know, though 
 we may make a guess. We may attempt a rough 
 estimate from two phenomena magnetism and cohesion. 
 We shall see that magnetic lines of force are linear vortices 
 in the ether, in the interior of which the pressure is con- 
 siderably less than that of the general ether, and that 
 magnetic "attraction" between two bodies is due to this 
 general pressure striving to close the partial (or complete) 
 vacuum. If we could obtain an absolute vacuum, then 
 the force of such an attraction would be a measure of the 
 general, or normal, ether pressure, and by Equation (1) 
 we could obtain the density. Now the greatest magnetic 
 force which it has as yet been possible to obtain, is some- 
 thing like 2000 pounds to the square inch, or roughly a ton 
 to the square inch. The question arises, "How much of 
 an absolute ether vacuum does this represent?" We shall 
 see that under the enormous and sudden voltages em- 
 ployed in generating electro-magnetic waves, it is quite 
 possible that actual ether vacua are attained in the axes 
 of the magnetic lines of force, but in the very moderate and 
 steady voltages employed in the lifting experiment de- 
 scribed above, it is improbable that any great rarefaction 
 can be obtained. Still we may say that it is probably 
 1^0 f a perfect vacuum, or something of that order. 
 When we say "of that order," we mean that it is probably 
 something like that, although it may vary by JQ either way. 
 If we could be tolerably sure of estimating its value within 
 a tenth, that would be sufficient. Assuming that a force 
 of 2000 pounds to the square inch corresponds to about 
 of a perfect vacuum, we should have, as the general 
 
MECHANICS 7 
 
 pressure of the ether, about 2,000,000 pounds to the square 
 inch, which is 1.4 X 10 11 dynes per square centimeter. This 
 would make its density, by Equation (1), something like 
 10~ 10 that of water. This is probably somewhere near 
 the truth showing that the ether has a most extraordinary 
 tenuity, while exerting an enormous pressure. The pres- 
 sure is intelligible when we reflect that it belongs to a 
 single continuous mass, bounded only by the confines of 
 the universe. This great resistance of the ether to com- 
 pression has sometimes been referred to as its rigidity, 
 which is manifestly a misuse of terms. The ether, being 
 a perfect fluid, has, of course, no rigidity. A fluid under 
 a pressure of a thousand pounds is no whit more rigid than 
 when under a pressure of one pound. 
 
 We may consider then the density of all gross matter, 
 or the density of all atoms, as roughly something like 
 10 10 times that of the ether. Taking the view that the 
 ether is the ground stuff out of which all forms of gross 
 matter have been elaborated, it is evident that it must have 
 been by some process of condensation, though under what 
 conditions such an enormous condensation was effected, 
 it seems difficult to imagine. If this view is correct, it is 
 quite intelligible how the numerous infinite properties 
 ascribed by the schoolmen to atoms, may be derived, viz., 
 infinite hardness, unbreakableness, uncrushableness, in- 
 finite elasticity, infinite smoothness, and what not. 
 
 Assuming that the phenomenon of cohesion is due to the 
 close co-aptation of the surfaces of atoms, which are thus 
 pressed together by the total pressure of the ether, we 
 find, for steel, that the cohesion or tenacity is something 
 like 100 tons to the square inch. For unspun silk, which 
 is the strongest substance we are acquainted with, it is 
 nearly three times as much. This changes our estimate 
 but little, so that we might consider the pressure of the 
 ether as somewhere between 10 10 and 10 11 dynes per 
 square centimeter, and its density as somewhere between 
 
8 ELECTRICAL 
 
 10- 10 and 10- 11 that of water, or of atoms in general. 
 These estimates are to be considered rather as a minimum, 
 and the actual values may be somewhat more. 
 
 Lodge, starting from Lord Kelvin's vortex theory of atoms, 
 argues that as they occupy only a portion of the space bounding 
 a body, and as they are the only material parts of the body, the 
 density of the ether, which is a continuum, must be much greater 
 than that of gross matter. He considers that the vortex rings 
 which constitute the atoms have the identical density of the 
 ether, but, as they are few and far between, the net density, as 
 compared with the ether, is almost infinitesimal. According to 
 his reckoning the pressure is 10 33 dynes per square centimeter, which 
 corresponds to an amount of energy equal to 10 33 ergs in every 
 cubic centimeter. The density is 10 12 . Taking only a cubic 
 millimeter of space, the ether energy in this small space he states to 
 be "Equal to the energy of a million horse-power station working 
 continuously for forty million years." And there is, in a cubic 
 millimeter, "A mass equivalent to what, if it were matter, we should 
 call 1000 tons." This estimate is too low, for the density of a 
 vortex ring is not that of the general ether, but much less. 
 
 It is hardly necessary to say that the vortex theory of atoms 
 is not a very safe hypothesis to start from, even though Lodge 
 argues that "It is so good that it deserves to be true." It is doubt- 
 ful if Lord Kelvin himself ever considered it more than a "curious 
 speculation." We shall show later on that gross matter must be 
 very much more dense than the ether. 
 
 In our further study of the ether, it is evident that we 
 can only become aware of the existence of this medium 
 through its motion. Dead ether, or ether at rest, can in 
 no way affect our senses, either directly or indirectly; so 
 that we are now forced to inquire into what kinds of motion 
 are possible in such a material as we know the ether to be. 
 Generally, we may say there is only one kind of motion 
 a motion of certain portions relatively to others, or a 
 streaming or flowing of certain portions past others, con- 
 stituting ether currents. Whether the ether ever streams 
 over great distances, as seems indicated by the immense 
 spiral nebulas, where gross matter may be in the process 
 of condensation and worlds are being formed, lies beyond 
 
MECHANICS 9 
 
 our present scope. We shall confine ourselves to cases 
 where it flows from a point of higher pressure to a point 
 of lower pressure over finite distances, as in conductors: 
 and over infinitesimal distances in the free ether. In the 
 free ether there may be a flow over very short distances 
 from a point of higher pressure to one of lower pressure, 
 consisting of a surging backward and forward between a 
 condition of compression to one of rarefaction. Such 
 short alternating ether currents are the essence of all 
 longitudinal waves, and we know that such waves must 
 exist in a fluid like the ether, possessing both elasticity and 
 inertia. Further linear vortices may exist in such a 
 medium, consisting of closed current sheets surrounding 
 an axis of lesser density than the general ether. And such 
 linear vortices will persist indefinitely, since there is no 
 friction in the ether between its different parts. The 
 excess pressure of the external ether is supported by the 
 centrifugal force of the rapidly rotating current sheet. 
 Or, designating the outward centrifugal force of the cur- 
 rent sheet per unit of surface by/, and the interior pressure 
 by Pi, while the external, or normal pressure isP,/ =P Pi. 
 These linear vortices will always form closed curves, for 
 while it is conceivable that the two ends of a vortex fila- 
 ment might be closed by two atoms, or by two continuous 
 surfaces of atoms the only bodies impermeable to the 
 ether we do not know certainly of any such instances. 
 
 There are further two ways in which a disturbance may 
 be propagated in such a medium, viz., by longitudinal 
 waves of the well-known form, and by the translation 
 through the ether of such vortex rings as we have just 
 considered, constituting what are known as electro- 
 magnetic waves. 
 
 The above varieties of motion are the only ones possible 
 in such a medium, and we may tabulate them as follows : 
 
 1. Simple currents, where the ether moves in an effort 
 to relieve an increased pressure, driven, as we say, by an 
 
10 ELECTRICAL 
 
 electro-motive force: or where the ether continues in 
 motion from its own inertia, without any driving force and 
 meeting with no resistance, such as is the case with the 
 current sheets in our vortex rings. 
 
 2. Longitudinal waves, which are propagated by a 
 series of regularly alternating currents in the direction of 
 the wave. 
 
 3. Electro-magnetic waves, which consist of a spread- 
 ing out of vortex rings through space. 
 
LONGITUDINAL WAVES 
 IN THE ETHER 
 
 We shall first consider longitudinal waves in the ether, 
 which, since their perfect analogy is found in air waves, 
 have happily been completely studied. Since a fluid 
 
 medium, whether a gas or the 
 ether, possesses inertia, any 
 thrust against it will be resisted 
 just as much as if it were a 
 solid. The reaction will be 
 p. x i equal and opposite to the action. 
 
 Since it is elastic, the medium 
 
 will be compressed between these two forces acting in 
 opposite directions; and since it is free to move, it will 
 move also in the direction of the force. The action of the 
 thrust is therefore double. It sets the medium in motion 
 and at the same time compresses it, in each process doing 
 work and thereby storing up energy in the medium. The 
 first kind of energy is called kinetic energy and the energy 
 of compression is called potential energy. This latter 
 form of energy is also, in the last analysis, kinetic, or due 
 to motion, though this motion is concealed and not as 
 manifestly evident to the senses. Thus the energy of a 
 compressed gas, or its potential energy, is due to the motion 
 of its molecules, for we have seen that energy and motion 
 are inseparable. Likewise the pressure of the ether indi- 
 cates a huge store of potential enefgy, which must be due 
 to motion of some sort, though of the nature of this 
 motion, we are as yet in complete ignorance. It may 
 
 11 
 
12 ELECTRICAL 
 
 possibly be due to extremely minute vortices pressed 
 together, their current sheets moving with the standard 
 velocity of the medium, in which case the ether would be 
 a discrete structure. Such a structure would enable it 
 to have very great energy (pressure) with little mass, for 
 energy consists of two factors mass and motion. Beyond 
 the normal pressure, at some point which we might call 
 the critical pressure, it might be possible to break down 
 these vortices and condense them into non-vortical gross 
 matter. But every indication seems to point against a 
 discrete structure, and rather to a continuum, in which 
 case the energy may possibly be due to a general pulsation 
 throughout its mass. We shall consider the ether a con- 
 tinuum, avoiding all speculation as to its internal motion. 
 Let us suppose our medium divided off into laminae 
 of equal thickness, 1,2, 3, 4, as represented in Fig. 1. Let 
 us further suppose that lamina 1 has been thrust by a force 
 to the right, thereby having imparted to it the two forms 
 of energy described above. It is evident that these two 
 forms of energy will be limited at the first short interval 
 of time to the immediate vicinity of the thrust, but as 
 time goes on the changed portions of the medium will 
 shift their positions and the disturbance will travel along 
 as a wave. The lower portion of Fig. 1 indicates the 
 instantaneous position and condition of the laminae after 
 a certain interval of time has elapsed. The disturbance 
 has extended to the outer boundary of 4, but not beyond. 
 Let Vi, v z , v s , Vt, be the velocities of the laminae at any 
 instant, and Ci, c 2 , c s , c*, the distances through which 
 they have been compressed. Now every lamina opposes 
 to compression the original pressure it possessed, which is 
 the normal pressure of the medium, and which we will 
 designate by P, plus the resistance of its inertia. Or the 
 
 compressional force is P +m , where m is the mass of 
 
 dt 
 
 the lamina. The work of compression will therefore be 
 
\dc. 
 
 MECHANICS 13 
 
 On lamina 4, this work will be 
 
 P + m jdc* = PC 4 4- ^- , where v* represents the 
 dt ' 2 
 
 velocity of the lamina at the instant we are considering, 
 with corresponding expressions for the other laminae. 
 Hence, designating the potential energy at any point, at 
 any instant, by W, and the kinetic energy by T, we have 
 W = PC + T. Or the potential energy is equal to the 
 normal pressure into the distance the lamina has been 
 compressed, plus its kinetic energy. In other words, the 
 kinetic energy of a lamina is equal to the work of compres- 
 sion done upon it in excess of the work done by the normal 
 pressure. The wave set up before such a single thrust is 
 known as a compressional, or positive, wave. It travels 
 along with a uniform velocity, compressing and moving 
 along successively all parts of the medium in its path, 
 and leaving them at rest, but set down at a certain definite 
 distance from their original position, viz., the distance, or 
 amplitude, of the thrust. 
 
 Referring again to Fig. 1, it will be seen that while the 
 medium to the right, against which the thrust was made, 
 transmits a compressional wave with uniform velocity 
 in the direction of the thrust, the medium to the left, away 
 from which the thrust was made, will equally transmit 
 an expansional wave, towards the left. And by the same 
 reasoning as before, the work of expansion at any point 
 will be equal to the kinetic energy at that point, plus the 
 work done against the normal pressure during the ex- 
 pansion. In either case, we have the formula W = PC -f T. 
 
 If we thrust the lamina 1 forward and backward, 
 always through the same limits, we have what is called a 
 vibrational wave. After one complete excursion forward 
 and back, it is evident that no work will have been done 
 
 by the normal pressure, or dc = o. Hence the term PC 
 
14 
 
 ELECTRICAL 
 
 vanishes, and for a complete or finished vibration, the 
 total potential energy of the wave will be equal to the 
 total kinetic energy. The average kinetic energy, or the 
 average potential energy, is half of its maximum value. 
 Hence the whole energy, if represented by a single form, 
 would be equal to the maximum value of that form dis- 
 tributed throughout the whole wave. As *Lord Rayleigh 
 puts it "In a progressive wave of any type one-half of the 
 energy is potential and one-half is kinetic. The total 
 energy of the wave is equal to the energy derived rom 
 compressing its whole mass from its minimum to its 
 maximum density, or to the energy of the whole mass 
 moving with its maximum velocity." 
 
 This is an important general principle in nature, viz., 
 that where no hindrance is opposed, or where two kinds 
 of energy are free to change or flow into each other, 
 they always become equal. The wave contains a certain 
 definite quantity of energy divided into two parts. The 
 potential energy always strives to release itself into 
 kinetic energy, but when an equalization has been effected, 
 no more potential energy can flow into kinetic energy, 
 and vice versa, since no form of energy can rise above its 
 source. 
 
 The intimate structure of a longitudinal vibrational 
 wave is shown in Fig. 2. 
 
 * Lord Rayleigh. Theory of Sound. Par. 245. 
 
