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first three cases. And as the red ball is struck with greater and greater force, so does the rate of motion along the line of discontinuous balls become higher and higher.
The balls might have been of wood, metal, or glass. Let us suppose them to have been of pine, and placed, with the exception of the red ball, in actual contact. Let now the red ball move at the rate of ten feet per second, and strike the first white ball as before. The white balls being now in actual contact, the motion produced by the blow would to the eye be so extremely rapid that it would appear instantaneous. That is, directly the first white ball was struck, the orange one at the opposite end would move. If, however, great care were taken, and very refined methods of measurement of time were adopted, it would be found, that the rate of motion was not nearly instantaneous. In this particular case, in which pine balls were supposed to be placed in a line, the motion along the line would be at the rate of 10,900 feet per second. Let now the red ball strike at the rate of twenty feet per second, will the rate of motion be doubled? And if the red ball move at the rate of thirty feet per second, will the rate of motion along the continuous line of balls be trebled? No. No matter what may be the rate of motion of the striking ball, the rate of motion along the continuous line of balls is not altered. The rate would still be 10,900 feet per second. If the balls had been of glass, instead of pine, the rate of motion would have been from 12,000 to 17,000 feet per second; if of platinum, 8000 to 9000 feet per second; if of fir, from 13,000 to 18,000 per second. In water the velocity of sound is about 5000 feet per second. In air and oxygen the velocity of sound is about 1000 feet per second; and in hydrogen 4000 feet per second.* In all cases the rate does not vary with the striking force, while, as we saw in the case of a line of discontinuous balls, the rate of motion did vary with the striking force.
We see then these laws : first, that the rate of motion along the line of discontinuous balls varies with the rate of motion of the striking body; second, that the rate of motion along a continuous body does not vary with the striking force. That is, through solids, liquids, and gases, the rate of motion is invariable. These two laws are not defined with mathematical precision. Indeed, in a mathematical definition the foregoing terms could not be very
well used, though they clearly enough indicate the characteristics of discontinuity and continuity in the means of communication of motion
Tyndall's Lectures on Sound, and Deschanel's Natural Philosophy.
or vibration. The rate of transmission of sound depends upon the degree in which the body can be compressed longitudinally and expanded laterally. Cork can be compressed very much, and the velocity of sound in cork must be extremely low. Diamond, on the other hand, is of the very opposite character, and therefore the velocity of sound in diamond should be extremely great. All solids and liquids are porous or full of empty spaces, and of course gases are extremely so. Longitudinal compression and lateral expansion are really the resultant action of a single movement. The loss of motion laterally is greatest in soft bodies. If lateral expansion
ould be prevented, then as the porosity of the body grew less and less the rate of transmission of sound would become greater and greater. The rate of motion of a compressive vibration depends very greatly upon the porosity of the body along which the vibration passes, and so indeed does a vibration produced by a pull. When, bowever, we refine to an indefinite extreme upon this conception, we shall see, that as the porosity of the body becomes extremely small, the rate of motion of a compressive vibration becomes extremely great, and can be conceived to become indefinitely great, if the force applied be adequate. In the case of a vibration produced by a pull, however, the rate of transmission is limited by the strength of the material. It is the inertia of a body, that causes longitudinal compression and lateral expansion, and the elastic power being equal, the greater the density, that is the greater the inertia, the less the velocity with which a vibration travels. On the other hand, the elastic strength being equal, the less the density, that is the less the inertia, the greater the velocity with which vibration travels.
Good ordinary steel bars stand a strain of 30 tons to the square inch. If the steel bars, however, are tempered, or annealed in oil, they will stand a strain of 90 tons to the square inch.* The following particulars regarding the very best made steel wire are extremely valuable :- A sample of No. 22 (Birmingham) pianoforte steel wire sustained 31 kilometres of its own length. Its density was 7.727. The weight it would bear is at the very high rate of 150 tons per square inch, or its strength is five times that of good ordinary steelbars.f We may suppose that Young's modulus of elasticity for steel is increased in the same proportion. The velocity of sound in
* See Anderson's “Strength of Materials,” Longman’s Text Book of Science.
+ See Sir W. Thompson's article on “Elasticity,” in the Encyclopædia Brittannica, 9th edition.
ordinary steel is 16,400 feet per second. In the case of the No. 22 (Birmingham) steel wire, this rate would have to be multiplied by the square root of 5, that is by 2-24. The velocity of sound in this wire would thus be nearly 37,000 feet, or about seven miles per second.
We have now to consider, how the ether can have the property of continuity in a degree as high as that, which can only be expected in a rigid solid, and yet have the tenuity and noncohesiveness of the very rarest gases. The density of the ether is enormously less than even the lightest gas we know anything about—hydrogen. The less the density of a body the less the inertia of its particles, and consequently the greater the rate of transmission of vibration, provided that its elastic strength remains the same. When, however, we reduce the density of a body, we also reduce its elastic power. The greater the cellular capacity of a body, the lower the velocity with which a vibration is transmitted. If we place a number of stout steel rings in a row, and in actual contact, the rate of vibration along them would be of a certain value. If we halve the thickness of rings, however, we reduce the density or inertia of the rings by one-half, but, and here is the important point, we reduce the elastic power of the row by more than one-half, because, in this case, the elastic power depends upon the rigidity of the rings. And, if we reduced the thickness of the rings of steel so as to make the space occupied by the row of the density of air, they would be more flexible than silk threads, and no vibration whatever could be transınitted along such a row of thin flexible rings. Yet, a hollow silken ball expanded, say with hydrogen, is to the ether as dense as the heaviest solid is to the thinnest air. Yet the ether, it is to be remembered, has to be as rigid as a solid.
