Return to Physics of the Ether

51. Mode of the Production of Motion through Vibration. — We shall now endeavour to investigate the mode or physical process by which motion is produced through vibration; and that not specially with the view to add proof to the circumstance that motion can be produced through vibration, this being already an observed fact in certain known experimental cases : just as, for example, we might investigate the mode or physical process by which a vibrating tuning-fork attracts a piece of card, without any view to add proof to the observed fact that the vibration of the fork can produce the attraction.

We have referred to the observed cooling of a heated substance in the free ether as a direct illustration of the fact that the motion of the molecules is being given up to the ether, and that, therefore, the emitted waves must on the whole contain an excess or surplus of energy, this surplus of energy representing precisely that lost

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by the molecules of the substance in the act of cooling down. We have now, therefore, to consider the mode or physical process. by which the vibratory motion of a mass or molecule communicates a certain excess or surplus of energy to the surrounding medium.

As a simple and generally applicable example, we may take the case of a tuning-fork vibrating in air. Then considering any one of the emitted waves : the physical disturbance of the air, termed " a wave," is of such a nature that the component molecules of the one half of the portion of air forming the wave have received an increment of velocity, the component molecules of the other half of the portion of air forming the wave having suffered an equal decrement of velocity; also the amount of condensation in the one half of the wave is the equivalent of the amount of rarefaction in the other half. An air wave may therefore be properly regarded as a mass of air in which the uniformity of the distribution of the molecules and of their velocity has been disturbed in such a way that a transference of matter and of velocity has taken place from one half the mass of air to the other half.

52. But it may now be shown as an important point that although the increments of velocity equal the decrements, that nevertheless the special physical conditions under which these increments and decrements are experienced are such that a certain excess or surplus of motion is imparted to the air, or exists in the wave. This deduction follows from the consideration that the portion of air whose molecules receive an increment of velocity is condensed in the act of receiving it, owing to the advance of the vibrating mass (or prong) towards the portion of air which receives the increment of velocity; while, on the other hand, the portion of air whose molecules suffer a decrement of velocity is rarefied in the act of losing it, owing to the recession of the vibrating mass from this portion of air; so that, therefore, although the increments and decrements of velocity experienced by the molecules situated in the corresponding halves of the wave are equal, yet from the effect of the condensations and rarefactions, the number of air molecules which receive an increment of velocity is greater than the number which suffer an equal decrement, so that a certain excess of motion exists in the mass of air forming the wave, or the vibrating fork therefore imparts a certain surplus or excess of motion to the surrounding air. The quantity of air which thus in each wave receives an increment of motion for which there is no corresponding decrement, is represented by the difference in mass between the condensed and rarefied half of the wave. Since this difference in mass between the condensed and rarefied half of the wave, i.e. the condensations and rarefactions increase with the vibrating energy of the fork, and also the increments of velocity themselves increase; it follows, therefore, that the excess or surplus of energy imparted by a vibrating mass to the surrounding medium must increase in a rapid ratio with the vibrating energy. This con-

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sideration would have its special application in the case of molecules where the vibrating energy is known to attain a high intensity.

53. Secondly, it may be shown that an excess of energy is imparted to the surrounding medium by a vibrating mass or molecule, due to a second separate physical cause, which we shall now consider. We have observed that the speciality of a vibrating movement is to affect the normal velocity of the component particles of the medium in such a way that equal increments and decrements of velocity are experienced.

