Sympathetic Vibratory Physics

SECTION V.

67. The Physical Conditions of the Equilibrium of Molecules. — In proceeding to consider the physical conditions governing the equilibrium of molecules, it may be stated, first, that the equilibrium of a molecule of matter depends on the equilibrium of pressure of the medium about it.

We have observed that a vibratory movement of matter, under such conditions that the waves are reflected and thereby stationary vibrations are formed in the medium, is well qualified to disturb the equilibrium of pressure of the medium. If we suppose the imaginary case of a vibrating molecule of matter completely isolated, then stationary vibrations could not be formed in the medium, the equilibrium of pressure of the medium about the molecule could not be disturbed, and the molecule would be in equilibrium. But if we suppose a second molecule placed in proximity, then the medium about the molecule is specially disturbed at that side where the second molecule is situated, due to the formation of stationary vibrations in the medium intervening between the molecules by mutual reflection of the waves, a rare- faction of the intercepted vibrating column of the medium which abuts against the opposed molecules being the result. The condition of equilibrium of the molecules will therefore depend upon the fact whether the pressure of the intervening vibrating ether column is greater than, equal to, or less than the ether pressure at the remote sides of the molecules, where the normal ether pressure exists; the molecules being driven in the one direction or in the opposite, or remaining in equilibrium, according to the relation of these two pressures.

Now, the rarefaction which attends the stationary vibration of the intervening ether column would, by reducing the ether density, i. e. by reducing the number of ether particles which impinge against the sides of the molecules which oppose each other (i. e. the side of each molecule where the vibrating column terminates), tend to cause a mutual approach of the molecules under the action of the superior number of ether particles which impinge against the remote sides of the two molecules where the ether density possesses its normal value, this physical effect corresponding to an " attraction."

On the other hand, the direct action of the pulsations of the vibrating ether column, or the direct action of the increments of energy given to the particles of the column, would, considered by itself alone, tend to propel the molecules farther apart, a physical effect corresponding to a " repulsion."

These are, therefore, the two opposing physical influences which determine the position of equilibrium of each molecule, each mole- cule being driven in the one direction or in the other, or remaining in equilibrium, according as the direct influence of the pulsations of the intercepted ether column or the indirect influence of the rarefaction attendant on these pulsations attains the upper hand, or the two opposing influences become equal.

68. It follows, therefore, that two molecules can only be in equilibrium under those special physical conditions when by a special adjustment of distance and vibrating energy these two opposing physical influences happen precisely to counteract each other; the

molecules being urged in the one direction, or in the opposite, "attracted," or "repelled," according to which influence pre- dominates under the existing physical conditions.

69. When the separating distance of two molecules is made to vary, this change of distance is necessarily accompanied by an important change in the physical conditions about the molecules. Firstly, a variation of distance is attended by a change in the relative proportions of the intercepted vibrating ether column, whose length is determined by the intervening distance, and upon the physical state of which the conditions of equilibrium of the molecules intimately depend. Secondly, a variation of distance is attended by a change in the energy of the stationary vibration of the intercepted ether column. When the molecules are placed in very close proximity, the intercepted ether column becomes short relatively to its breadth, the lateral area afforded for expansion becomes contracted, and the pulsations of the column are more concentrated against the opposing molecules, tending to separate them; also the energy of the stationary vibration of the column has been increased, owing to the increased proximity of the molecules. It would appear reasonable to conclude from this that the physical influence producing a " repulsion " would predominate in the nearest proximity to a molecule — an inference which accords with observed facts.

On the other hand, when the separating distance of two molecules is increased, the intercepted ether column becomes long relatively to its breadth, more lateral area is afforded for expansion, which would conduce to a rarefaction of the column, a result favourable to an "attraction." Also, the energy of the direct action of the pulsations of the column has been reduced by the increase of distance. To take an illustrative case : The aggregation of vibrating molecules, known as the " solid," comport them- selves in such a way that when the distance of the molecules is reduced, they "repel," and when the distance is increased the molecules " attract," or a solid resists an attempt both to compress and to dilate it, each molecule taking up a position or point of stable equilibrium, the situation of which point varies by a change of vibrating energy (change of " temperature "). In order for the general phenomena of alternating " attraction " and " repulsion " exhibited in the case of molecules to be produced, it is only necessary that the two opposing physical influences which deter- mine the equilibrium of the molecules should not preserve the same constant ratio to each other under the varying physical conditions attendant on a change of distance. Thus the diminution of the ascendant influence up to equality and beyond, by an increase of distance, would produce alternating attraction and repulsion, separated by a neutral point of equilibrium.