Starting with the observed facts, that sound travels in air at the rate of 1090 feet per second, while light is propagated through the ether 186,000 miles in the same time (that is to say, 901,000 times as fast), we are enabled to say how many fold the elastic force of the air, or its resistance to compression, would require to be increased in proportion to the inertia of its molecules, to give rise to an equally rapid transmission of a wave through it. The elastic force of the air would require to be increased 1,148,000,000,000 fold. Let us suppose now that an amount of our etherial medium equal in quantity of matter to that which is contained in a cubic inch of air (which weighs about one-third of a grain), were enclosed in a cube of an inch in the side. The bursting power of air so enclosed, we know to be 15 lbs. on each side of the cube. That of the imprisoned ether then, would be fifteen times the above immense number (or upwards of seventeen billions) of pounds. Do what we will, adopt what hypotheses we please, there is no escape, in dealing with the phenomena of light, from these gigantic numbers; or from the conception of enormous physical force in perpetual exertion at every point, through all immensity of space.
* Sir John Herschel-Elementary Treatise on Light.
One great mathematical physicist has calculated the elastic force of the ether and makes the proportion vastly greater.
In the above extract the italics are Sir John Herschel's own. Taking the row of rings, as described in the previous paragraph, we may consider them as rotating about their centres. If the velocity of rotation is great, the force is proportionately great. The centrifugal force, using the term in the sense in which it is ordinarily employed, will be also great, and will make these extremely flexible rings equivalent to approximately rigid rings. In this case of rotating rings, we can make the rings indefinitely thin without reducing their elastic force in a greater proportion than that, in which we reduce their density, that is, their inertia.
Let us now consider what would be the elastic force of these rings, if they were made of the best pianoforte steel wire. The rings could be conceived to rotate with such a high velocity that the centrifugal tension would be just as much as the wire would bear, that is, the tension would be at the rate of 150 tons to the square inch. We may assume the effective centrifugal force as being at the rate of about sixty tons to the square inch. If we conceive a pile of these rings resting edgeways on one another, the lowermost one would be flattened by a height of nearly three miles, if the pile were raised at the surface of the earth. We saw that the velocity of sound along the wire was rather more than one-third of what may be called its “breaking-length.” The numbers were—“ breaking-length,” nineteen and a quarter miles; velocity, seven miles. In the same way with this pile of rings, we may consider the velocity of vibration along the pile per second to be more than one-third of the height which could be supported by the lowermost rapidly rotating ring. The velocity with which a vibration would in this case be transmitted, would be one mile per second. As a body of steel can expand freely in a lateral direction, while in the case of the ether no lateral expansion is permissible, the velocity in the ether would be in a higher proportion. In conceiving matter in an extreme state of tension and tenuity we may consider its porosity reduced to an indefinite extreme. The ether may, therefore, be considered as having the matter of its corpuscles almost inextensible, and the rate of transmission of motion along the matter of the ring itself would, in such cases, be almost instantaneous. The velocity of transmission along the pile of rings was reckoned at one mile per second. To enable a row of such rings to transmit a vibration with the velocity of light (186,000 miles per second), and under the same conditions,
the tensional strength of the wire of the rings would have to be increased 186,000 fold, in a bar with free lateral expansion the increase would be as the square of 186,000. Further consideration of the molecular and porous structure of matter would probably, however, reduce the seeming difference between the strength of the best steel and the matter of the ethereal corpuscles,—for the strength of the steel wire depends on the force of cohesion. Now the force of cohesion is probably the force of an elastic reaction, and would be greatly less than the real strength of the matter of which steel is constituted.
This article has discussed only the application of the principle of rotation, and has not considered how corpuscles could rotate in the ether. In a paper on "The Cause of Gravitation," read before the Southland Philosophical Society, the writer has discussed the form and action of such a corpuscle. It would take too much space to explain. It may, however, be stated that, in the “paper” referred to, it is shown, that an “ethereal corpuscule” may have nearly the form and action of a smoke ring *
The numbers given are in all cases rough approximations, for it is perfectly useless basing exact calculations on single instances. Witness for example, the differences, the great differences, in the velocity of sound in different specimens of wood, glass, and steel. One authority in mathematical physics determines the elastic force of the ether to be twenty thousand billions (20,000,000,000,000,000) times the elastic force of good steel. The rotation of a corpuscle with an extreme velocity, however, saves us from imputing to the attenuated ether such stupendous forces.
T. WAKELIN, B.A.
* See article “Vortex,” Chambers's Encyclopedia, or Tait's Advances in Physical Science, for an illustration of a smoke ring.