MECHANICS 15 
 
 The equal laminae in the lower part represent the 
 medium at rest, and the upper part shows the transposition 
 and compression of these same laminae at a certain instant 
 during the passage of a wave The dotted curve repre- 
 sents graphically the density at different points, the com- 
 pression or rarefaction being proportional respectively to 
 its height above or below the line A B. The positions of 
 the prong of a tuning fork corresponding to the several 
 points of the wave are shown below. The laminae in the 
 forward or rarefactional part of the wave are moving 
 backward, while the laminae in the rearward half are all 
 moving forward, as indicated by the small arrows. The 
 distance a, or the extreme distance which a particle moves 
 on either side from its position of equilibrium, is called the 
 amplitude of the wave. The extreme lamina/ 1 has just 
 come to rest and its normal density, after swinging forward 
 through the amplitude a, and is just preparing to swing 
 back. Its subsequent positions relatively to its position 
 of equilibrium, and its density, are shown by the successive 
 laminae in the rear. The disturbance is supposed to be 
 progressing towards the right, as shown by the large arrow, 
 having originated at some point to the left. But it is 
 possible for a wave to proceed outward from a disturbance 
 with its compressed parts moving backward, and its rare- 
 fied parts moving forward. Thus if we had a membrane 
 containing a compressed gas, with a vibrating body in the 
 interior giving off waves with the compressed halves 
 moving outward, we should expect the waves leaving its 
 surface to have the motions of their respective halves 
 reversed. For the compressed half, when passing through 
 the membrane escapes into a rarer medium and expands 
 suddenly, while the expanded half moving backward, 
 towards the membrane, does so against a higher pressure 
 and should be compressed. On the other hand, if the 
 pressure within the membrane is lower than that of the 
 outside medium, the motion of the respective halves 
 
16 ELECTRICAL 
 
 should be unaltered. In both cases the waves proceed 
 regularly outward, away from the disturbing body, but 
 with this peculiar difference, viz., that the directions of 
 the motion of their compressed and rarefied halves are 
 reversed. We shall, conventionally, define a wave with 
 its compressed portions moving away from the disturbing 
 source, as a positive wave; and a wave with its condensed 
 parts moving towards the disturbing source as a negative 
 wave. A single compressional wave, due to a unidirec- 
 tional thrust (explosion) has sometimes been called a 
 positive wave, and a single unidirectional expansive wave 
 has accordingly been termed a negative wave. Our 
 definition above, however, applies only to bidirectional, 
 or vibratory, waves. 
 
 If we should expand one-half of a wave from its original 
 
 length - , where / is the length of the wave, to its actual 
 
 length in the expanded half, which is - + 2a, and should 
 likewise compress the other half from its original length 
 
 - to its actual length 2a, the energy so expanded would 
 
 clearly be equal to the compressional or potential energy 
 of the wave. The work of expanding - to \- 2a is, since 
 
 JL JL 
 
 the pressure is inversely as the volume, or p = P 
 
 l+2c 
 where c is the expansion, W 
 
 Developing the logarithm by Maclaurin's theorem, and 
 neglecting higher powers of a, since the amplitude is 
 
 4 Pa 2 
 supposed to be small, we have W = 2 Pa -\ -- . 
 
MECHANICS 17 
 
 Likewise the work of compression, from a length -to a 
 
 length 2a, isW=2Pa + . The total potential 
 
 energy in the wave is, therefore, . Considering 
 
 a unit cross section of the wave, its mass is Dl, where D 
 is the normal density of the medium. Let v be the average 
 velocity of a lamina during a complete vibration. Then 
 since a lamina traverses a distance 4a while the wave 
 progresses a wave length, /, and designating the velocity 
 
 of the wave by V, we have v = . The total kinetic 
 
 energy of the wave is ^"~ = . But this must be 
 
 equal to the total potential energy. Hence V =^l _. 
 
 There is a difference between a gaseous medium and the 
 ether in that the molecules take up a part of the space 
 and the compression is not actually measured by the ratio of 
 
 2a to - . The formula for a gas becomes V = */ k , 
 
 where k is the ratio of the two specific heats. (See "The At- 
 mosphere," by the author.) The motion of the molecules 
 of gross matter constitutes the phenomenon of heat, and 
 since the ether, as far as we know, is a continuous medium, 
 such a thing as heat is foreign to its nature. The ether 
 can be neither hot nor cold, although it transmits vibrations 
 from gross matter which render other bodies hot or cold. 
 
 The formula V = ^ i s an important one for all media. 
 
 It must be remembered that it holds only where the am- 
 plitudes are so small that powers above the square may be 
 
18 ELECTRICAL 
 
 neglected. Where the amplitudes are so great that higher 
 powers cannot be neglected, the velocity of propagation of 
 a disturbance may be very much greater. Thus in the air, 
 violent unidirectional disturbances, such as explosions, 
 may be propagated with very high velocities, the velocity 
 increasing with the intensity and suddenness of the thrust. 
 The same is true of the ether, and the standard velocity, 
 
 V =3 X10 10 1 , holds good only for longitudinal waves 
 
 sec. 
 
 of small amplitude. Disturbance can be propagated with 
 a much higher velocity, although not with a lower velocity 
 in the case of longitudinal waves. 
 
 We have said that the ether is without viscosity: it is 
 frictionless. But when a stream or current of ether 
 impinges upon an impermeable surface, it must exercise 
 a pressure upon such a surface. It flows freely between 
 and through molecules, but not through atoms. The space 
 occupied by atoms is not occupied by ether, and the ether 
 must flow around such bodies. 
 
 We shall assume that the pressure exerted on a surface 
 S is proportional to the density of the ether current, and 
 to the velocity with which the current is flowing, so that 
 we may write p = vDS. When a current of ether is 
 flowing in a conductor it has to make its way past the 
 atoms and thus exerts a pressure upon them. A counter 
 pressure is equally exerted upon the current which is 
 thus resisted to this extent. Let us call the electro-motive 
 force, or the driving pressure, or the pressure gradient, E. 
 The current starts from zero velocity and rapidly increases 
 its velocity. Calling the mass of ether which flows 
 through a cross section of the conductor in unit time m, 
 
 //7J 
 
 we have E p = E vDS = m . The current will 
 
 dt 
 
 increase until the resulting driving force, or the accelera- 
 tion becomes zero. When this point is reached, the 
 
MECHANICS 19 
 
 velocity of the current becomes uniform. The condition 
 for such a state is E = vDS. Let us call the back pressure, 
 or resistance, when unit mass of ether is flowing in unit 
 time, R. The value of R will naturally depend on the 
 total atomic surface opposing the flow, and will be differ- 
 ent for different substances. We can write our condition, 
 
 ^ 
 
 then, E = vDR or vD = . But vD is the mass or 
 
 R 
 
 quantity of ether which is flowing through a cross section 
 of the conductor in unit time, and this measures the 
 current strength. Calling the quantity of ether flowing 
 
 r? 
 
 in unit time C, we have C = , which is Ohm's law. 
 
 R 
 
 This law confirms exactly, experimentally, our assumption, 
 then, that p = vDS. Ohm's law not only states the 
 axiom that when a current is constant, or flowing with a 
 uniform velocity, it has no acceleration, but it also states 
 that the resistance is proportional to the quantity or mass 
 of ether flowing in unit time. The resistance thus meas- 
 ures a velocity as well as a density. Theoretically the 
 condition of equilibrium would never be reached. Prac- 
 tically it is reached in a very short time. The driving 
 force of the current does work in overcoming the re- 
 sistance offered by the atomic surfaces. In overcoming 
 this resistance it sets the atoms into vibration about their 
 positions of equilibrium, with the result that the energy 
 of the current, which is EC, becomes transformed into 
 kinetic energy of the atoms (molecules). In a fluid con- 
 ductor (mercury), this pressure results in visible motion, 
 as seen in electro-capillary phenomena. C representing 
 the mass of ether flowing in unit time, the atomic kinetic 
 energy, or the heat developed, is proportional to ECt, 
 which is known as Joule's law. 
 
 Returning to Fig. 2, it is evident that the velocity of 
 the flow of the expanded ether in the wave must be 
 
20 ELECTRICAL 
 
 slightly greater than that of the compressed ether. It is 
 further evident that the average velocities in the two 
 halves must be inversely as the densities. Thus the con- 
 densed ether in the compressed half flows a little more 
 slowly than the rarer ether in the expanded half; but as 
 the pressure exerted upon a surface is proportional to 
 the density and the velocity, we are led to the important 
 result that the average pressures exerted upon a surface 
 are the same in both halves. 
 
 Let us suppose that a particle denser than the ether 
 is in the path of a longitudinal wave. As the condensed 
 half of the wave sweeps over it it will urge the particle 
 forward. Let v be the average velocity of the ether 
 particles, and v l the average velocity of the denser particle 
 during the passage of the condensed half of the wave. 
 Evidently the denser particle will lag behind the ether 
 particles. We shall assume that Dv = Z)V, where D 
 and D 1 are the respective densities, or the average velocities 
 will be inversely as the densities. Let 5 be the distance 
 which the denser particle has moved, while an ether 
 particle has moved 2a, thus completing a half wave. If 
 M is the mass of the denser particle, and m the mass of an 
 equal volume of ether, then Ms = 2am. Their distance apart 
 
 at the end of a half swing will be, therefore, '* 
 
 M 
 
 Likewise, on the backward swing, the denser particle and 
 a corresponding mass of ether, starting from rest, will, 
 at the end of the swing be the same distance apart. Or 
 
 the denser particle always lags a distance 2 a 
 
 behind the corresponding ether particle. The time taken 
 
 by each half wave to clear the ether particle is , while 
 
 2V 
 
MECHANICS 21 
 
 the time taken by the compressed half to clear the denser 
 
 particle is -, and the time taken by the 
 
 2V MV 
 
 expansional half to clear the denser particle is 
 
 l_ la (Mm) 
 
 2V MV 
 
 The current pressure, therefore, which is D^, acts for a 
 shorter time upon the denser particle during the passage 
 of the condensed half, and for a longer time during the 
 passage of the expanded half. It is evident that the 
 pressure gradient which is equal on both sides and acts 
 for the same time can have no effect. The net result, 
 then, is that a backward pressure, equal to DV, acts for 
 
 4a(M m) , . 
 
 a time equal to during the passage of every 
 
 MV 
 
 complete wave. This will be equivalent to a backward 
 acceleration, acting continuously, of 
 
 Dy 4a(M m) 
 ~T MV 
 
 where t is the time of a complete vibration. 
 
 Dv 4a (Mm) 16a 2 (Mm) 4a (Mm) 
 
 _ , j_) = iJ'O . 
 
 MVt I Mt Ml 
 
 Measuring the density of the ether by its pressure, P, 
 
 ,,dv P16a* (Mm) E(Mm) 
 
 we have M = . - ' = -, 
 
 dt I Mt Mt 
 
 where E is the total energy in a complete wave per unit 
 
 cross section. We have already seen that E = P . 
 
22 ELECTRICAL 
 
 If M < w, the acceleration becomes reversed, and we 
 see that a body less dense than the ether will be urged 
 forward in the direction of the motion of the condensed 
 half. This is evident, since, in this case the compressed 
 half will act upon the body longer than the expanded half 
 
 by a time equal to - .. If the particle consists 
 
 MV 
 
 of matter very much denser than the ether, as is the case 
 
 with all gross matter, the fraction, - , becomes prac- 
 
 M 
 
 77 
 tically unity, and the force will be . Every atom of 
 
 gross matter, therefore, which sends out positive longi- 
 tudinal waves, and these are the only kind of longitudinal 
 waves which atoms are capable of radiating, will attract 
 
 ^ 
 every other atom with a force S, where 5 is the surface 
 
 of the attracted atom. 
 
 If the waves radiate from a spherical surface Si, Si 
 
 measures the flow of energy from its surface in unit time, 
 and this flow through all other concentric spherical sur- 
 faces remains constant. Hence the attraction of such a 
 body on all spherical shells surrounding it is constant, 
 and equal to the total outflow of energy in unit time. 
 
 Since every atom in an attracting body sends out such 
 waves, the total attraction will be proportional to the 
 mass of the body, and since the total surface of the atoms 
 acted upon in the attracted body is proportional to the 
 number of atoms, or to its mass, the total attraction is 
 
 MM 1 E 
 proportional to . 
 
MECHANICS 23 
 
 Since the total wave energy flowing through any 
 spherical surface, surrounding the disturbing source, 
 in unit time, remains constant, the wave energy at any 
 point, or its intensity per unit of surface, varies inversely 
 as the square of the distance. Hence, the attraction of a 
 
 MM 1 E 
 body on a distant body is proportional to . , where 
 
 r is the distance between them. This is Newton's law. 
 We have kept the term attraction because it is sanctioned 
 by long usage, but it must be remembered that in nature 
 there is no such thing as a drawing of bodies together. 
 It is a "vis a tergo," or a pushing together, the forces being 
 applied to the surfaces of the atoms. 
 
 If the attracted body is dead, i.e., not sending out any 
 waves, it can exert no attraction, but is simply attracted. 
 If both bodies are alive radiating waves their attrac- 
 
 MM 1 E .MM 1 E l 
 tions on each other are respectively . and . . 
 
 Where E = E 1 and t = t l , the mutual attractions are 
 equal. Both the wave energy sent out by a vibrating 
 atom, and the action of such waves on an atom are pro- 
 portional to their surfaces, or cross sections. Whether 
 all atoms radiate waves of the same frequency and con- 
 taining the same amount of energy per unit of radiating 
 surface, we do not know. If their motion (vibration) is 
 derived from the internal motion of the ether, as seems 
 possible, such would be the case. We should have a 
 case, then, analogous to the Brownian vibrations seen in 
 small material particles suspended in a liquid, where the 
 invisible internal motion of the molecules becomes visible 
 in the larger particles. We shall see that the motion to 
 and fro of an atom results in the radiation of an electro- 
 magnetic, or heat, wave, and a longitudinal wave at right 
 angles to it. If such stronger longitudinal waves are the 
 
24 ELECTRICAL 
 
 only ones participating in attraction we should expect the 
 attraction to be a function of the temperature of a body, 
 so that a body at the absolute zero would be attracted 
 but could not attract. But of all these matters we are in 
 complete ignorance. It is to be remarked, however, that 
 the energies radiated by the two kinds of waves are not 
 equal and that with increasing frequencies of the vibrations 
 the energy passes off almost exclusively in electro-magnetic 
 waves. 
 
 Where M<C m, we have seen that there is repulsion 
 instead of attraction. Since in this case, the bodies acted 
 upon have a density less than that of the ether, their 
 inertia is very slight and they are driven almost imme- 
 diately to their limiting velocity, which is that of the wave 
 itself. Comets' tails and the corona of the sun must 
 represent some form of extremely tenuous matter, since 
 they are repelled with the velocity of light. 
 
 If the attracted body is moving, then a Doppler effect 
 will result. If moving against the waves, then more 
 waves will pass it in a given time, and the frequency will 
 be raised factitively. t will become relatively smaller 
 and the attraction increases. If the attracted body is 
 moving with the wave, for the same reason the attraction 
 will become less. But the frequency of all longitudinal 
 waves in the ether is so extremely high, that a few miles 
 more or less of relative velocity is wholly negligible. The 
 greatest velocities so far observed for dense matter among 
 the heavenly bodies hardly exceeds 200 miles per second. 
 Compared with the enormous velocity of wave propaga- 
 tion, viz., 186,000 miles per second, this is insignificant. 
 