70. We will now notice a few of the facts as they actually exist. Although there are some exceptions in the case where the

vibrating periods of the molecules differ, there is a broad or general agreement in certain of the effects observable, more particularly in the case where the vibrating periods of the molecules are the same. The aggregation of molecules in the solid state in the vast variety of materials forms an instance where the vibrating period of the aggregated molecules is the same. Now, in the general case of molecules of similar vibrating periods, and also in certain other instances, the first marked effect observable on approaching the molecules towards each other, is a repulsion; then by a further approach there is an attraction, and in the closest proximity there is again a repulsion. Thus, in the general case of solid bodies, two separate portions of the same substance will not readily unite even when pressed together, or the molecules in the first instance repel. It is practicable in certain cases to apply a sufficient pressure to overcome this first repulsion, and to bring the molecules into proper proximity for the attraction to come into play. Thus, two freshly cut surfaces of lead may be made to unite by pressure, this being also the case with glass and some other substances. After this degree of approach has been attained, i.e. after the molecules have taken up those positions of stable equilibrium which constitute the aggregation of the molecules in the solid state, then a pressure is necessary in order to cause a further approach, and the molecules recoil or recede into their previous positions of stable equilibrium when this pressure is removed; so that therefore the attraction changes into a repulsion in the nearest proximity to the molecules.

71. Since, therefore, the repulsion experienced on the first approach of two molecules changes into an attraction by a further approach of the molecules, it follows that a certain point must exist at a certain definite distance outside a molecule (the vibrating energy being supposed kept constant), at which point, if a second similar molecule be placed, it is in equilibrium; but if the molecule be placed a short distance outside this point, it is repelled; and if it be placed a short distance inside this point, it is attracted. Accordingly, since the shifting of the molecule to a short distance to either side of this point causes it to be driven farther away from the point, this point might, therefore, be termed " the neutral point of unstable equilibrium," where repulsion changes into attraction.

Further, since after this neutral point has been passed and the attraction coming into play, the molecules are urged a short distance towards each other, each molecule then takes up a position of stable equilibrium, where attraction changes (inversely) into repulsion; it follows that a second neutral point must exist outside a molecule (in nearer proximity to the molecule than the first neutral point), at which point, if a second similar molecule be placed, it is in stable equilibrium. Since also when the molecule is shifted to a short distance to either side of this second neutral

point, it returns to it again when left to itself, or when the disturbance ceases; this second neutral point in nearest proximity to the molecule might, therefore, be termed "the neutral point of stable equilibrium."

72. As an illustration of this deportment of molecules when, instead of separate portions of a solid, separate or discrete molecules are concerned, we may take the case of a vapour or gas. As a generally applicable example, we may take the case of iodine. This substance exists as a vapour at the same temperature at which it exists as a solid, as is in general the case with solids more or less. The discrete molecules of iodine, therefore, which compose the vapour, although at a temperature (vibrating energy) suited to the formation of the solid state, yet these molecules can rebound from each other in the free translatory motion of the gaseous state without uniting. The discrete or separate molecules, therefore, as was to be expected, deport themselves towards each other as two separate portions (i. e. parts composed of a number of molecules) of the solid substance, or the discrete molecules forming a vapour or gas comport themselves towards each other, as the outer layer of the molecules of a portion of the solid substance would comport themselves to the outer layer of the molecules of another separate portion of the same substance, i.e. the molecules in the first instance repel.

As an example of a similar fact in a case where the vibrating periods differ, we might instance the case of oxygen and hydrogen gases, a mixture of which in a proportion suited to an explosion may be kept for any length of time without the molecules uniting; and although the molecules are interchanging motion among them- selves in free translatory motion, they do not under normal conditions come into sufficient proximity to unite. In order to effect this, some disturbing cause is necessary, such as, for example, the application of incandescent matter (matter in intense molecular vibration), or perhaps a sudden forcible concussion.