But it is an important principle to observe, that when masses of matter experience equal increments and decrements of velocity so that the mean velocity remains unaltered, that, nevertheless, the energy being as the square of the velocity, the value for the energy does not remain unaltered. Thus, if we take the case of two equal masses having equal velocities, which we may express by V, the energy in each case being expressed by V 2 , and the total energy therefore by 2 V 2 . If now we suppose one of the masses to receive an increment of velocity v, its velocity therefore becoming V+v, the other mass experiencing an equal decrement of velocity, its velocity becoming V — v; then although the mean value for velocity has remained unchanged, yet the value for energy has by no means remained unchanged, for the energy of each mass being as the square of its velocity, the total energy now becomes (V + t>) 2 + (V - v) 2 = 2 V 2 + 2 v\ Now the value for the total energy before this change of velocity took place was only 2 V 2 . The total energy has therefore, by merely changing the velocities by equal amounts (so as not to affect the mean velocity), received a notable increase represented by the amount 2 v 2 . This is an important point, on account of the direct and practical bear- ing which it has on the phenomena of vibratory motion; the above indicating that the change of the velocities of the component particles of the medium by equal amounts, which it is the special function of a vibratory motion of matter to effect, is itself a direct cause whereby a certain excess or surplus of energy is communicated to the medium.

54. Hence, taking this cause into account, together with the one previously considered, it may be observed that there exist two separate influential physical causes by whose action the vibrations of masses or molecules are in all cases attended by the communication of a certain excess or surplus of energy to the surrounding medium.

The deduction that by the vibrations of masses or molecules a surplus of energy is imparted to the surrounding medium, is clearly of direct and practical importance as regards the phenomena of "attraction," &c, for the communication of energy to the component particles of a medium implies necessarily, under certain conditions, an expansion or rarefaction of the medium, and

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a rarefaction of the medium is the very condition required for an "attraction."

The observed fact of the resistance offered by an aeriform medium to the passage of masses, or indeed the simple observation of the resistance encountered in waving a fan, constitute other illustrations of the fact that the vibrations of masses are attended by the communication of a surplus of energy to the surrounding medium.

55. Since the presence of other vibrating masses cannot possibly influence the amount of energy imparted by a vibrating mass to the surrounding medium, it follows that a substance at normal temperature is losing as much heat or is imparting as much energy to the surrounding ether as if the substance were completely isolated, or as if everything around were at the absolute zero of temperature, only the substance under normal conditions maintains its temperature unchanged, from the fact that the sub- stance is receiving as much heat from surrounding objects as it expends. Taking normal temperature at 60° Fahr., then this represents an absolute temperature of 519 of Fahrenheit's degrees, reckoned from the absolute zero.

Since the waves developed in the ether by substances at normal temperature do not affect the senses, on account of the perfect state of equilibrium of motion which exists, or only an increase of temperature above the normal can affect the senses; in order, therefore, to be capable of forming a just idea of the amount of energy which is being given up to the ether continually by substances at normal temperature, it will only be necessary to sup- pose the temperature raised as much above the normal as the normal temperature is above the absolute zero, in which case substances would be giving up to the ether an addition of energy precisely equal to the energy which they were giving up at normal temperature. Accordingly, normal temperature being taken at 60° Fahr., we have therefore to add 519° to this temperature, giving 579° Fahr. A substance therefore at the burning temperature of 579° Fahr. has only received an addition of vibrating energy which is equal to that which it possessed at normal temperature, and which its molecules were actually imparting to the ether without affecting the senses. From this it may be judged what an amount of energy is being continually given up to the ether by the molecules of substances at normal temperature. If we take the case of water, which is a good radiator, and suppose a quantity representing one pound to be spread out into a layer or film, so that the vibratory motion of the molecules can be freely imparted to the ether, the area of the film being supposed such that the mass of water by radiation and absorption exchanges an amount of heat represented by only seven-tenths of a degree Fahr. per second, then it may be computed that the vibrating molecules of the pound of water at normal temperature are working up to about one-horse power in the amount of energy being continually given up to the

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ether. These considerations have their direct application as regards the intensity of the static and dynamic effects capable of being produced by the vibrations of molecules.