 We have seen that the attraction exerted by a wave 
 
 E'er 
 
 upon an atom is -- . Since we find that different kinds 
 
 of atoms have different "weights" or are acted upon more 
 strongly by the same waves, they must have different 
 
MECHANICS 25 
 
 average cross sections. A priori it would be highly im- 
 probable that all atoms should have the same average 
 cross section. Hence, we are justified in inferring that, 
 since their atomic weights vary through a range of from 
 1 to 238, their average cross sections must vary through 
 a like range, and their linear dimensions must vary through 
 a range of from 1 to 16. But we are not justified in infer- 
 ring anything as to their size or shape, or anything else 
 beyond this. 
 
 Possibly, if it is true, as is generally believed, that in 
 the crystalline state, atoms arrange themselves symmetri- 
 cally, and if it were found that crystals weighed more when 
 pointed in one direction than in another, we might infer 
 that their dimensions in one direction were greater than 
 in another. But nothing of the sort has ever been found, 
 or even tried. 
 
 We may sum up the results so far obtained as follows: 
 The attraction and repulsion of bodies at a distance, such 
 as is everywhere observed, can only take place through a 
 medium. Without a medium, no action at a distance 
 would be possible. Various actions gravitational, elec- 
 trical, magnetic, etc. are effected without the interposi- 
 tion of gross matter, and it is certain that these actions 
 are transmitted through the ether. Motion can only arise 
 from motion: hence these actions are transmitted by 
 motion of some kind in the ether. All motions that are 
 possible in a medium do occur. The only possible motions 
 in a fluid medium are three. 
 
 1 . Translational motion, or a streaming of the medium. 
 We can effect motion at a distance by striking an object 
 with a projectile. 
 
 2. A peculiar kind of alternate streaming in opposite 
 directions, constituting longitudinal waves. We have seen 
 that such a motion is capable of effecting attractions and 
 repulsions. 
 
 3. Vortex motion. We shall examine this form of 
 
26 ELECTRICAL 
 
 motion, which consists of streaming in closed curves, 
 directly. We shall see that while this form of motion is 
 capable of causing attractions and repulsions of a peculiar 
 nature, which we recognize as magnetic, they are incapable 
 of causing the general attractions and repulsions with 
 which we are familiar. As stated before, we have omitted 
 a general vortex motion of the ether, not in closed curves, 
 such as possibly has led to the formation of celestial sys- 
 tems (spiral nebulae and solar systems), as not lying within 
 our present scope. 
 
 Hence gravitational attraction must be due to longi- 
 tudinal waves. Since the amount of wave energy flowing 
 through a closed surface remains constant, its concentra- 
 tion, or intensity, is inversely proportional to the square of 
 the distance. Whence Newton's law follows, viz., the 
 attraction between two bodies is proportional to the 
 product of their masses, and inversely proportional to 
 the square of the distance between them. 
 
 ES 
 
 The wave force , which includes both attraction and 
 t 
 
 repulsion, may perhaps best be called the differential 
 inertianal pressure. Gravitational pressure implies gross 
 matter, but we shall see that condensed and rarefied ether 
 is equally subject to this force. We shall find that a mass 
 of condensed ether, or a positive charge of electricity, 
 gives off only negative waves, while a mass of rarefied 
 ether, or a negative charge of electricity, gives off only 
 positive waves. Hence all gross matter attracts all other 
 gross matter and all masses of condensed ether, while 
 repelling all masses of rarefied ether. On the other hand 
 condensed ether repels condensed ether and attracts 
 rarefied ether, while rarefied ether repels rarefied ether and 
 attracts condensed ether. 
 
VORTEX FILAMENTS 
 IN THE ETHER 
 
 In all elastic fluids, vortex filaments are readily formed. 
 The condition is simply that a rotating sheet of the fluid 
 shall by its centrifugal force support the excess of pressure 
 of the general medium over the lessened pressure in the 
 interior. In a gas, friction soon reduces the rotational 
 energy of the sheet, so that they cannot long persist: but 
 in the ether, which has no viscosity, such vortices persist 
 indefinitely and would persist forever unless destroyed 
 under special conditions which we shall investigate later. 
 In an incompressible liquid, and all liquids are little com- 
 pressible, apart from friction, the formation and persist- 
 ance of linear vortices is rendered difficult because the 
 necessary lessened pressure in the interior, which holds the 
 outer rotating sheet, can hardly be attained short of a 
 complete vacuum in the axis. In a gaseous medium a 
 linear vortex need not be a closed curve, provided its two 
 ends are shut off by surfaces impermeable to the medium ; 
 but in the ether such linear vortices always form closed 
 complete rings. 
 
 Such vortex rings are very familiar to us. A locomotive 
 puffs them out of its smoke stack, and, when they are 
 accompanied by smoke, they are visible; otherwise not. 
 Smokers learn how to blow them. They accompany the 
 blast of a gun; visible with black powder; invisible with 
 smokeless. They are easily made by tapping smoke out 
 of a box through a circular orifice. This formation is not 
 to be explained as due to the friction of the gas on the 
 
 27 
 
28 ELECTRICAL 
 
 edges of the orifice. All gases, of course, are subject to 
 friction, but this is very slight. It is due to a stoppage 
 and diversion of the currents at and in the vicinity of the 
 edge, while the central stream flows on unobstructed. 
 Certain currents at the edges are stopped and even begin 
 to flow backward. A line of lessened pressure forms, and 
 the central streams are pushed back over this and by their 
 momentum are carried around it. Once formed, it must 
 persist, unless, as in the case of gases, its energy is used 
 up by friction. In a conductor the molecules are more 
 densely packed together near the surface than in the 
 interior. This is especially marked at the surface where 
 a peculiar differentiated condition exists which is known 
 as a "surface tension." The mutual attraction of the 
 molecules is here all towards the interior with no counter- 
 balancing action from the exterior. In the centre, the 
 attractions oppose each other from all directions so that 
 here the density and tenacity are least. It is for this rea- 
 son that a wire cable is much stronger than a rod of the 
 same material of equal cross section. The flow of a steady 
 electric current is greater in the axis of a conductor than 
 in the peripheral portions. Hence we have a condition 
 favorable to the formation of vortices. The current is 
 less obstructed in the centre, and more obstructed in the 
 peripheral portions, so that it is natural to expect that 
 vortex rings of ether will be thrown off surrounding the 
 conductor. And, in fact, we find that whenever a current 
 is flowing in a conductor, it is always surrounded by such 
 vortex rings. Further such rings are always rotating in 
 such a direction that the inner edge of the ring moves in 
 the direction of the current which formed it, while the 
 outer edge moves in the opposite direction. 
 
 A small length of a vortex filament may be regarded 
 as a cylinder made up of an infinite number of concentric 
 cylindrical sheets, each rotating with an angular velocity, 
 G>. The pressure at the surface is the normal ether pres- 
 
MECHANICS 29 
 
 sure, P. The increment of pressure outward from the 
 axis, due to the centrifugal force, is dp = pdr . ra)*. The 
 
 density, p = . Hence log -* = - I r 2 a 8 ) 1, a 
 
 being the radius of the cylinder. The pressure falls 
 logarithmically from the surface to the axis, the fall 
 increasing as the square of the angular velocity. 
 
 Let us suppose that the original whirl imparted to the 
 vortex was violent enough to cause a complete vacuum 
 in the axis, or the filament consists of a current sheet 
 surrounding a complete vacuum. The normal pressure 
 of the current sheet is P at every point, and therefore the 
 filament cannot collapse about its axis, but there is also a 
 lateral pressure, P, which is unsupported, and which 
 therefore tends to expand the circumference of the ring. 
 The absolute potential energy of the current sheet, or its 
 potential energy measured from an absolute zero, is half 
 its pressure into its volume. Taking, h t as the thickness 
 of the sheet, and 5 as its surface, its total potential energy 
 
 PSh Pu 
 
 is = , where u is the volume of the sheet. Now 
 
 2 2 
 
 the moment of momentum of the sheet, or wr 2 <w, will 
 remain constant, but the thickness of the sheet, h, and r 
 will diminish as the ring expands. However the volume 
 
 of the sheet u, and its total potential energy , will 
 
 remain constant. This potential energy tends to expand 
 the ring and thereby to impart kinetic energy to it as a 
 whole. It does not, however, lose its energy by so doing, 
 since it is automatically kept at a constant point, by 
 drawing from the rotational energy whatever it loses as 
 kinetic energy. It is evident that when the kinetic energy 
 of the ring becomes equal to the potential energy of the 
 
30 ELECTRICAL 
 
 sheet, a condition of equilibrium will have been reached, 
 and there is no further exchange between the energies. 
 
 At this point = , or V = -u = -\J , and 
 
 we see 
 
 u 
 
 that the ring will spread out with the standard velocity. 
 
 This is on the supposition that its flight is unresisted. 
 We have seen that any body moving through the ether 
 must be resisted by an amount proportional to the velocity 
 with which it moves, and to the surface which it opposes. 
 A single ring, therefore, no matter with what velocity it 
 is thrown out, must soon come to rest, or move so slowly 
 that the resistance it experiences does not overcome the 
 expansive effort of the potential energy. However, in 
 opposing the resistance, it throws up a compression wave 
 in front and an expansion wave behind, and these longi- 
 tudinal waves travel ahead with the standard velocity. 
 If the foremost ring is lagging, it is overtaken by these 
 waves from the rings which have been given off subse- 
 quently, and since it is a body less dense than the ether, 
 it will be urged on by these waves and quickly take their 
 step. The result is that all the rings will almost immedi- 
 ately be moving out with their natural velocity, as if they 
 were unresisted, and in fact they are unresisted for the 
 effect of the longitudinal waves which they set up is to 
 cause the ether to move with them at the standard velocity. 
 
 The ring cannot collapse about the axis of the filament 
 because the pressure of the external ether, P, is balanced 
 at every point of its surface by an equal and opposite 
 centrifugal force. There is, however, a differential ex- 
 ternal pressure tending to compress the ring into a smaller 
 circle. For calling the distance from the centre of the 
 ring to the axis threading the filament, R, and the radius 
 of a cross section, r, let us cut the ring into two parts by 
 a vertical cylinder passing through the axis of the filament. 
 
MECHANICS 31 
 
 The component of the surface parallel to the cylinder on 
 
 +r +r 
 
 the inner side is 2n \ (R x) dy = 2ir \ (R Vr*y*) dy 
 
 7T 2 r 2 . Likewise the component of the outer 
 surface parallel to the cylinder is ^irrR + TT*r*. Hence 
 the differential pressure inward is 2 P7T 2 r 2 . 
 
 Taking the case of a vortex with a central vacuum 
 where the expansional pressure of the current sheet is P, 
 this is equivalent by Laplace's formula to a radial pressure 
 
 p 
 
 outward of . The total amount of this pressure outward 
 R 
 
 p 
 
 is evidently . ^irrR = P . 4irr. Where r is so small 
 R 
 
 that we can neglect its square in comparison with its first 
 power, the differential external pressure, 2P7T 2 r 2 , is neg- 
 ligible. But when a vacuum does not exist in the axis, 
 and the average pressure of the sheets is below P and 
 r comparatively large, it is evident that a position will 
 generally be found where the expansional pressure will be 
 exactly balanced by the differential external pressure, and 
 in this position the ring will remain stationary. 
 
 In a vortex filament with a central vacuum the centri- 
 fugal force per unit of surface must equal the external 
 pressure. The surface of the ring is ^ir^rR and its 
 volume, U, is 27T 2 r 2 R. Hence 
 
 r, - nn ~> T-> TT mv z 
 m p t and ^- = P[/ = , 
 
 where v is the velocity of the current sheet. Or 
 
 /2P /2P 
 fl = *y = ^ -. D l is the average density of the ring, 
 
 u 
 and is less than that of the normal ether. The velo- 
 
32 ELECTRICAL 
 
 city of the current sheet must therefore be greater 
 than the standard velocity. P U measures the rota- 
 tional, or magnetic, energy of the vortex. 
 
 I~P 
 The formula V = ^1 i s an important one in our 
 
 theory. It is the velocity with which longitudinal waves 
 of small amplitude are propagated, as well as that of 
 electro-magnetic waves. However, vortices without vacua 
 may move rather slowly. There is a position of equil- 
 ibrium where for low-rotational vortices the differential 
 external pressure balances the interior expansional pres- 
 sure. A vortex generated about a wire carrying a current 
 may move out comparatively slowly, and the lower limit 
 of such a velocity is evidently zero, or a vortex may be 
 generated in a position of equilibrium. 
 
 When the vortices are generated under a moderate 
 pressure which rises with no great suddenness, the rotational 
 energies will be low far under the vacuum point and 
 the rings proceed to their position of equilibrium which 
 they maintain when the current becomes steady. The 
 position of equilibrium is not now the one we have pointed 
 out for a single filament, but, since vortex lines when 
 pressed together exert a lateral pressure on each other, 
 the figure of equilibrium will be the resultant of all these 
 lateral pressures. It is evident that when such a tube 
 becomes compressed the centrifugal force increases, since 
 the moment of momentum of the current sheet, or mr z <*), 
 must remain constant. 
 
 Let us suppose that we have applied an electro-motive 
 force to a conductor say a charge of positive electricity, 
 or condensed ether, has been applied to one end, and a 
 charge of negative electricity, or expanded ether, to the 
 other end, thereby establishing a pressure gradient. An 
 equilibrium of pressure is quickly established. In a 
 certain metaphysical sense, it might be considered that 
 
MECHANICS 33 
 
 not only has positive electricity flowed in one direction 
 but negative electricity has also flowed in the opposite 
 direction, and such is still the general conception, although 
 the convention has been made that the direction in which 
 the positive electricity flows shall be considered the direc- 
 tion of the current. Actually, however, no negative 
 electricity flows here, any more than, when we compress 
 a gas in one globe and exhaust it in another, and connect 
 them, the rarefied gas flows into the compressed gas. 
 The simple unquestionable fact is that condensed ether 
 has expanded into rarefied ether positive into negative. 
 In nature motion can only take place in the direction of 
 a force, not against it. 
 
 We have started our current, but it does not reach its 
 full strength at once. It is delayed for a time while it is 
 building up its system of concentric vortices surrounding 
 the conductor. As layer after layer of the rings are being 
 shot out, and succeeding layers are being sub-posed, the 
 pressure, or electro-motive force, is doing considerable 
 work, both in manufacturing the partial vacua and in 
 pushing them away from the wire. It consequently can 
 expend only a part of its energy in propelling the current 
 against the resistance offered by the atomic surfaces. 
 
