Return to Physics of the Ether
163. Absolute Quantity of Energy in the Unit Volume of Space. — We shall now consider more particularly the energy enclosed by the ether, with the endeavour to give some idea of the absolute value of the energy represented by the motion of the ether particles contained within a given portion of space, with the object, if possible, to fix upon a limiting value for this energy, or the lowest value consistent with what physical facts would require.
The conditions required in order to determine the amount of energy enclosed in the unit volume of space are clearly, first, a knowledge of the quantity of matter in the form of ether contained in the unit volume of space (i. e. the density of the ether); and secondly, the normal velocity of the ether particles. Now, although we do not know the density of the ether independently, nevertheless since density is determined by pressure and velocity
of component particles, if, therefore, by a known limiting value for the velocity of the ether particles, a limiting value for the ether pressure can also be fixed upon, then a limiting; value for the ether density is thereby given. The limiting value for the velocity of the ether particles is given by the measured velocity of a wave of light. As regards the value for pressure, we take the estimate already fixed upon : that this amounts to 500 tons per square inch as the lowest limiting value. There are valid grounds for inferring that this value for pressure has been under-estimated; for we assumed the total ether pressure as a small multiple of the observed difference of pressure in the case of " cohesion/ whereas, as before remarked, it is a known fact that the force required to separate chemically combined molecules must be many times greater, this indicating the high intensity of the controlling ether pressure, and showing that an estimate of this pressure from the case of " cohesion " must .be but an inadequate representation of the reality. The tremendous energy developed in explosives, which is the very energy of the ether itself, is a direct indication of the intensity of the ether pressure, which is the necessary accompaniment of this energy.
That this value for pressure has been under-estimated, a bare consideration of the dependent value for density would almost show, for the ether density corresponding to this pressure (ttAtutf °f the atmospheric density) represents a density so insignificant as to be less than that of the best gaseous vacua.
164. The actual density of the ether might, therefore, well be greater than the above estimate. A greater density would, of course, involve a proportionally greater pressure. It is, however, well to keep in view that there is not the slightest mechanical impediment to the existence of an extremely intense pressure, for so long as the pressure about a molecule of matter is under normal conditions perfectly balanced, it can be of no special import what its value is. If, for example, it were an essential condition to a steady and perfectly balanced pressure that the density of the ether, i. e. the quantity of matter relatively to the volume of space, should be infinitesimal, then the observed steadiness of the stable aggregation of molecules determined by the ether pressure would warrant the inference that such was the fact. But the actual physical conditions are quite otherwise; for an addition to the quantity of matter contained in the unit volume of space, or an addition to the number of ether particles, so far from rendering the pressure due to the motion of these particles less steady, would only render it more steady; and thus, although by this increase in the number of particles (increase of density) the pressure might be greatly increased, the concealment of the existence of the pressure from the senses would, on account of the perfection of the equilibrium, be if possible more effectual; and although the value of the energy enclosed might thus be greatly
augmented, the reduced length of path of the particles would only serve to remove the motion still farther beyond the reach of detection by the senses. Hence we may observe the perfect mechanical possibility of the existence of an ether density very much greater than the above estimate. We will, however, take the above estimate for the ether density as a basis for deducing the value of the enclosed energy, it being only our object to arrive at a limiting value for this energy, having therefore valid grounds for concluding that the results arrived at for the value of this energy will be less than the facts as they actually exist.
165. To give an idea, first, of the enormous intensity of the store of energy attainable by means of that extensive state of subdivision of matter which renders a high normal speed practicable, it may be computed that a quantity of matter representing a total mass of only one grain, and possessing the normal velocity of the ether particles (that of a wave of light), encloses a store of energy represented by upwards of one thousand millions of foot-tons, or the mass of one single grain contains an energy not less than that possessed by a mass of forty thousand tons, moving at the speed of a cannon ball (1200 feet per second); or other- wise, a quantity of matter representing a mass of one grain endued with the velocity of the ether particles, encloses an amount of energy which, if entirely utilized, would be competent to project a weight of one hundred thousand tons to a height of nearly two miles (1.9 miles).
This remarkable result may serve to illustrate well the intense mechanical effect derivable from small quantities of matter possessing a high normal velocity, the extremely high value of the effect depending on the fact that energy rises in the rapid ratio of the square of the speed,
166. A cubic foot of air weighs 56.5 grains, so that with the above limiting value for the ether density (7,254,800 that of air), a quantity of ether representing the total mass of one grain would be contained in a cubical portion of space with side of cube equal to about forty-five feet. Hence a portion of space of these moderate limits contains, in the energy of the concealed motion of the enclosed ether, not less than the above prodigious work- producing power.
167. With the above limiting values for normal velocity of particles and density, we may give a few more numerical results illustrative of the energy enclosed by this great physical agent. The energy in the form of concealed motion contained in one cubic foot of space amounts in units of work to not less than ten thousand seven hundred foot-tons. This is the energy which a projectile of one quarter of a ton would possess when moving at the rate of 1600 feet per second. Since this velocity happens to be that of the molecules of air in their translatory motion at normal temperature, it may be of interest to note that the energy
enclosed by a cubic foot of ether represents the energy of translatory motion of the molecules (not taking into account the vibrations of the molecules) of a quarto of a ton of air. This amount of air would occupy a cubical space with side of cube equal to about forty-one feet, and the energy of the translatory motion of the molecules of this mass of air would be competent to project it to a height of about seven miles.