73. The Reciprocity of Attraction and Repulsion. — It is a note* worthy fact that a complete reciprocity exists in the phenomena of attraction and repulsion, or, in other words, each of the two masses or molecules concerned is acted on with precisely equal energy. This has been experimentally proved, in the series of experiments before noticed, to be a characteristic of the effects produced by vibrating masses generally.

In one case specially described, a vibrating tuning-fork was suspended in such a way as to be free to move, and on a piece of card being held near the fork, the latter moved towards the card, precisely as (conversely) the freely suspended card would have moved towards the fixed vibrating fork. The description adds : " Hence, to whatever cause the approach is due, the action is mutual."

Now, it may be shown that this mutual action is one of the

necessary consequences of the fact of the existence of stationary vibrations in the medium between the influencing masses, as in this special case, in the column of air intercepted between the vibrating prong and .card; the same considerations applying to vibrating molecules as to any vibrating masses whatever.

The physical characteristic of a stationary vibration being a mutual or reciprocal reflection of the pulsations of the intervening column of the medium from the surfaces of the opposed masses, reciprocity of action is therefore a necessity, the energy of the movement of either mass depending solely on the relation that the pressure of the intervening column of the medium in stationary vibration bears to the normal pressure of the medium; as in the present case, the energy of the movement (approach) of either the fork or the card depends on the relation that the pressure of the intercepted rarefied column of air bears to the normal air pressure, and this pressure of the vibrating air column intercepted between' the prong and card must be mutual or equal for each surface, since the pulsations of the column are mutually reflected. The intercepted vibrating air column abuts against the opposing surfaces of the prong and card, the pressure being propagated between the surfaces by mutual reflection, so that a perfectly mutual or reciprocal action becomes a necessity; indeed, the one pressure owes its existence to the opposite reacting pressure.

In the same way in the case of molecules, reciprocity of action is the necessary consequence of the mutual reflection of the emitted waves; the common movement of two vibrating molecules towards or from each other (attraction or repulsion) depending solely on the fact whether the pressure of the intercepted ether column in stationary vibration is greater or less than the normal ether pressure.

74. From the above considerations, therefore, the general conclusion follows that one of the necessary results of a stationary vibration of the medium is to make the effects perfectly reciprocal or mutual.

It may further be shown that the effects are not explicable by the vibrations of the masses themselves alone, but that the stationary vibration of the intervening medium is the sole physical cause concerned in the phenomena of attraction and repulsion, and the mere emission of waves without the action of the stationary vibration of the medium would be incompetent to produce the effects.

This may be proved from the following considerations. Firstly, the production of waves is not in itself attended on the whole by a rarefaction or absolute displacement of the medium, the condensation in the one half of the wave being the equivalent of the rare- faction in the other half, and it is only when the waves become stationary by mutual reflection, and the energy thus accumulates at a fixed spot, that a permanent rarefaction of the medium can

be produced. Now, since a rarefaction of the medium constitutes the only possible physical means by which an attraction (approach) can be produced by vibration, and, further, since a rarefaction is only possible under the condition of a stationary vibration of the medium, it therefore follows that a stationary vibration of the medium can be the sole physical cause concerned in producing an attraction.