 The field of vortex lines, or the magnetic field, throws 
 the medium surrounding the wire into a state of strain. 
 There is a force pressing radially from all directions upon 
 the wire, which is balanced by the pressure of the current. 
 There is also a pressure along the vortex filaments and 
 they behave as if they were tense strings, always striving 
 to shorten themselves. We have already pointed out how 
 it is possible for a fluid, isotropic medium to be put under 
 strains in particular directions by motion. 
 
 The current finally becomes steady. There is now a 
 condition of equilibrium and the rings remain stationary. 
 The driving force is exactly balanced by the resistance, or 
 counterpressure, as stated in Ohm's law. But if the cur- 
 
34 ELECTRICAL 
 
 rent again increases, the whole system moves outward 
 again, and a new set of rings is shoved under them, until 
 a new condition of equilibrium is established. If the 
 current decreases, the ring system falls back towards the 
 wire, and the innermost are absorbed again into the 
 current from which they sprang. 
 
 The vortex filaments are lines of magnetic force. Every 
 current must be accompanied by a magnetic field*, and 
 the currents represented by the current sheets have their 
 magnetic field wholly internal. The direction of the 
 magnetic force (or line) is perpendicular to the direction 
 of the current and this condition must necessarily exist 
 under all circumstances. If we twist a wire into a spiral 
 coil and send a current through it, the circular lines of 
 magnetic force which surround a straight wire, will, in 
 this case, become merged into a system of closed lines 
 threading the coil through its interior, and the direction 
 of rotation in the vortices will depend upon the direction 
 of the current. The magnetic lines and current direction 
 are perpendicular to each other, as always. 
 
 Let us suppose a vortex ring just touching the wire 
 with its inner edge. It is pressing upon the wire with a 
 certain force, but this pressure is exactly balanced by the 
 pressure of the ether in the current and the ring conse- 
 quently cannot contract. But if the pressure in the cur- 
 rent falls, the ring begins to contract into the wire. But 
 instead of doing this, it rolls itself out into a linear current 
 on the surface of the wire in the direction of the original 
 current. 
 
 This falling back of the vortices upon the wire when 
 the current decreases, or is broken, is called self-induction, 
 or the "extra current on break." It has been supposed 
 that it was due to the inertia of electricity. Undoubtedly 
 the ether has inertia, but it is very slight. Practically all 
 of the extra current is due to the discharge of the energy 
 
 * Linear currents in the free ether are the sole exception. 
 
MECHANICS 35 
 
 stored up in the magnetic field surrounding the wire. 
 The building up of this field takes some time, compara- 
 tively speaking, while its collapse on breaking the current 
 (or wire) is sudden, though not instantaneous. No action 
 in nature can take place instantaneously, although it has 
 been the custom to consider gravitation an instantaneous 
 action. 
 
 The vortex lines which are thrown off by a current 
 under moderate pressure and formed with no great sud- 
 denness, have, as we have seen, only partial vacua, and do 
 not go to great distances from the wire, even theoretically. 
 They do not extend indefinitely into space, but remain 
 rather close, and when the current ceases, all of the 
 energy, which has been thus stored up in the neighborhood 
 of the conductor, is recovered. Not so, however, the 
 violently formed vortices having complete vacua, which 
 constitute electro-magnetic waves. The energy in this 
 case is thrown out into space and permanently lost. 
 
 Let us return to the case of a wire in which a current 
 is just starting. Let us suppose a second wire, parallel 
 to the first and near it. During the formative period of 
 the current, while the circular vortices are being shot out, 
 these rings must cut the second wire on their out- 
 ward journey. The filament, on 
 meeting the wire, wraps itself 
 around it, reunites its ends on 
 the other side, and continues 
 on as a straight filament. This 
 is indicated in Fig. 3. For an 
 
 instant, a vortex ring surrounds the wire, but, as we have 
 seen, this instantly rolls itself out into a linear current 
 in the second wire, having a direction opposite to that 
 in the primary wire. The direction of an induced 
 current is, of course, determined by the direction of the 
 current sheet at the point where it first touches the wire. 
 When the current in the primary becomes steady, its ring 
 
36 ELECTRICAL 
 
 vortices become stationary, and the induced currents in 
 the secondary wire cease. If the current in the primary 
 now decreases or is broken, the vortex field falls back 
 towards the primary, and such rings as are outside the 
 secondary must cut it on their return journey. In this 
 case the inner edges of the vortices touch the second- 
 ary first, and the rotation is such as to shoot the induced 
 current in a forward direction. During the outward ex- 
 cursion the ring system cuts the secondary wire more 
 slowly, while the inward fall is of the nature of a 
 collapse, or a greater number of lines cut the wire in the 
 same interval of time. The electro-motive force of the 
 induced current comes from the rotational energy of the 
 vortex filaments. The total number of lines cutting the 
 wire, outward and back, is, of course, the same, and the 
 same amount of electricity flows in the reverse and direct 
 induced currents. The direct induced current, however, 
 is under a higher pressure, and lasts a shorter time. 
 
 The motion between the filament and the secondary 
 wire, need, of course, only be relative. Thus if the vortex 
 field is stationary, and the wire moves through it, the 
 induction effects will be the same. Referring to Fig. 3, 
 if a magnetic line is just above the wire and we send a 
 current through the wire in the direction of the previous 
 induced current, the first vortex ring surrounding the wire 
 will break at the top and become continuous with the 
 magnetic line, as shown in the figure. At this instant 
 the magnetic line is partly bent around the wire, and, since 
 such lines always strive to preserve a minimum length, 
 it will straighten out, thereby pressing together the lines 
 below and separating those above. The lateral pressure 
 will move the wire upward. The direct pressure of the 
 vortex surfaces on the wire is resisted by the pressure of the 
 current in the wire. The vortex cannot enter the wire, 
 and the latter is forced directly upward. Only a single 
 layer of vortices covers the wire at any instant. The 
 
MECHANICS 37 
 
 magnetic lines above get below the wire by this process 
 of merging with the surface (current) vortices, and then 
 straighten out below. 
 
 If we move the wire downward, a current is induced in 
 the wire. If we send an equal current in the same direc- 
 tion, the wire is moved upward, and we shall have to use 
 the same force in moving the wire downward as that with 
 which it reacts upward. 
 
 If we surround the primary wire with a metallic cylinder, 
 then every vortex travelling outward will, on striking its 
 inner surface, unroll itself completely into a linear current 
 travelling backward. The entire vortex will thus have 
 disappeared. As no vortex can escape outside the cylinder, 
 there will be no magnetic field external to it. On breaking 
 the primary current, only those lines which are between 
 the wire and the cylinder are left to collapse. Conse- 
 quently the "extra" current in the primary will be reduced 
 by the amount of the lines which have been lost in the 
 cylinder, and there will be no direct induced current in the 
 secondary. This shows that electro-magnetic waves cannot 
 penetrate a conductor. The reverse induced current on 
 the inner surface of the cylinder, however, sends out a 
 vortical system of its own, and the electro-magnetic waves 
 which left the primary are thus reflected from the secondary. 
 A conductor is therefore impermeable to electro-magnetic 
 waves, but it reflects them. This is precisely what takes 
 place at the reflecting surface of an ordinary mirror. 
 Light, which consists of electro-magnetic waves, cannot 
 penetrate the surface of the quicksilver, but is reflected. 
 The energy of the reflected wave can never equal the energy 
 of the original wave, since a portion of this energy is used 
 up in driving the currents induced in the conductor. 
 Hence conductors are opaque to electro-magnetic waves, 
 while non-conductors transmit them and are therefore 
 transparent. This latter statement must be modified to 
 the following extent. While all non-conductors are trans- 
 
38 
 
 ELECTRICAL 
 
 parent to electro-magnetic waves of sufficient length, yet 
 when these waves become exceedingly short and the 
 molecules of a body are comparatively large, so that waves 
 and molecules are not so greatly apart in the order of 
 magnitudes, currents are generated inductively in the 
 molecules which send back waves of the same length as 
 the impinging wave. The induced currents are thus 
 able to resonate with the frequency of the impinging wave 
 more or less, with the result that the energy of the wave is 
 used up in a comparatively short thickness of the di- 
 electric. In such a case little of the energy gets through, 
 and a small portion is reflected. Owing to this molecular 
 inductive action, a portion of very short electro-magnetic 
 waves is always reflected, even in the most transparent 
 media. Thus glass, which easily transmits light, neverthe- 
 less reflects a small portion of it. 
 
 
 
 
 L 
 
 0000 
 
 B 
 
 Let us suppose that a vertical wire, AB, is traversed by 
 alternating currents. A series of vortex rings will be driven 
 out, one set of them rotating one way, the next set rotating 
 in the opposite direction. Fig. 4 represents a section 
 through the wire showing three trains of vortices, C, D, E, 
 consisting of four vortices in each train. C rotates to the 
 right, D to the left, and E to the right again. We shall 
 suppose the alternations to be very rapid some millions 
 
MECHANICS 39 
 
 in a second. Of course, it is possible to detect the mere 
 passage of such a train of electro-magnetic waves, and 
 signals could be given by sending out such a train, then 
 stopping, and then sending again. And in fact this is 
 done in wireless telegraphy. The dot and dash messages 
 of the wireless codes are signaled by sending short trains 
 and long trains with stops in between. But it has not 
 yet been possible to construct an instrument which could 
 distinguish between the alternations in a continuous train. 
 
 Let us suppose such trains of vortices striking at some 
 distant point upon an instrument capable in some way of 
 distinguishing between the alternations. Let us examine 
 in what way the differentiation of such whirls could pos- 
 sibly be effected. Considering a single vortex, it would 
 appear that, since the upper and lower edges arrive simul- 
 taneously at any point, and are moving in opposite di- 
 rections, any effect which these motions might separately 
 produce, would certainly nullify each other. And con- 
 sidering the front and back edges, since the contiguous 
 edges of the neighboring vortices move in opposite di- 
 rections and are in close juxtaposition, thus arriving at 
 practically the same instant, it would seem hardly possible 
 that any instrument could distinguish between individuals 
 in a train of vortices rotating all the same way. It might 
 detect the front of a train and the rear, but during the 
 passage of the train no indication could be given. 
 
 However, at the junctions of the oppositely rotating 
 trains, the motion of the rear edge of the last vortex co- 
 incides with the motion of the front edge of the next fol- 
 lowing vortex. Hence at these dividing lines there will 
 be a doubled upward motion followed by a doubled down- 
 ward motion, and so on alternately. It would seem pos- 
 sible that such a simulated or quasi transverse vibration 
 might be detected. Considering only these up and down 
 components of the motion, which are the only ones that 
 could possibly be detected, it is evident that they would 
 
40 ELECTRICAL 
 
 form a curve like that represented under the trains C, D, 
 E. 
 
 Let us suppose that we make out alternations still 
 more rapid billions of them in a second. It is impossible 
 to get such frequencies in conductors, or oscillators of 
 finite dimensions, but using an atom as an oscillator or 
 by making an atom vibrate backward and forward, it 
 is possible to obtain such frequencies, and the vortex 
 trains sent out by such an alternating current would be 
 reversed with this order of frequency. Such vibrations 
 would be something like 5 X 10 14 times a second, or the 
 same as the frequency of light vibrations. These vortices 
 are shot out with a velocity of 3 X 10 10 centimetres per 
 second, which is the velocity of light, and all electro- 
 magnetic waves An atom vibrating with such fre- 
 quencies sends out trains in which every vortex is pre- 
 ceded and followed by one rotating in an opposite di- 
 rection, or every train of the same kind consists of only 
 one vortex. This is represented in F, Fig. 4. 
 
 Taking account only of the up and down motions, 
 which are the only components of the vortical motion 
 which could possibly be detected, we see that this motion 
 is represented by the curve under F. It is a simple sine 
 wave, a complete wave length being equal to two vortex 
 diameters. We pointed out that the only hope of de- 
 tecting such alternating trains was that there might be 
 some instrument capable of being affected by the up and 
 down, or transverse components of the motion, which, 
 though acting in opposite directions, nevertheless do not 
 act together at the same instant but are separated by a 
 minute interval of time. Now there is such an instrument, 
 and it is competent to detect the transverse components 
 of electro-magnetic waves, provided the alternations are 
 of the requisite frequency. This instrument is the eye. 
 
 It has previously been supposed that, in transmitting 
 light waves, the motion of the ether was purely trans- 
 
MECHANICS 41 
 
 versal. But it is impossible for a fluid medium to execute 
 such motions, and it cannot transmit waves with trans- 
 verse vibrations. This is a property of solids alone which 
 are capable of undergoing shearing strains. Hence the 
 many incongruous and impossible descriptions of the 
 ether. It was said to be a fluid with the properties of a 
 solid, a jelly, a "kind of glorified pitch," and what not. 
 Of course nobody ever understood these descriptions, 
 and especially not the learned expounders themselves. 
 It has done harm to many, in that they have been led to 
 pretend to understand what was impossible of compre- 
 hension, and it has outraged reason which should be kept 
 sacred. 
 
 We have stated that electricity is the ether and the 
 ether is electricity they are synonymous. To any one 
 who is not convinced after reading the foregoing pages, 
 the argument may be put in a more formal way. We 
 saw that we were able to produce a current in a conductor 
 by simply touching a vortex filament, or line of magnetic 
 force. The question arises "Where did the electricity in the 
 the conductor come from?" Electricity is a material 
 substance of some kind it is something. Now anything 
 that exists, that is material, cannot be manufactured from 
 nothing, neither can it be destroyed. The electricity 
 which we have brought into the conductor must have 
 existed somewhere else before. It did not exist in the 
 conductor, for a careful examination showed not a trace 
 of electricity on it or in it. It did exist then, in the 
 magnetic line. But a magnetic line is simply ether in 
 motion. This can be easily proved, and in fact nobody 
 doubts it, although it has not heretofore been recognized 
 that a magnetic line is simply a vortex filament. Con- 
 sequently electricity can be nothing else than the ether. 
 The present mathematical investigation showing that 
 such an assumption leads necessarily to all the observed 
 phenomena, and conversely that such phenomena can only 
 
42 ELECTRICAL 
 
 be produced by such a mechanism, lends cumulative evi- 
 dence that is irresistable. 
 
 Certain metals iron, nickel and cobalt possess a 
 curious property in that their molecules are capable of 
 being set in rotation about an axis and of continuing this 
 rotation indefinitely. If we place such a body in a mag- 
 netic field, the axes of these molecules are dragged into 
 the magnetic lines and begin rotating with the velocity of 
 the vortex. They reinforce thus greatly the whirl and 
 are said to have a very high "permeability" for magnetic 
 lines. The theory of Ampere was that in a magnet, little 
 currents were continually circulating around its molecules, 
 and that the axes of these currents were all turned in the 
 same direction. It is true that there are currents circu- 
 lating about the magnetic lines, but these currents are 
 not limited to the molecules, but are continuous current 
 sheets forming a vortex. Further the molecules are not 
 stationary, but are rotating with the vortex. By their 
 momentum they reinforce the whirl and keep up the ro- 
 tation even when the magnetic field is withdrawn. We 
 might consider these molecules as an assemblage of little 
 fans, whirling the ether around and along the magnetic 
 lines. It is clear why the energy of the whirls is so greatly 
 increased, since on the original magnetic field, the in- 
 dependent field of the molecules is superposed. 
 