56. In dealing with the question as to the mode in which motion is produced by vibration, we will suppose a special illustrative case as serving best to put the FlG * 2 * subject in its clearest light. Let us

• „ 4l „ i suppose a cylinder or tube (Fig. 2)

containing air, a piston fitting into one end of the tube, the other end being closed. The piston placed just within the tube is supposed to admit of being put in rapid vibration, the limits of oscillation of the piston being supposed so small compared with the length of the tube that the influence of the change of volume of the enclosed air does not come into account. Then it follows necessarily from the previous considerations that a certain surplus of energy is imparted to the enclosed column of air by the vibrations of the piston. But since it is impossible to impart energy to the molecules of a mass of air without that mass tending to dilate, it follows that the confined column of air will, under the action of the vibrating piston, tend to expand and thus exert a pressure tending to drive away or repel the base of the cylinder and piston, and to expand the cylinder laterally, the energy of the effect being only limited by the energy with which the piston can be made to vibrate or oscillate. Since the surplus of motion imparted to the molecules of the air column . accumulates at every stroke of the piston, it follows that the pressure would increase continually by simply continuing, even at a slow speed, the vibration of the piston, if it were not for the fact that an increase of the translator^ motion of the air molecules is necessarily accompanied by an increase of the vibratory motion (heat) of the molecules, which form of motion can communicate itself to the molecules forming the cylinder, and thus be conducted away or dissipated, a limit being thus set to the rise of pressure which is thus made dependent on the energy of vibration of the piston. In the actual state of the case, therefore, the inference follows that the pressure will only rise until a stage is reached at which the amount of heat conducted away or dissipated through the cylinder is the precise mechanical equivalent of the work done in maintaining the oscillation of the piston, deducting therefrom the small unavoidable resistances due to the friction of the piston against the tube, &c.

57. If the sides of the cylinder were supposed to be partly formed of some elastic substance capable of distension, then the pressure exerted by the enclosed air would be necessarily followed by an expansion of the enclosing envelope, and this by a rarefaction of the enclosed air, the degree of rarefaction thus attainable being only limited by the degree of vibrating energy capable of being imparted to the piston. From these considerations

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we may deduce the important general conclusion that matter in stationary vibration tends forcibly to dilate and displace anything which hinders its free expansion.

58. We will now consider more closely the mode of vibration of the air column in such a case. It is evident that the air column would be thrown into stationary vibration by the reflection of the pulses of air from the base of the cylinder. We will first suppose, for simplicity, that the period of vibration communicated to the piston corresponds with the vibrating period of the air column, the air column in such a case vibrating as a whole in synchronism with the piston.

We then observe that the increments of velocity given to the air molecules are reflected from the base of the cylinder, back upon the piston, and in this case the time taken for a complete reflection is that of a single vibration, so that in this case an additional increment of velocity is given to the molecules of the air column at every stroke of the piston, which, if it were not dissipated in heat, would cause a continuous rise of pressure, and a continually increasing effort of the air to expand and rarefy itself.

59. A vibratory motion of matter would thus, in fact, appear to be one of the best possible mechanical means of communicating motion to the particles of a medium, and thereby causing the medium to expand forcibly and rarefy itself. In fact, when the physical conditions of the case are analyzed, we have the particles of the medium impinging continually with their normal velocity against a given mass of matter, so that it is only necessary to put this mass of matter in motion in order to communicate motion to these particles, and a vibratory motion is the form of motion specially adapted for this object, since by this form of motion the mass can communicate, continually, motion to the particles of the medium, and yet the mass can maintain a fixed position. Hence a vibratory motion of matter may be justly said to constitute the best-adapted mechanical means of accumulating motion in the particles of an aeriform medium, and thereby causing, under suitable conditions, a forcible rarefaction of the medium, this rarefaction of the medium being the physical condition required for an "attraction."

60. It may be further observed as an important point, as generally characteristic of the stationary vibration of a medium, that the motion of the oscillating air column, as in the present illustrative case, takes place in such a way that the condensed portion of the reflected wave meets the oscillating mass (piston) at its advance, while the rarefied portion of the wave meets the piston at its recession, so that for this special cause the increments of velocity are given at each impulse to a greater number of air molecules than would be the fact if the air column were not already in stationary vibration, so that for this special cause

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the work done by the vibrating piston 'upon the air column is augmented. The experiment of holding a vibrating tuning-fork over a resonance jar, when the fork loses its motion much more rapidly than under normal conditions, serves to illustrate the fact of the greater amount of work done by a vibrating mass upon the air when the air is in stationary vibration.