75. When justly viewed, the observed experimental fact previously referred to, where a fixed card attracts or causes the approach of a freely suspended vibrating tuning-fork, affords in itself a complete illustration of the truth of this principle. In this case the card does not vibrate at all, and yet the card acts upon the fork with the same force that the vibrating fork acts upon the card. This equality of action, therefore, proves at once that the vibrations of the fork give it no special advantage, or the waves emitted by the fork have of themselves no special influence independent of the stationary vibration of the intervening air column; for if this were the case, the effect would be one-sided and not mutual. The very fact that the mass which does not vibrate at all can produce as great an attraction as the mass which vibrates, itself proves that that which is concerned in the effect must be something independent of the vibrations of the mass itself, and, moreover, something placed under such physical conditions as to make the effect mutual. This is only true of the intercepted column of the medium in stationary vibration, whose pressure (whatever its value) must affect both opposing masses equally, the effect being solely dependent on the stationary vibration of the intervening medium, the effect produced by a mass being (by a given energy of vibration of the intercepted column of the medium) independent of the fact whether the mass vibrates or not; or by a given energy of the stationary vibration of the intercepted column of the medium, the effect is the same whether one or both masses vibrate, or they vibrate with different degrees of energy. This point is further illustrated by the observed perfect reciprocity of action in the case of aggregated molecules, whose vibrating periods and vibrating intensities differ (chemically combined molecules). The stationary vibrations produced in the intervening medium by the mutual reflection of the emitted waves, therefore, constitute the sole physical cause concerned in the effects comprised under the phenomena of " attraction and repulsion," and the action of the stationary vibrations is also the sole means by which the reciprocity of the effects admits of being explained.

76. The only conceivable way in which a vibrating suspended tuning-fork could be affected by the presence of a distant card, is that the medium about the fork is in some way affected by the presence of the card. Now, since the card does not itself vibrate, the only possible way that it can affect the medium about the

fork is by reflecting the impinging waves back upon the fork, by which stationary vibrations are produced in the intervening medium, and to these stationary vibrations alone, therefore, can the approach of the fork possibly be referred. Further, since in the converse case when the fork is fixed and the card movable, the card is acted on with precisely equal force, it follows, there- fore, that the same physical cause, i. e. the stationary vibrations of the medium, must be solely concerned in this case also, i. e. in both cases, whether it be the approach of the vibrating fork or the approach of the card.

It may be further observed in the illustrative case of the vibrating freely suspended fork and fixed card, that unless the reflection by the card of the emitted waves, back upon the fork (and the consequent production of stationary vibrations in the intervening medium), be taken into account, by which means the medium about the fork at that special side of the fork where the card is situated is specially affected, it would be a complete impossibility to explain why the presence of a card should cause a vibrating suspended fork to commence moving towards it; for unless these stationary vibrations were produced, the medium about the fork would be in precisely the same physical state when the card is present as when the card is absent, and consequently there would be no more reason for the suspended fork to commence moving in a particular direction (to be " attracted ") when the card is present than there would be when the card is absent, the same reasoning applying in the case of molecules as in the case of any masses of matter whatever.

77. The above considerations all lead to the general conclusion that the stationary vibrations produced in the intervening medium are the sole physical cause concerned in the phenomena of attraction and repulsion, and that the mere emission of waves, independent of the stationary vibrations, would be incompetent to produce the effects.

78. There is one point, perhaps, worthy of notice in regard to the establishment of reciprocity of action, viz. that this must require a certain time to establish itself, excepting in that special case when both masses commence to vibrate at the same instant and with the same energy. Thus, if we suppose the case where one mass is put in vibration after another mass has been placed in the vicinity, then in such a case the inference is necessary that the action would be without reciprocity for a short period, or one mass would be acted on alone for a short period. Thus, if we take the illustrative example of a tuning-fork and card, and suppose that the card is first brought into the vicinity of the fork, and then that the fork is put into vibration; then it is necessary to conclude that the card would be influenced a certain fraction of time before the fork; for the vibrations of the medium become stationary at the card at the instant when the wave reflected

from the card meets the emitted wave, i. e. at the instant when the reflected wave commences its return, whereas the vibrations of the medium cannot become stationary at the fork until the reflected wave has completed its return, i. e. has traversed the entire interval between the card and fork, and has reached the fork. Until the vibrations of the medium become stationary at the fork, or until the emitted wave reflected from the card has reached the fork, the fork cannot possibly be influenced by the presence of the card, for before the reflected wave reaches the fork the medium about the fork continues to remain in precisely the same physical state as if the card were not present. Hence, in such a case, the inference is necessary that the one mass is affected before the other, although after the completion of the stationary vibration of the medium* reciprocity becomes perfect, the time required for reciprocity to establish itself being represented by the time required for the wave to traverse the intervening distance separating the masses. These considerations possibly might have a more important application in a case where the separating distance of the influencing masses was great.

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Physics of the Ether - SECTION V