 Fi^.5 
 
 Fig. 5 represents, on the left, two magnets with opposite 
 poles next to each other. The vortices traverse both 
 magnets with the intervening air gap and then close round 
 
MECHANICS 43 
 
 on the outside. Where the magnets are nearest the 
 vortices are crowded together and are of greater cross 
 section. When isolated the number of lines in the two 
 magnets is twice as great, but when in this position, they 
 join hands, a positive end grasping a negative end, and 
 though the number of lines is halved, the energy is greatly 
 increased in the air gap. The outer lines are farther 
 apart and much more tenuous. The lines repel each 
 other laterally with considerable force (centrifugal), but 
 are pressed together by the general etheric pressure, thus 
 assuming a pattern of equilibrium. They always tend to 
 shorten and it is evident that the attraction which the 
 two magnets exert on each other is due to their being 
 pressed together by the general etheric pressure. In the 
 right hand of Fig. 5 are two magnets with similar poles 
 opposed. Similar lines do not join hands, since if two 
 such lines met head on, they would be rotating in opposite 
 directions. They turn away and are crowded back, since 
 all such lines repel each other laterally. This results in 
 an elastic distortion of the original patterns, and since 
 these patterns always strive to regain their original 
 symmetrical shape, the magnets are pressed apart. 
 
 The attraction is due to the general etheric pressure 
 striving to close up the partial vacua in the tubes, while 
 the repulsion is due to the lateral repulsion of the lines 
 striving to overcome the distortion of their original 
 patterns. 
 
STATIC ELECTRICITY 
 
 Ether is a condensed state of higher density than 
 the normal ether is a differentiated condition which we 
 call positive ether or positive electricity. Likewise ether 
 in a rarefied condition is negative ether or negative elec- 
 tricity. While ether in motion constitutes an electric 
 current, if that be not a tautological statement, positive 
 and negative ether at rest are what is known as static 
 electricity. 
 
 We have seen that gross matter at the surfaces of 
 solids and liquids is in a differentiated condition. The 
 molecules here are crowded together and the matter is 
 much denser than in the interior. The surface is in a 
 state of strain, having a "surface tension," a condition 
 which gradually falls off towards the interior. We have 
 also seen that gross matter exerts an attraction or re- 
 pulsion on all other matter, according as that matter is 
 denser or less dense than the ether. This action is es- 
 pecially strong at infinitesimal, or small, distances, rapidly 
 falling off, so that at a very small distance from a molecule 
 it is practically negligible. A charge of condensed ether 
 will therefore be attracted and held by a material surface, 
 while a charge of negative ether will be repelled from 
 such a surface. In the interior of a conductor, since such 
 actions are from all directions, the ether cannot remain 
 in a state of strain, but must be at the normal density 
 throughout. A charge of positive or negative ether 
 placed at some point in the interior of a conductor would 
 therefore move to the surface, where it would be held. 
 Even if it were on a surface presenting a concavity, it 
 
 44 
 
MECHANICS 45 
 
 would represent here a surface tension T, which, by 
 Laplace's formula, would give rise to a normal pressure, 
 
 P n = , where R is the radius of curvature of the surface. 
 jR 
 
 Since this normal pressure is directed towards the interior, 
 the charge could not maintain its position, but would 
 move through the conductor to the convex side to a 
 position of equilibrium, where the normal pressures, 
 directed outward, would be balanced by the equal and 
 opposite attractions of the surface. 
 
 We shall assume that in a conductor the atoms have 
 contact with each other at some point, so that a contin- 
 uous surface is furnished over which the charge can move. 
 In a non-conductor, the atoms (molecules) not being in 
 contact, charges may be held by each molecule, since this 
 ether is not able to move away, and may be held locally 
 in a state of strain. 
 
 A positive charge on a surface is held by the attraction 
 of the surface acting on the denser ether. Now this 
 attraction is proportional to the density of the ether, 
 and since all the layers apply their "weight" cumulatively 
 to all the under layers, the lower-most layers will be denser 
 and more strongly attracted. We can consider the sur- 
 face to be covered by an atmosphere of dense ether which 
 decreases in density progressively upward, until at a 
 certain short limit, which is the height of the atmosphere, 
 the pressure, or density, becomes equal to the normal 
 pressure of the ether. The case is analogous to the 
 atmosphere of the earth, which decreases in density 
 logarithmically upward, until it acquires the density of the 
 ether. (See "The Atmosphere," by the author.) 
 
 When a negative charge is applied to a surface, the 
 gross matter repels it, and its density increases upward, 
 until at a short distance the height of the charge at- 
 mosphere the density becomes equal to the normal 
 
46 ELECTRICAL 
 
 ether density. The previous case is reversed, and we 
 have an inverted atmosphere. The analogous condition 
 for the earth would be that it were imbedded in an infinite 
 ocean of air having the present density at the surface, 
 and that the earth should repel the air. In this case, the 
 earth would have an inverted atmosphere. For both 
 positive and negative charges, we shall consider the 
 pressure (density) at the surface, as the pressure, or 
 potential, of the charge. Actually, every charge contains 
 all pressures in its atmosphere from the normal ether 
 pressure up to (or down to) the maximum (or minimum) 
 pressure of the charge. 
 
 If we continue to introduce new masses of ether below 
 the superincumbent layers, we shall have to do work. 
 We may do this work by forcing ether onto the surface 
 against the maximum pressure, or we may condense the 
 ether first and then transfer it to the surface. As we con- 
 tinue to add thus new masses (charges) of ether, the pres- 
 sure (tension) of the lowest layer will continue to rise. 
 This cannot go on indefinitely, since the pressure of the 
 lowest layer will finally reach a point where it is equal to 
 the attracting or holding force of the surface matter. 
 When this happens the lowest layer bursts or breaks away, 
 leaving the surface bare of any charge. From Laplace's 
 
 formula, P n = , it is evident that the bursting pressure 
 R 
 
 will be reached at a very low point on a sharply convex 
 surface, where the radius of curvature is small. 
 
 In the same way, if we keep introducing negative ether 
 onto the surface, below the other layers, a point will be 
 reached where the repulsion will be unable to withstand 
 the increasing external pressure, and the system will 
 break down. Since the outer normal ether pressure acts 
 with (in the same direction as) the attraction on a positive 
 charge, and against the repulsion on a negative charge, 
 
MECHANICS 47 
 
 it is evident that a considerably higher pressure can be 
 reached in the layer next to the surface in a positive 
 charge, than the corresponding negative pressure in a 
 negative charge. Or the breaking negative pressure of 
 a negative charge is considerably below the corresponding 
 positive pressure for a positive charge. It has long been 
 known that a negative charge breaks down under a less 
 pressure than a positive charge. For a similar reason a 
 negative charge is dissipated more quickly than a positive 
 charge of the same potential. 
 
 Let us suppose a spherical conductor with a positive 
 charge, surrounded by a concentric metal spherical shell, 
 with a non-conducting space separating them. The 
 longitudinal positive waves given off by the surface of the 
 conductor cause the successive layers of the charge to 
 pulsate. We may consider these layers to pulsate syn- 
 chronously. The influence of the charge may be to 
 polarize the vibrations of the surface molecules, so that 
 they all vibrate in the same direction and synchronously. 
 As the compressed halves of the longitudinal waves 
 emerge from the denser medium of the charge into the 
 free ether, they become transformed into expansional 
 halves, and vice versa, the expansional halves of the 
 original waves, on emerging into the free ether become 
 transformed into compressional halves. The character of 
 the waves after passing through the charge therefore 
 becomes reversed, and the charge radiates from its surface 
 negative waves. Or, considering a positive charge to be 
 contracting and expanding, it is evident that the con- 
 traction, or backward movement, must result in increased 
 condensation, while the expansion, or forward movement, 
 must result in a rarefaction. It is inevitable, therefore, 
 that the waves emanating from its surface must have their 
 condensed halves moving towards the disturbing source, 
 and their expanded halves moving away from it. The 
 reverse is the case for negative charges. Hence positive 
 
48 ELECTRICAL 
 
 charges radiate negative waves and negative charges 
 radiate positive waves. 
 
 Now as the waves emanating from the positive charge 
 strike the inner surface of the enveloping shell, they apply 
 to it in quick succession, positive and negative charges, 
 viz., their condensed and expanded portions. If the 
 central positive charge were removed, and we should apply 
 successively positive and negative charges to the inner 
 surface of the shell, they would immediately flow to the 
 outer surface and there neutralize each other. But with 
 the central positive charge in position, the negative charges 
 are held (attracted) and cannot flow to the outer surface. 
 The result is that as the waves deposit their charges, they 
 become separated, the positive charges appearing on the 
 outer surface and the negative charges accumulating on 
 the inner surface. It may appear unintelligible why the 
 two charges do not neutralize each other on the inner 
 surface, but experiment shows that if we have a bound 
 (induced) charge on one side of a conductor and no charge 
 on the other side (removed by earthing), we can apply an 
 opposite charge to the conductor which will reside on the 
 previously uncharged side, and it makes no difference to 
 which side we apply this charge. In the case of our shell, 
 the explanation probably is that the waves are simply 
 transmitted through the bound negative charge as through 
 a rarer medium, and appear intact on the outside. 
 
 We have said that the total energy of a unit mass of 
 ether is proportional to its absolute pressure. The ether, 
 therefore, represents a tremendous amount of energy. 
 It conserves this energy from the fact that its total body 
 is at a uniform pressure and there is no other source of 
 higher or lower potential from which it may gain or lose 
 energy. Where this original energy came from, and by 
 what mechanism it manifests itself, i.e., by what form of 
 motion its pressure is exercised, has, as yet, been the subject 
 of the barest surmise. 
 
MECHANICS 49 
 
 We shall assume that the rate of energy outflow, or the 
 rate of the dissipation of the energy of a body, is pro- 
 portional to its potential or pressure. Two bodies radiate 
 their energy to each other, but if they are at the same 
 potential, the gain is equal to the loss and their potentials 
 remain unchanged. A charge of ether, having a greater 
 potential than the normal ether, must dissipate its energy 
 at a rate proportional to the excess of its pressure above 
 that of the general ether. Practically it is found that a 
 charge of electricity is dissipated at a rate proportional to 
 its pressure above the normal, just as a hot body cools at 
 a rate proportional to its temperature above its sur- 
 roundings (Newton's law*). Temperature is the analogue 
 of a potential or it can be considered a heat potential. 
 Thus a positive charge continually loses energy, and a 
 negative charge continually gains energy. We have every 
 reason to believe that the energy of a charge is dissipated 
 through longitudinal waves. 
 
 Stephan has found that for very high temperatures (such as 
 that of the sun) the rate of radiation is best represented by the 
 fourth power of the absolute temperature. We have to do here 
 with electro- magnetic waves (heat), and the ratio of the output of 
 energy in unit time to the potential of the source does not remain 
 constant, as with longitudinal waves, but increases progressively 
 as the potential rises. 
 
 The quantity, Q, or mass of ether in a charge is pro- 
 portional to its volume by its pressure, p, above the 
 normal. The volume of the charge is Sh, where 5 is its 
 surface and h is the height of the charge. Since h is always 
 small and does not vary appreciably we can assume the 
 volume to be sensibly proportional to the surface, and 
 therefore Q = pS. Let E be the energy in a wave given 
 
 off by unit surface of a charge. Then , where t is the 
 
 time of a complete wave vibration, is the output of energy 
 
 * We exclude, of course, leakage by conduction and convection. 
 
50 ELECTRICAL 
 
 per unit surface, per unit time. This is proportional to the 
 
 pressure, or = kp = k . Or - - = kQ. Hence the 
 
 t o t 
 
 rate at which the energy flows across an enveloping sur- 
 face is proportional to the charge. 
 
 The radiations from our three charges are all directed 
 away from their respective surfaces, so that the external 
 positive charge can in no way influence the internal 
 charges. If a charge were outside and wholly detached, 
 it would merely induce charges on the outer surface of 
 the shell and therefore could in no way influence the 
 internal charges. This is a general principle, viz., that 
 no external charge can in any way influence, or exert a 
 force upon, an internal charge. But a charge placed in 
 the interior of a hollow conductor can influence outside 
 charges through the induced charge which appears on 
 the outer surface. We shall hereafter not consider this 
 external charge, as we are to deal only with the internal 
 charges. Whether we remove it by earthing, or not, will 
 make no difference. 
 
 We have said that the waves radiated by the central 
 charge apply successively positive and negative charges 
 to the outer and inner surfaces of our shell. But this 
 cannot go on indefinitely. When the outflow of energy 
 from the inner charge is equal to that which it gains from 
 the central charge, its energy can no longer increase, but 
 remains stationary. Since the total energy flowing into 
 the inner charge is proportional to Q, the central charge, 
 and the total energy flowing out of the inner charge is 
 proportional to Q 1 , its own charge, when Q = Q l there 
 can be no further increase, and the induced charges on 
 the shell become, practically instantaneously, equal to the 
 central charge, and remain so. 
 
 We have seen that the attraction of longitudinal waves 
 on a body having a density different from that of the ether 
 
MECHANICS 51 
 
 )1 ) 
 
 is . S, where E is the energy in a unit cross 
 
 section of the wave, and D l t and 5, are the density and 
 surface respectively of the body acted upon. The central 
 charge will therefore attract the inner charge with a force 
 
 proportional to - 1 . 5 2 , where Si, is the surface 
 
 of the central charge, and S 2 and D 2 , the surface and den- 
 sity of the inner charge. But we have seen that we can 
 
 write - - = Q, and since the density of a charge is pro- 
 portional to its absolute pressure above zero, we can 
 
 p p 
 
 write the attractional force, Q. S 2 . Calling pi, 
 
 Pz 
 
 and p 2 , the pressures of the two charges above and 
 
 below the normal pressure, this becomes Q^ -. But 
 
 P 2 
 
 pzSz = Q, and the attractive force is proportional to 
 . Likewise we find that the attraction of the inner 
 
 QZ p p 
 
 charge is . Now the fraction is sensibly the 
 
 PI PI 
 p p /p P\2 
 
 same as , since they differ only by , and 
 
 P P\P 
 
 (Pi P) 2 is very small and P X P is relatively very 
 large. Hence, although the attraction of the central 
 charge on the inner charge is very slightly greater than 
 vice versa, yet they are sensibly equal, and the mutual 
 attraction is proportional to Q 2 . 
 