61. We will now, for further illustration, imagine the vibrating period of the piston to correspond with the vibrating period of the half column. Then the air column would, as is known

under these conditions, break up into

Fkk3 - two oscillating halves or segments

__„ - 41 + i i i (Fig. 3), vibrating in synchronism with

the piston, the two halves of the column rebounding from each other at the centre of the cylinder, and then rebounding simultaneously from the piston and the base of the cylinder. This case serves to illustrate well the expansive action attendant on the oscillations of the air column, the impacts of the halves of the column tending to drive out the ends of the cylinder; an<l since aeriform media propagate pressure equally in all directions, the sides of the cylinder must tend to bulge outwards, so that if the cylinder were partly com- posed of some elastic material it would expand laterally, this expansion being necessarily followed by a rarefaction of the en- closed air column, the degree of rarefaction thus attainable being only dependent on the vibrating energy of the piston. This illustrative case serves to convey a mechanical idea of the mode in which matter in stationary vibration tends to expand in every direction and displace that which confines it. If the character of the motion constituting a stationary vibration of matter be considered, as in the present case, it may be noted that each half of the air column simply performs a movement of oscillation between the centre and ends of the cylinder, so that each oscillating half of the column might be supposed replaced by an elastic sphere, which performs a reciprocating movement analogous to that of the half column, the two spheres rebounding from each other at the centre of the cylinder, and then rebounding simultaneously from the piston and base of the cylinder, the two spheres thus performing motions precisely analogous to those previously performed by the halves of the air column, the motion accumulating at each stroke of the piston, and the two spheres tending by their impacts to repel the ends of the cylinder in the same way as was the case with the oscillations of the two air masses.

62. If the piston were supposed to be made to oscillate to a more rapid period, then the air column would, as is known, divide into a greater number of oscillating parts or segments (Fig. 4), the principle involved in the motion being, however, precisely the same as in the case of two segments or in the case when the column oscillates as a whole. The segments into which an air column

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divides under the influence of vibration are well shown by the known experiment of putting a glass tube, having dust scattered in its interior, into stationary vibration by friction, when the enclosed air column being thus thrown into stationary vibration, the dust divides into a series of segments showing the corresponding division of the vibrating air column.

Pig. 4. Pia. 5.

• • • i : 7; Z , 3 .4

We may, therefore, again suppose the oscillating segments of the column (Fig. 4) to be replaced by elastic spheres (Fig. 5), each of which performs the reciprocating movement of the corresponding segment. Every alternate sphere, such as all those marked with the odd numbers, would at any given instant be moving simultaneously in one direction, while those marked with the even numbers move simultaneously in the reverse direction, this being the motion corresponding to the segments of the air column.

63. Now, it may be remarked as a point of interest that the character of this motion of the segments of the air column, or any column of a medium in stationary vibration, represents the character of the normal motion of the integral particles of the medium, when the resolved components of the motions of the integral particles of the medium in any two opposite directions are taken; precisely the same diagram having previously served in treating of the motion of the integral particles of an aeriform medium. It will be evident that this must be so, or the principle of the motion must be the same in both cases, since in both cases the character of the motion must be such that the column can be in equilibrium and maintain as a whole a fixed position in space, and, as before referred to, this is the only possible form of motion which satisfies these conditions, the motion in both cases taking place in such a way that as much matter at any given instant is moving in one direction as in the opposite. Thus it will be ob- served that the segments into which the column is divided move in such a way that the same quantity of matter is moving at any given instant in one direction as in the opposite, the sum of the segments moving in either direction representing half the column. A consideration of this analogy in the form of motion serves to show in a striking light the expansive action attendant on a stationary vibration of matter, or the motion of this oscillating masses of air into which the column is broken up tends to expand the column in all directions, or to dislocate and throw asunder its parts, just as the normal motion of the integral molecules of the column tends to expand it in all directions; indeed, the effect of throwing the air column into stationary vibration is simply to