 If two charges are on non-conductors (such as pith 
 balls), where inductive action is not possible, and one 
 body does not surround the other, but they arc small 
 
52 ELECTRICAL 
 
 compared with their distance apart, the mutual attraction 
 
 00 l 
 
 becomes proportional to =~-, since the energy per unit 
 
 r 2 
 
 surface falls off inversely as the square of the distance. 
 This was discovered by Coulomb experimentally, and is 
 known as Coulomb's law. 
 
 If the medium between the two charges becomes denser, 
 so that the velocity of wave proportion becomes less, 
 or t becomes greater, or, what is the same thing, the 
 quantity of energy flowing in unit time becomes less, the 
 attraction between the charges becomes less, since the 
 
 
 force is proportional to 5 . Q 1 , 5 being the surface of 
 
 the radiating body. 
 
 Two bodies charged with opposite charges of electricity 
 attract each other because the charges exert attractions 
 on each other. The charges cannot leave the bodies since 
 they are held by the surface attraction and the bodies are 
 forced to follow the movements of the charges. The 
 atoms, of course, attract each other, but since this action 
 is upon discrete specks of surface, while that of the charges 
 is upon large continuous surfaces, the atomic attraction 
 is insensible, while the electrical attraction is comparatively 
 very large, and very appreciable. 
 
 Returning to our shell, let p be the pressure which the 
 central charge had before it was introduced into the hollow 
 conductor. Then, at that time, Q = kpS, or, for a given 
 pressure, the capacity was proportional to the surface, k 
 being the proportionality factor. Inside the conductor, 
 the pressure becomes p Q 2 , since it is lessened by the 
 amount of the mutual attraction of the charges. Since the 
 charge must remain the same, we have 
 
 Q =kpS =fe' (p-Q*) S, 
 where k l is a new proportionality factor of capacity. 
 
MECHANICS 53 
 
 _ _ P The new specific capacity factor is, therefore, 
 k P-Q, 
 
 very much greater than the old one, or it will be possible 
 to load the same surface with a much greater quantity of 
 electricity before reaching the same potential. Hence, by 
 allowing the central surface to be in communication with 
 some source of electricity, kept at a constant potential, 
 it will be possible, by the aid of the attraction of the inner 
 induced charge, to load it with an enormously greater 
 quantity of electricity than if it were isolated. 
 
 If we fill the space between the two charges with some 
 denser dielectric, which reduces the velocity of wave 
 propagation, we shall get a new factor of specific induction. 
 The mutual attraction of the two charges is proportional 
 
 0* 
 
 to ~, becoming less as t l becomes greater. The attraction 
 
 exercised by a material surface on a charge is proportional 
 to the pressure of the charge. Let g be this attraction 
 per unit of surface. Then the surface attraction on the 
 
 Qt 
 
 charge will be gp, and gp = p, or Q f =p(g I)* 1 . 
 
 ti 
 
 If we keep the central charge connected with a source of 
 electricity at constant potential, p, the electricity flowing 
 in will increase the charge, but as the quantity increases, 
 the inner induced charge also increases, and their mutual 
 attraction, tending to lower the pressure, increases as the 
 square of the quantities. Q 2 is proportional to t l . Hence 
 as the velocity of wave propagation in the medium de- 
 creases, the load of electricity at a given potential becomes 
 greater. If we take the ratio of the quantity of electricity 
 with which we must load the central conductor to bring 
 it up to a certain potential when a dense dielectric is used, 
 to the quantity necessary to bring it to the same potential 
 when only ether intervenes, we shall obtain the specific 
 
54 ELECTRICAL 
 
 inductive factor of the dielectric. This quantity is 
 usually designated by K, and is called the specific in- 
 ductive capacity. 
 
 K = Ih = /Z, where t 1 and V 1 are the time 
 
 of a wave vibration and its velocity in the dielectric, 
 and t and V are the corresponding quantities in the 
 ether. K is not constant for the same dielectric, but 
 varies with its temperature and from other circum- 
 stances which we shall discuss later. Assuming K to 
 be determined for a given temperature, and in a simple 
 induction, i.e., one without complicating factors, the 
 attraction between two opposite charges would be pro- 
 
 00 l 
 portional to -^ , and the specific inductive capacity of 
 
 the dielectric would be K = _ /JL. The mutual attraction 
 
 between the central and inner charges of our shell varies 
 
 as JL or as the velocity of wave propagation in the 
 K* 
 
 medium separating them, but if the central charge be 
 kept in communication with a source at constant potential, 
 the attraction will not vary, no matter how the dielectric 
 
 Q2 
 
 varies, for = p (g 1), which shows that the attraction 
 
 remains constant. 
 
 We have hitherto considered the action of the dielectric 
 as simply that of transmitting longitudinal waves. But if 
 we place a solid dielectric between the two plates of a 
 condenser the molecules will become loaded individually 
 by induction. The waves will deposit positive charges 
 on one side and equal negative charges on the other. 
 
MECHANICS 55 
 
 They will become polarized in the direction of the waves. 
 Now in a single conductor, as soon as the inducing charge 
 is removed, the equal and opposite induced charges im- 
 mediately reunite, but in a nonconductor, the molecules 
 have their charges aligned so that the molecule next ahead 
 turns an opposite charge to that on the molecule next 
 behind. These opposite charges attract and hold each 
 other, so that when the electric field is removed, the 
 charges do not reunite, but maintain their positions. 
 They are now an independent source of energy and send 
 out waves in the direction in which they are aligned. 
 The case is analogous to that of a magnet, which, even 
 after the polarizing source is removed, maintains its in- 
 dependent field in the same direction. Hence the induced 
 charges in a condenser, which, for a given potential, are 
 greater as the wave velocity decreases, are still further 
 increased by this action in the dielectric. The molecules 
 have stored up an independent source of energy which is 
 super added to that of the original field. 
 
 If we place a plate of mica in a strong electric field 
 (between the plates of a condenser), the mutual attraction 
 of the induced charges on its molecules puts it in a state 
 of strain. It is as if the plate were pressed between the 
 jaws of a vise. If the pressure becomes too great, some 
 of the molecules, along a line of weakest resistance are 
 forced away from their positions of equilibrium and a 
 fracture results. If we peel off leaves from the plate, we 
 shall find that throughout there are always charges of one 
 kind on one side and charges of the opposite kind on the 
 other, no matter how thin the leaves are. This action is 
 not so strongly marked in liquids, and of course when the 
 electric field is removed, no polarization remains. A solid 
 dielectric so internally polarized has been called by 
 Heaviside an Electret, from its analogy to a magnet. The 
 strain in a transparent dielectric like glass is easily demon- 
 strated by a ray of light. Since it is compressed in the 
 
56 ELECTRICAL 
 
 direction of the field, it will behave like a uniaxial crystal, 
 subjecting light to a double refraction, and transmitting 
 an ordinary ray and an extraordinary ray. 
 
 We have seen that the specific inductive capacity of a 
 substance varies inversely as the square root of the velocity 
 
 of wave propagation in it, or K = */ . This is for a 
 
 simple inductive action. But, for solid and liquid di- 
 electrics, this is complicated by the electret action, and 
 the induction becomes a more complicated function. It 
 is further complicated by the temperature of the substance 
 since the condition of the molecules as to motion must 
 markedly affect all inductive action. It would therefore 
 be difficult to derive a formula connecting all these vari- 
 ables. Even experimentally it is extremely difficult to 
 determine the inductive factor with reasonable accuracy. 
 Various investigators give rather different determinations 
 for various substances. Thus we have 
 
 FOR SHELLAC Faraday 1 . 55 
 
 Thornton 2.49 
 
 Everett 2.00 
 
 FOB SULPHUR Thornton 4 . 03 
 
 Ganot 4.73 
 
 Everett 2 . 24 
 
 FOR RESIN Thornton 3.09 
 
 Ganot 2.55 
 
 Everett 1.77 
 
 FOR GLASS Everett 1 . 75 
 
 Thornton 6 to 10 
 
 V 2 
 According to Maxwell's theory K = ^ . This is known 
 
 y 
 
 as Maxwell's law. Since is the index of refraction of a 
 
 V 1 
 
 substance for longitudinal waves, K = n 2 , where n is the 
 
MECHANICS 57 
 
 index of refraction. We have found that in a simple 
 (uncomplicated) induction, K = V~n. A few substances 
 have been found which conform to Maxwell's law more or 
 less, but *" Exceptions are much more numerous than 
 accordances." Likewise it is possible to select a list 
 which conforms approximately to the formula K = V~n> 
 but neither of these formulas represent all the conditions, 
 and neither can be considered a law. 
 
 When two different substances are rubbed together, 
 the vibrations of the molecules on the opposing surfaces 
 become polarized and are directed across the junction. 
 Waves are set up, which according to the relative condi- 
 tions existing in the two kinds of molecules, are in one 
 direction or the other. Simple contact is sufficient to 
 set up such waves. Thus when zinc and copper are 
 brought together, positive waves flow across the junction 
 from the zinc to the copper. These waves deposit charges, 
 and the wave force keeps the negative charges at the 
 copper end and the positive charges at the zinc end. 
 When glass and resin are rubbed together, the glass ac- 
 quires a positive charge; the resin a negative charge. In 
 a circuit of different metals such waves are set up at the 
 junctions, but their algebraic sum is zero, and therefore 
 no current flows. However, if the wave energy at one 
 junction is differentiated from the rest by heating or cool- 
 ing, a feeble current ensues. 
 
 A charged spherical body sends out its waves radially. 
 A small charge in its neighborhood will be attracted or 
 repelled along a radial line, if no other charged body be 
 near. If another charged body be near, this likewise will 
 radiate waves in straight lines from its surface, the radia- 
 tions from both bodies taking place exactly the same as if 
 the other were not present, providing the charges are on 
 nonconductors, and their distribution cannot be altered 
 inductively. 
 
 * Ganot's Physics. 
 
58 ELECTRICAL 
 
 If we explore the combined field with a small charge, 
 it will move in a path, the direction of which at any point, 
 is the resultant of the forces arising from the two inde- 
 pendent fields. If the two bodies are oppositely charged, 
 the path will be a curved line leading from a positive charge 
 on the surface of one body to an equal negative charge 
 on a certain point of the other body. We could map out 
 the different curved paths which such a small charge would 
 follow starting from different points of one surface, and 
 these paths would represent the combined field of force 
 between the two bodies. These different paths are called 
 lines of electric force. They have however no actual 
 existence, but are merely mathematical figments. What 
 actually exists are the wave trains being given off by each 
 charge, and these pursue their course absolutely unin- 
 fluenced by one another. This is not the case with mag- 
 netic lines, which are physical realities actual linear 
 vortices in the ether and the presence of other lines 
 influences their condition greatly, leading to their merging 
 together or repelling each other. 
 
 The case of a conductor offers a peculiar situation as regards the 
 specific inductive factor, K. It has been considered that K for 
 a conductor must be regarded as infinite, in which case the velocity 
 of wave propagation would be zero. This would have to be in- 
 terpreted that no longitudinal waves can exist in such a medium. 
 We might perhaps equally well consider K here as zero, or the 
 wave velocity infinite. The fact appears to be that there is really 
 no such thing as an inductive coefficient for a conductor, and we 
 might as well speak of the temperature of a charge of electricity. 
 
 Starting with the hypothesis that static charges of 
 electricity were simply differentiated portions of the ether, 
 denser or less dense than the general ether; that such 
 charges continually give off longitudinal waves of two 
 different kinds, according as they are positive or negative, 
 positive charges giving off negative waves and negative 
 charges giving off positive waves; and that all electrical 
 actions at a distance (attractions and repulsions) were 
 
MECHANICS 59 
 
 due to these waves; we have been able to deduce theo- 
 retically all known facts regarding electrical actions. 
 The steps in the reasoning are 
 
 1. Action at a distance can only be effected through a 
 medium. 2. That medium is the ether. 3. Such 
 action can only be effected by some kind of motion in 
 the medium, and this motion must be imparted by the 
 acting body. A dead body cannot act, although it may 
 be acted upon. So far we are upon uncontrovertible 
 ground. 4. Longitudinal waves necessarily cause such 
 actions (attractions and repulsions) and, excluding mag- 
 netic actions which have no place in electrical actions, 
 they are the only kind of motion in the medium capable 
 of effecting these actions. 
 
 An exception may be taken to No. 4. It may be said 
 that, granted longitudinal waves can produce such actions, 
 there may possibly be some other kind of motion, which 
 we have not thought of, capable of producing exactly the 
 same effects. The probability of any other kind of 
 motion producing the many diverse and complicated 
 phenomena of electricity; of the exact agreement of all 
 its effects with those of longitudinal waves, though itself 
 different, is infinitesimal. 
 
ELECTRO-CHEMISTRY 
 
 In Fig. 6 we have a cell containing dilute sulphuric 
 acid in which zinc and copper plates are immersed. To 
 each plate is connected a wire of the same material. 
 When the wires are not in contact 
 no ac ti n f an y kind takes place, 
 but when the wires touch, at the 
 H ? S O 4 J surface of contact longitudinal waves 
 
 are set up, the direction of which is 
 determined by the nature of the two 
 pj A 5 kinds of molecules. When zinc and 
 
 copper are in contact the direction 
 of the waves is from the zinc to the copper, so that a 
 positive charge is produced and held in the zinc end, while 
 a negative charge is applied to and held on the copper 
 plate. If the positive charge on the zinc plate could 
 flow through the liquid to the copper plate, a current 
 would flow and there would be an immediate equalization 
 of potential. But the molecules of liquids are not in 
 contact and a current, therefore, cannot flow through 
 a liquid. They are absolute nonconductors. Under an 
 enormous pressure, a path could be broken through the 
 molecules by a charge, just as it is possible to break down 
 any dielectric, but this is not conduction. Our plates 
 oppositely charged therefore form a condenser, of which 
 the liquid is the dielectric. The liquid, in fact, becomes 
 a fluid electret. It is under a state of strain, and its 
 molecules arrange themselves with their negative charges 
 pointing towards the zinc, and their positive charges 
 pointing towards the copper. 
 
 60 
 
MECHANICS 61 
 
 Now the atoms of a chemical compound are held to- 
 gether as molecules by the action of equal and opposite 
 charges on the various atoms. Thus, in HCl, there is a 
 positive charge on the hydrogen atom, and an equal 
 negative charge on the chlorine atom. The atoms never 
 come into actual contact, but are held together by the 
 mutual attraction of their two opposite charges. It has 
 been supposed that they revolve about their common 
 inertianal centre, just as two heavenly bodies do, the cen- 
 trifugal force balancing the attractional force, but this is 
 a matter which does not concern us here. The important 
 point is that what is known as chemical affinity between 
 atoms is due simply to the attraction of equal and opposite 
 charges on the atoms or radicles. 
 
 But to return to our liquid electret. The molecule of 
 sulphuric acid is composed of two atoms of hydrogen, 
 each with a definite charge of positive electricity, and a 
 radicle 50 4 which holds a negative charge equal to the 
 positive charges on the hydrogen atoms, or equal to double 
 the charge on a single hydrogen atom. In the electric 
 field between the two plates the atoms arrange themselves 
 in the direction of the strain (wave) lines the hydrogen 
 atoms being nearest to the copper, and the radicle 50 4 
 nearest the zinc. The molecules of the liquid do not come 
 into actual contact with the plates. Hence, in an un- 
 polarized condition, no charge exists on the plates ac- 
 quired either inductively or by direct application. But 
 in a polarized condition the hydrogen atoms next to the 
 copper plate all face towards this plate, and the 50 4 
 radicles next to the zinc plate all face towards this plate. 
 Extra charges are thus induced on the two plates the 
 hydrogen atoms inducing an equal charge of negative 
 electricity on the copper, while the 50 4 radicles induce an 
 equal charge of positive electricity on the zinc. The 
 result is that the molecules immediately next to the two 
 plates become torn apart, the positive halves being urged 
 
62 ELECTRICAL 
 
 in one direction, while the negative halves are urged in 
 the other. These two oppositely charged parts of a 
 molecule are called ions. The negative ions (50 4 ) are 
 urged towards the zinc, while the positive ions (H) are 
 repelled from the zinc and urged towards the copper. 
 Thus there is a procession of hydrogen ions towards the 
 copper, and a procession of S0 4 ions towards the zinc. 
 This is called the "Migration of the ions." As soon as the 
 two hydrogen atoms are detached from the molecules, 
 they mutually repel each other, while the 50 4 radicle 
 remains intact with its double charge. This double 
 negative charge is able to detach an atom of zinc which 
 has, of course, an equal positive charge, and thus a new 
 molecule of ZnSO< is formed. The hydrogen atoms with 
 their single charge are unable to detach an atom of copper, 
 and being drawn into actual contact give up their charges 
 to the copper. The action may be summed up as follows : 
 The hydrogen atoms which previously held positive 
 charges and were bound in an H 2 S*0 molecule, are now 
 isolated and without charge. The zinc atoms on the 
 surface, which previously held only a weak charge, though 
 sufficient to polarize the field, have now acquired a strong 
 positive charge, viz., that of which the hydrogen atoms 
 have been deprived, and by virtue of the acquired charge 
 are now the positive halves of a new molecule, ZS0 4 . 
 The transference of the positive charges from the hydro- 
 gen atoms to the zinc atoms has been effected through the 
 connecting wire. A current has flowed from the copper to 
 the zinc. The charges produced by the contact of the 
 wires were weak. They play little part in the process, 
 except by setting up the original field and determining 
 in which direction the action shall take place. The 
 principal part is played by the strong induced forces. 
 The mutual attraction between the double charges on the 
 S0 4 radicles and the double charges on the zinc atoms, 
 which was proportional to 4Q 2 , was sufficient to detach 
 
MECHANICS 63 
 
 the zinc atoms, while the mutual attraction between the 
 charges on the hydrogen atoms and on the copper atoms, 
 which was proportional to Q 2 , was insufficient to detach 
 a copper atom. Otherwise stated, the chemical affinity 
 between Zn and S0 4 is four times greater than that 
 between Cu and H. Certain atoms are capable of taking 
 only a single definite charge of electricity. Other atoms 
 may take double or three times this minimum amount, 
 but it is always an exact multiple of the minimum amount. 
 Atoms taking only the minimum charge are called univa- 
 lent; atoms taking twice this amount, bivalent, and so on. 
 This is perhaps because univalent atoms all have the same 
 maximum capacity. We may suppose atoms of a higher 
 valency to have a greater maximum capacity. Thus a 
 bivalent atom, or one capable of holding two univalent 
 atoms, is able to support two minimum charges, each 
 charge holding one of the univalent atoms. Since the 
 attraction between atoms is always inductive, their 
 charges in a molecule must be equal and opposite. In 
 every case the algebraic sum of the charges in a molecule 
 must always be zero. 
 
 While the univalent charge must be regarded as the 
 saturation charge for the atom, beyond which it cannot be 
 loaded, the charge on an atom of higher valency may be 
 far from the saturation point. Thus in HgCl, Hg has 
 only the minimum charge, and is not saturated, for it 
 easily holds twice this amount in the compound HgCh. 
 In our previous experiment with the galvanic cell, in which 
 we converted a molecule of J/ 2 50 4 into a molecule of 
 ZnS0 4 by transferring the positive charges on the hydrogen 
 to the zinc atom, we have done work. For the current 
 which flowed in the wire heated the wire, thereby expending 
 energy. Hence the electrical energy in the ZnS0 4 mole- 
 cule must be less than that in the H 2 SO t molecule. The 
 quantity of electricity is the same, but the pressure must 
 be less. We have seen that the mutual attraction of two 
 
64 ELECTRICAL 
 
 charges lowers their pressure. The attraction on the 
 hydrogen charges lowers their pressure by an amount 
 proportional to 2Q 2 , while the attraction on the zinc 
 charge lowers its pressure by double this amount, or pro- 
 portionally to 4Q 2 . The charges on the hydrogen atoms, 
 therefore, have forced their way through the resistance 
 of the wire by sacrificing a part of their pressure. 
 
 If we place two platinum electrodes in a cell containing 
 H 2 0, and give one electrode a positive charge and the 
 other a negative charge by attaching them to some 
 electro-motive source, such as a galvanic cell, we have 
 again our liquid condenser, or electret. Since the hydro- 
 gen atoms are positively charged and the oxygen atoms 
 negatively charged, they will stretch themselves along 
 the strain lines, the oxygen atoms towards the positive 
 electrode, the hydrogen atoms towards the negative elec- 
 trode. Immediately at the surfaces of the electrodes, the 
 molecules will be torn apart, and the hydrogen atoms will 
 give up their charges to the negative electrode, while the 
 oxygen atoms give up their charges to the positive elec- 
 trode. The procession of ions begins, and each atom will 
 deposit its charge as if it were a living carrier with a bucket- 
 ful of a certain definite quantity of electricity. The 
 buckets of the oxygen carriers hold exactly twice as much 
 as those of the hydrogen carriers, but as there are twice 
 as many of the latter as of the former, the total quantities 
 transferred are equal for both sides. Each carrier makes 
 only a single journey. When the atom has deposited its 
 measure it is discharged and is no longer subject to the 
 influence of the field. 
 
 Suppose we are using the zinc-copper-acid cell for the 
 electro-motive source. It will seem as if a current were 
 flowing, but actually there is no flow. The two cells are 
 absolute nonconductors, breaking the metallic circuit 
 at two places. However, in both cells, the carriers are 
 busy ferrying over the electricity, we might say, from one 
 
MECHANICS 65 
 
 bank to the other. In the galvanic cell, the ferrymen are 
 the hydrogen atoms and the S0 4 radicles, while in the 
 water cell, the ferrymen are the H and atoms. It is 
 as if a fluid were being pumped along in a hose, but at two 
 places the hose is broken. The only way to overcome these 
 obstacles is to form two bucket lines, and at each break 
 a line of buckets is seen forwarding the fluid with full 
 buckets in one direction while a line of empty buckets is 
 coming back in the other direction. The number of 
 buckets used measures very accurately the amount of 
 fluid transferred. 
 
 In the water cell, we have decomposed the water mole- 
 cules, and this process of tearing apart molecules is called 
 electrolysis. The oxygen is deposited at the positive 
 electrode and the hydrogen at the negative electrode, 
 without any charges, whereas they previously had equal 
 and opposite charges, and by virtue of these charges were 
 able to combine into molecules forming water. The 
 galvanic cell has done work, while the water cell has had 
 work done upon it. The amount of current, or quantity 
 of ether, necessary to transfer given amounts of electro- 
 lytes is readily computed, and vice versa, the amount of 
 electrolytes deposited gives us a very accurate measure of 
 the amount of current used. It is evident that twice the 
 amount of current will be necessary to deposit a given 
 amount of Hg from the compound HgCl 2) as from the 
 compound HgCl. 
 
 Grotthuss (in 1805) framed a hypothesis that the mole- 
 cules of an electrolyte aligned themselves along the strain 
 lines, their positive and negative sides being directed 
 towards the opposite electrodes. This they undoubtedly 
 do. He further supposed that under a sufficiently power- 
 ful current in the liquid (at that time it was supposed that 
 a current could flow through a liquid) the molecules were 
 disrupted throughout the entire line, the positive half of 
 one uniting immediately with the adjacent negative half 
 
66 ELECTRICAL 
 
 of the next one, and that at the extreme ends only a single 
 ununited component was left. Clausius very properly 
 objected that a very great force must be required to dis- 
 rupt all the molecules simultaneously, and that below a 
 certain minimum strength of current, no decomposition 
 could occur. Now the action of even the weakest fields 
 can produce some decomposition. When the molecules 
 are facing promiscuously, those next to the electrodes can 
 exert no inductive action upon them, but if a field is 
 sufficient to polarize at least some of them, then the in- 
 ductive action of those molecules directed towards the 
 surface acting jointly, is appreciable, and decomposition 
 results. The actual disruption of the molecules takes 
 place only directly at the surfaces of the electrodes, and 
 not in other parts of the line. 
 
 According to the modern theory, the molecules of a 
 compound in solution are always more or less dissociated, 
 their ions continually separating and recombining. The 
 theory further assumes that electrolysis is carried on solely 
 by such dissociated ions, and that if no dissociated ions 
 were originally present, electrolysis would be impossible. 
 But electrolysis can be carried on equally well with or 
 without free ions in the original solution. Even if free 
 ions should be present previously to applying the electric 
 field, they will carry on only a part of the process, for there 
 must also be a disruption by induction of the extreme 
 molecules next to the electrodes. Since in framing any 
 explanation it is wise to postulate no more conditions than 
 are absolutely necessary, and since the assumption of 
 previously existing free ions is unnecessary for the explana- 
 tion of electrolysis, we shall not consider it in the present 
 discussion. Whether under other circumstances and in 
 connection with other phenomena, it is necessary to as- 
 sume such dissociation as a general condition of all solu- 
 tions, is a question which does not concern us here. It 
 may be remarked that the theory was originally pro- 
 
MECHANICS 
 
 67 
 
 pounded because it was thought that electrolysis could be 
 explained in no other way. 
 
 In Fig. 7, we have a diagrammatic representation of the 
 condition of the charges in a water molecule when (1) in 
 
 H 
 
 o 
 
 <) 
 
 H 
 
 Fig.7 
 
 the interior of the liquid, and when (2) close to the surface 
 of an electrode. In the former position the charges 
 mutually attract each other towards the centre of the 
 molecule. In the latter position, the charge on the oxygen 
 atom is attracted by the positive charge on the electrode, 
 while the hydrogen charges are repelled, and released 
 from their former strain they assume a more normal 
 condition spherical. It is evident that the attraction 
 of the electrode on the oxygen charge is greater than the 
 resultant in this direction of the attractions of the hydro- 
 gen charges. Hence the molecule must be disrupted. 
 
MAXWELL'S THEORY 
 
 The name and work of Maxwell have exercised such a 
 great influence in the domain of electricity that it would 
 seem proper, in such a book as this, to touch briefly upon 
 a few main points of his theory. Some idea of his "Elec- 
 tricity and Magnetism" may be formed from the com- 
 ments of various writers. One describes it as "Pretty 
 stiff reading." Another says, "To ask a student to at- 
 tempt to assimilate the contents of the two volumes of 
 Maxwell in a year, or even in two years, is only to expose 
 him to the severest pangs of mental indigestion. Again 
 Maxwell's own views are there presented by him with not 
 the greatest clearness, while severe demands are made 
 upon the student's mathematical attainments." Lodge 
 says of it, "Much of it is rough hewn. It contains nu- 
 merous misprints and errata, and part of the second 
 volume is so difficult as to be almost unintelligible. Some, 
 in fact, consists of notes written for private use, and not 
 prepared for publication." The fact is that some parts of 
 Maxwell's book cannot be understood simply because 
 they are not understandable, and some other parts because 
 they are not so. Thus, while the advice, often lightly 
 given, to "Read Maxwell," can hardly be recommended as 
 affording, even to a mathematician, a profitable return for 
 the time spent, still it is advisable that the student of elec- 
 tricity should have some knowledge of Maxwell's theory, 
 if it can be considered a theory. For Herz said, "Max- 
 well's theory is simply Maxwell's system of equations." 
 
 Nevertheless, we owe to this great man the beginnings 
 of the enormous advances both theoretically and in 
 
 68 
 
MECHANICS 69 
 
 practical applications which have transformed our civil- 
 ization in a generation. Faraday had spent his life in 
 emphasizing the fact that the acting body was not the 
 only thing deserving of attention, but that very important 
 things were also happening in the immediate neighborhood 
 of an electrified or magnetized body. Whence, as was in- 
 evitable, a number of later writers have proclaimed that 
 the dielectric played the chief role in all actions, that of 
 the acting body being insignificant. But Faraday never 
 said that, for after all the originating source is "the thing," 
 although not the only thing, as had been thought before. 
 
 Maxwell did not discover the ether, but he rediscovered 
 it. He called the attention of mankind to this greatest 
 part of the universe, of which they had previously been 
 sublimely unconscious, and, compared with which, the 
 mass and energy of gross matter is infinitesimal. Only 
 one hundred years before Maxwell, the world had known 
 little more of electricity than Aristotle did. In his time 
 old habits of thinking persisted. The idea of action at a 
 distance without an intervening medium was general, 
 although Newton had clearly recognized the necessity of 
 such a medium. Maxwell shook himself free of all the 
 old fetters, and building where Faraday left off, discovered 
 that all electrical actions were carried by the ether. 
 He also found that light waves instead of being the vi- 
 brations pictured in the old undulatory theory, were of 
 a totally different character, and although he failed to rec- 
 ognize clearly and exactly what that character was, yet 
 he showed that they were electro-magnetic phenomena. 
 These two things may be summed up as his chief achieve- 
 ments and they are enough. 
 
 We shall now mention briefly some of the chief points 
 of his theory in detached statements. *"One can imagine 
 that the electro-magnetic strain condition arises through a 
 
 *Kalahne. Neuere Forschungen auf dem Gebiet der Electrizitat 
 und ihre Anwendungen. 
 