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superadd to its own molecular motion a palpable mass motion of its parts. This tendency of matter when in stationary vibration to expand or dislocate its parts is well shown by the experiment of throwing a glass tube into forcible stationary vibration by friction, when the tube may be split into a series of rings, its vibrating parts flying asunder. Here the expansion is resisted by the cohesion of the glass. In the illustrative case of the vibrating column of air confined within the cylinder, the expansion of the column is resisted by the external envelope or cylinder, which consequently has to bear the pressure; and if means were given for the air column to expand freely, a rarefaction of the air would be the result, the degree of rarefaction attainable depending only on the energy with which the column is thrown into vibration.

64. The tendency of matter in stationary vibration to dilate and cause displacement might even be illustrated by the simple experiment of shaking longitudinally a corked tube partly filled with water and held horizontally, when the cork might thus be forced out by the oscillating mass of liquid. Here the stopped ends of the tube, when the tube is shaken longitudinally, play the part of two oscillating pistons throwing the enclosed liquid into vibration. It can be of no consequence, as far as the principle is concerned, whether the matter thrown into vibration be water, air, or the ether; only to produce a given effect, the speed of vibration must of course be greater as the matter concerned is less dense. In the above case the relatively very great density of the water enables a perceptible effect to be produced even by the slow shaking of the hand. A stationary vibration of matter is, in fact, simply a violent shaking of the matter acted upon, which therefore tends to expand in every direction, and drive away that which confines it; and if the matter in vibration be free to expand, then a forcible rarefaction is the result.

The above considerations all lead to the general conclusion that the method of vibration is a mechanical process eminently adapted to disturb forcibly the equilibrium of pressure of a medium, which may be attended by forcible movements of masses of matter, whose positions of equilibrium are determined by the equilibrium of pressure of the medium about them.

65. In the application of the above deductions to masses vibrating freely in a medium, such as to the case of vibrating molecules and free vibrating masses generally, we have only to consider the state of the case when the envelope is wanting, such as the case when the enclosing cylinder, or the distensible envelope in the illustrative example is removed; when the piston would be oscillating freely opposite the base of the cylinder, in perfect analogy with the prong of a vibrating tuning-fork oscillating freely opposite a piece of card, or with two molecules vibrating in opposition to each other.

It will be evident that the effect of removing the lateral

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envelope will be to afford facility for the lateral expansion, and therefore rarefaction, of the intercepted air column, or the column of the medium intercepted between two opposed vibrating masses (or molecules), the absence of the envelope enabling the oscillating column of the medium to expand laterally with freedom, the column thereby becoming rarefied.

Thus, if we take the case of a vibrating tuning-fork held in proximity to a lightly suspended piece of card, then the increments of velocity imparted to the molecules of the column of air intercepted between the vibrating prong and the card, accumulate by repeated reflections between the opposing surfaces of the prong and the card, producing a rarefaction of the air column, whereby the excess of pressure of the air at normal density at the back of the card coming into action, drives the card towards the prong. If the fork be supposed to be maintained at a constant degree of vibrating energy, then the increments of energy which, under the action of the two physical causes before dealt with, are continually imparted to the molecules of the intercepted air column, and which accumulate by repeated reflections from the card and prong, would be necessarily followed by a continually increased rarefaction of the intercepted air column, were it not for the fact that a portion of the vibrating energy of the column is dissipated laterally into the surrounding medium, by which a fixed limit is put to the rarefaction of the air column, the degree of rarefaction being thus made dependent on the vibrating energy of the prong. The same considerations apply in the case of two molecules vibrating in opposition to each other, as in the case of any vibrating masses whatever, or masses of matter which emit waves.

66. The above deductions may be stated in one general conclusion, viz. that the vibrations of masses or molecules of matter are in all cases necessarily attended by a rarefaction or displacement of the intervening medium : this conclusion holding, however distant the masses may be from each other, or however feeble the vibrations; the intensity of the effect becoming greater by an increased proximity of the masses, or by an increase of their vibrating energy.