70 ELECTRICAL 
 
 change in the dielectric, which corresponds to a distortion 
 of the particles in an elastic body. Maxwell, following 
 Faraday, describes this change in the dielectric as a 
 dielectric displacement, though this need not necessarily 
 imply an actual displacement of the ether particles." 
 This is quoted to show the vagueness of some of his ideas. 
 Actually, there must be some displacement (motion) of 
 the ether particles. Maxwell's idea seems to be rather 
 that of a strain moving progressively through the medium 
 an abstract condition while the medium itself remains 
 at rest. 
 
 In every part of a dielectric both kinds of electricity 
 (positive and negative) are supposed to be present in a 
 neutral condition. In the phenomenon of induction, both 
 these electricities previously exist in unlimited quantities 
 in the conductor, and their separation results from a 
 stationary condition of strain set up in the medium. We 
 have seen that the induced charges are applied to the 
 conductor by the waves radiating from the inducing body, 
 and they are held apart by the wave force. According to 
 Maxwell these two kinds of electricity, which are present 
 everywhere, are not only separated in conductors, but also 
 in all dielectrics by a condition of strain. The separation 
 in dielectrics, however, is only through infinitesimal dis- 
 tances, and what he calls the dielectric displacements 
 consists of such separations of the two electricities. The 
 condition of strain which causes these displacements, and 
 the displacements themselves, or the cause and effect, 
 are treated as mathematically equivalent. It is as if a 
 lot of little balls were imbedded in the medium and had 
 their neutral electricity separated into its two components. 
 The displacement takes place successively along such a 
 row of balls in a line of force, by influence. Here we have 
 a curious reversion to the old idea of action at a distance. 
 It seems as if the idea of action through a finite distance 
 is repugnant, but this is obviated by strewing a lot of 
 
MECHANICS 71 
 
 minute balls throughout space, as, in that case, the action 
 will be only over infinitesimal distances. But to this 
 statement, Kalahne hastens to add that it should rather 
 be taken as a figurative presentation of the case, which 
 need not necessarily be actually so. Whenever we imag- 
 ine that we have some material platform to stand upon, 
 it is immediately torn down from under us. In a certain 
 sense, Maxwell was right in supposing that the two kinds 
 of electricity exist everywhere in a neutral state, for the 
 neutral ether becomes positive or negative electricity 
 according as it is condensed or rarefied. But Maxwell 
 did not understand it in this sense, since to him the ether 
 was incompressible. 
 
 Lines of electric force are merely mathematical repre- 
 sentations of observed phenomena, independent of any 
 special suppositions as to the nature of the dielectric dis- 
 placement. In a condenser which is charged by a current 
 source, while the charge on the plates is increasing and the 
 current is flowing, the lines of force in the dielectric in- 
 crease. Maxwell considered the increase of the lines of 
 force, or what is equivalent, the dielectric displacement 
 currents, could be regarded as a direct continuation of the 
 current. There was thus, wherever a current was flowing, 
 no such thing as an open circuit. All circuits were closed 
 circuits, and every part of a circuit had its current with 
 its accompanying magnetic field. In the conducting part 
 there was an ordinary current, while in the dielectric 
 there was a displacement current. If we are content to 
 deal with metaphysical abstractions, we may accept this 
 view, but if we have strict regard for the actual facts, it is 
 not so. We have seen that the waves traversing the field 
 in a dielectric, consist of alternating currents in the direc- 
 tion of the lines of force. These, in a certain sense, may be 
 considered displacement currents, but they are not Max- 
 well's displacement currents, which flowed only one way. 
 
 The ether is a dielectric, and Maxwell considered that 
 
72 ELECTRICAL 
 
 displacement currents occur in the ether, as in all di- 
 electrics. He thought that each displacement current 
 should have its own magnetic field, just as current in a 
 conductor is surrounded by a magnetic field. As a matter 
 of fact currents in the free ether, such as the to and fro 
 currents of a longitudinal wave, or the hypothetical dis- 
 placement currents of Maxwell, do not have any magnetic 
 field. The magnetic field accompanying a current in a 
 conductor is formed by the resistance opposed to the 
 current by the atomic surfaces. 
 
 Assuming displacement currents in the ether and that 
 they are accompanied by magnetic fields, it is possible 
 to form equations which express the time relation of the 
 variations of the electric force (which we can consider in- 
 differently a line of electric force or a displacement current) 
 to its magnetic field, or to the space distribution of the 
 magnetic strain condition. This gives us one set of Max- 
 well's equations for electro-magnetic disturbances in space. 
 
 Then he considered that the variation of the magnetic 
 force should likewise cause variations in the electric field, 
 or displacement currents. The next step was to suppose 
 that the magnetic forces and the electric forces possessed, 
 what are known in mathematics, as conjugate properties. 
 That is, the expressions for the variations of the one 
 quantity in terms of the other, can conversely give the 
 variations of the other in terms of the first, by simply 
 interchanging the symbols of the one for the other. 
 
 There was now a difficulty. One set of equations 
 those for the electric forces had an expression for a 
 displacement current. There could be no such thing as 
 a magnetic displacement current, or a magnetic current 
 of any kind. So the corresponding expression was simply 
 left out. Thus Maxwell's two sets of equations were 
 derived one set for the electrical forces, the other set 
 for the magnetic forces. 
 
 The mechanism by which the propagation of these 
 
MECHANICS 73 
 
 electro-magnetic waves is accomplished is left "in the air." 
 There are not necessarily any actual physical vibrations, 
 or any motion even, although their possibility is not nec- 
 essarily excluded. The process is simply a periodic and 
 progressive rise and fall of electric and magnetic forces 
 from point to point in space. Certain hypothetical forces, 
 which are pure abstractions, are dealt with in certain 
 equations, and a result is obtained. It is shown that both 
 the magnetic and electric forces lie in the plane of the wave 
 and are perpendicular to each other. Of course electric 
 and magnetic forces, mutually interdependent, must be 
 perpendicular to each other. 
 
 If we should begin to make some mental image as to 
 the nature of these disturbances, we should be told that 
 we must not think of anything tangible, not even of 
 motion, but merely of a passing rise and fall of energy at 
 some point, and that the electric and magnetic forces were 
 perpendicular to each other. 
 
 Now we have seen that an electro-magnetic wave con- 
 sists of a spreading out of vortex tubes. The electric 
 force, or the current sheet, which corresponds to what 
 Maxwell calls the displacement current, is circular and 
 has all directions. One of these directions is, of course, 
 in the plane of the wave, and the direction of the magnetic 
 force, or axis of the tube, is in the plane of the wave. Now 
 it happens that the only motion of the current sheet which 
 can possibly be detected by the eye, or in any other way, 
 is the one in the plane of the wave, since the effects of the 
 motions in all other directions are self-eliminatory. This 
 motion and the magnetic line lie in the plane of the wave, 
 and they are perpendicular to each other. So far we have 
 a corroboration of Maxwell's theory as to the position and 
 direction of the forces. It follows that a vortex tube is a 
 practical realization of Maxwell's abstract reasoning, as 
 far as that is possible, and it is fairly evident that there 
 can be no other motion which is such a realization. 
 
MISCELLANEOUS 
 
 We have hitherto stood upon tolerably firm ground. 
 We can assume with a fair degree of confidence that the 
 ether and electricity are synonomous. A positive charge 
 of electricity is a condensed mass of ether. A negative 
 charge of electricity is a rarefied portion of ether. At- 
 traction and repulsion generally are due to longitudinal 
 waves, the action depending upon the kind of the wave 
 (there being two kinds), and upon whether the body is 
 denser or less dense than the medium. This action is 
 not confined to the ether, but is seen in all media. Thus 
 two tuning forks emitting longitudinal waves attract each 
 other. A tuning fork attracts a balloon filled with car- 
 bonic dioxide, while it repels one filled with hydrogen. 
 The radiations from the surface of a carbonic dioxide 
 balloon repel a similar balloon, while attracting a hydrogen 
 balloon. A hydrogen balloon repels a similar balloon while 
 attracting a positive balloon. Gross matter and negative 
 charges of electricity radiate positive waves; positive 
 charges of electricity radiate negative waves. Magnetic 
 lines are linear vortices in the ether, and electro-magnetic 
 waves consist of trains of such vortices travelling outward 
 with the normal velocity of the medium. Chemical 
 affinity is the attraction of equal and opposite charges on 
 the atoms or radicles of a molecule. 
 
 There are, however, many phenomena outstanding 
 which must continue to be the subject of speculation. 
 That light rays should continue in a straight line, as sound 
 waves do not, is easily intelligible from their vortex 
 structure. The great difficulty with the old undulatory 
 
 74 
 
MECHANICS 75 
 
 theory was how to account for polarized rays. Knowing 
 that such rays consist of trains of vortex tubes, the diffi- 
 culty is reversed, and it might seem that all rays should 
 be polarized. It is evident, however, that the promiscu- 
 ous positions of these tubes in ordinary light is because 
 the vibrations are continually shifting in direction. That 
 they should be deflected slightly from a straight course 
 on grazing a sharp edge, we should expect, since the 
 grazing side of a vortex will be slightly retarded or acceler- 
 ated according to the direction of its rotation, with the 
 result that the vortex will be deflected above or below the 
 edge. That the diffraction bands should be wider and 
 extend to a greater distance above the edge than below, 
 we likewise could have predicted. 
 
 We have seen that the rate of the outflow of energy from 
 a body at a higher potential than its surroundings is 
 proportional to the excess of its potential, when the energy 
 streams out in the form of longitudinal waves. This is 
 not the case when the energy is radiated in the form of 
 electro-magnetic waves. The number of vortices gener- 
 ated in a conductor in a given time is proportional to the 
 current and also to the suddenness with which the current 
 
 i 
 
 rises, or it is proportional to J _ Hence the number 
 
 o dt 
 
 of vortices generated in unit time should be proportional 
 to the square of the current. Now the magnetic energy 
 in a vortex we have seen to be measured by the square of 
 the velocity of the current sheet. This current sheet has 
 the same velocity as the generating current at the instant 
 that it leaves the wire, and a current is measured by its 
 velocity. Hence the total output of energy in unit time 
 should be proportional to the fourth power of the current, 
 and since the current is proportional to the pressure, it 
 should also be proportional to the fourth power of the 
 potential. Stefan's formula states that the electro-mag- 
 
76 ELECTRICAL 
 
 netic radiation (heat) of the sun is proportional to the 
 fourth power of its temperature or potential. Since the 
 surroundings of the sun into which this radiation takes 
 place are at the absolute zero, or the temperature of 
 space, the potential must be measured from the absolute 
 
 77 
 
 zero. Stefan's formula is = r 4 , or the amount of heat 
 
 t 
 
 radiated per unit surface of the sun per unit time is 
 measured by the fourth power of its absolute surface 
 temperature. It is more than a formula and can be con- 
 sidered as expressing a law. The amount of energy 
 radiated by a wire, in wireless telegraphy, in unit time, 
 should be proportional to the fourth power of the average 
 pressure in the wire. This law has not as yet been ex- 
 amined in connection with radio-telegraphy, but it would 
 doubtless find confirmation. 
 
 When an atom vibrates, or moves to and fro along a 
 line, it generates both electro-magnetic waves and longi- 
 tudinal waves. The edges of the condensed ether in front 
 curl round over the rarefied ether behind and thus a vortex 
 is formed, while from the central part the longitudinal 
 wave is started. Thus, with every excursion in one 
 direction the compressed half of a longitudinal wave is 
 formed as well as a vortex rotating in a definite direction, 
 while, with the return excursion, the expanded half of 
 the longitudinal wave is completed and another vortex 
 rotating in the opposite direction is formed. The direction 
 of the alternating currents in the longitudinal wave is the 
 direction of the vibratory motion, while the vortex rings 
 spread out in a plane perpendicular to this direction. 
 The electric forces (the currents) are perpendicular to the 
 magnetic forces (the vortex filaments), as is inevitable. 
 The two kinds of energy radiated are not equal, for while 
 we may suppose the longitudinal wave energy to remain 
 measurably constant, the electro-magnetic energy radiated 
 
MECHANICS 77 
 
 increases as the fourth power of the pressure, and this 
 varies as the frequency of the vibrations. Hence it would 
 seem probable that the attraction exerted by a body is not 
 influenced by its temperature, while the electro-magnetic 
 radiation varies as the fourth power of the temperature. 
 
 If we seal electrodes into a bulb from which a gas has 
 been partially exhausted, we can transfer electricity 
 through it. The transference is by convection, as in the 
 case of an electrolyte. The molecules of the gas receive 
 charges and are violently repelled. They become dis- 
 sociated into their atoms, either from the charges they 
 receive or from the violent impacts on the electrodes. 
 When the source of energy is, as usual, an inductorium, 
 the field is very strong and practically constant, the lines 
 of force extending from the anode to the cathode. 
 
 Certain bodies called electrons are produced, the nature 
 of which is not yet fully determined. They are certainly 
 not atoms of electricity, for electricity is the ether, and the 
 ether as far as we know is a continuum. If they were 
 ether atoms, they would not be differentiated from the 
 rest of the ether, and therefore could not be observed. 
 They may possibly be minute vortex rings rings without 
 any central lumen which are given off from the elec- 
 trodes as the current surges violently and brings up with 
 an impact on the end surfaces. We have seen that a 
 rising current in a wire is full of such vortices which are 
 shoved outward around the wire. From an end surface 
 they may be simply projected away normally to the 
 surface. 
 
 Such vortices are very much less dense than the ether. 
 Consequently they constitute a negative charge, and 
 may be considered to be mainly a negative charge with 
 practically no mass. In an electric field they are urged 
 towards the positive electrode with the standard velocity ; 
 in a magnetic field with its lines perpendicular to their 
 line of flight, they are deflected in the same direction as a 
 
78 ELECTRICAL 
 
 wire would be carrying a current from the anode to the 
 cathode. They should traverse the space from the 
 cathode to the anode with the standard velocity, and with 
 proper conditions they very nearly attain this velocity. 
 Where there are too many atoms and molecules of the gas 
 in their path, their progress is impeded, and their velocity 
 may fall to two-thirds of the standard velocity, or even 
 lower. 
 
 When electrons strike upon a resisting surface they give 
 rise to what are known as X rays. It is possible that 
 they are burst by the violent impact and cease holding 
 their vacua. They thus become dissipated into the gen- 
 eral ether and cease being a differentiated part of it. Their 
 energy, which is magnetic, becomes transformed into a 
 violent explosive ether wave, just as when a vacuum 
 bulb is dashed against an object an explosive air wave 
 results. As in air such a violent single unidirectional 
 wave may travel with many times the standard velocity, 
 so these explosive waves, or X rays, may move with a 
 velocity which is limited only by the energy expended and 
 the suddenness with which it is expended. But we are 
 here in the realm of speculation. 
 
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