168. That which appeals most directly to the senses as energy, and which our ideas naturally connect with the visible motions of large masses of matter, is but insignificant when compared with the energy of the concealed motions of molecules, and is as nothing when compared with the intensity of the energy enclosed by the ether in the motion of its particles.
It is our object to consider this question in all its points, for we do not content ourselves merely with putting forward the bare deduction, to which we have been necessarily led, that this energy exists; but it is our endeavour rather to show the consistency of the fact; or we examine all the points of the physical problem with the view to show that the existence of this intense energy on all sides as a physical fact admits of being brought into harmony with just mechanical principles, and of being practically realized and appreciated.
On the first consideration of the subject there may undoubtedly be a difficulty in forming a satisfactory conception of the existence of an agent enclosing such an intensity of energy as this; indeed, at the first thought there may even appear something wild in the idea of the continued presence of an agent competent to transfer motion to explosives; indeed, one would perhaps naturally ask, How can such an intensity of energy exist without making itself directly palpable to the senses in the normal state of the ether? The answer to this is, that it is theoretically deducible beforehand that the existence of such an intense store of energy is perfectly consistent with its concealment from the senses; indeed, that so far from concealment being inconsistent with its existence, it may be shown (on grounds already pointed out) that concealment is absolutely essential to its existence; in fact, that without considering the question as to its existence at all, it is theoretically deducible beforehand as an independent deduction that if such an intense store of motion did exist, then it would necessarily be concealed; and further, that the existence of a store of motion of a high intensity is the necessary consequence of the known impalpable quality of the ether; the agent becoming less and less palpable to the senses as the rapidity of the motion of its component particles increases; and therefore the less palpable the' agent, or the more effectual the concealment of the motion from the senses, the higher would one be warranted, on theoretic grounds, in assuming the intensity of the enclosed store of energy to be.
169. It is well to keep the above considerations in view, since
there is an undoubted tendency to ignore the existence of any- thing which does not appeal directly to the senses. If such a course were followed, however, a vast number of important physical facts would pass unknown, and work their influences unheeded, for the most important facts may Dot always lie on the surface. Thus, if we take the important phenomena of Heat, for example. The motion termed "Heat" is, under normal conditions, completely concealed, and how intense (as expressed in mechanical units) is the energy of the molecular motion of substances at normal temperature, this energy greatly surpassing the energy of the movements of large masses which appeal to the senses. If, therefore, the existence of this concealed energy be admitted and realized, then there can be no real difficulty in appreciating and harmonizing with just mechanical principles the enclosed energy of the ether; for if the gross molecules of matter attain such an intensity of motion as the mechanical equivalent of heat proves, then now much more may the minute component particles of the ether, whose motion is entirely un- obstructed, attain a high normal speed ? And when the existence of the rapid motion is once appreciated, then the existence of the intense store of energy follows as an absolutely necessary consequence.
170. The normal speed as deduced for an ether particle may naturally appear inordinately high, according to our general ideas of speed, which attach themselves to the motions of visible masses; but it is well to note that these motions of visible masses take place under physical conditions which are eminently unfavourable to the development of high speeds, whereas the concealed motions of molecules and particles take place under conditions eminently favourable to high speeds, so that the two cases are not fairly comparable.
Thus the movements of visible masses of matter near the earth's surface, where the motions come under the observation, cannot take place without continual and forcible obstruction by other matter (the air, &c), so that the attainable speeds are very limited in such a case, and yet this is precisely the case from which our general ideas of speed and energy are formed. The motion of the molecule of matter, on the other hand, can take place with comparative freedom, the ether being the only obstruction, and the resistance thus offered is but small. Hence we may observe that the motions of molecules take place with some rapidity, as illustrated, for example, by the rapid translatory motion of the molecules of gases, which by their interchange of motion can propagate waves at a considerable speed.
The motion of the ether particle, on the other hand, takes place under the most favourable conditions conceivable, for there is nothing whatever to obstruct or curb its free motion. Hence the possession of a high speed by the ether particles can be said to
be only consistent with the special physical conditions of the case. Even large visible masses of matter may attain high speeds when the physical conditions are favourable. Thus, in the free ether, masses of matter are known to attain speeds by which many miles are traversed even in a second of time, and quantities of matter in the form of comets are actually observed to be propelled round the sun at a speed of upwards of 300 miles per second. If, there- fore, it be realized that large masses of matter, whose motion must be obstructed to a certain extent by the presence of the ether, attain speeds represented by hundreds of miles per second, what difficulty can there be in realizing the existence of a high speed in the casa of the minute ether particle, which moves entirely without obstruction, and whose minute mass renders perfectly practicable a high speed without producing physical disturbance of the equilibrium of the molecules of matter which the ether surrounds?
Moreover, when it is considered that this motion of the ether particles constitutes the sole physical means whereby motion can be transmitted across the vast intervening distances of stellar space, and that even as the fact stands this transmission of motion by interchange of motion among the ether particles requires upwards of three years to traverse the intervening ether which separates the nearest star; then the above value for the normal velocity of the ether particles is surely no more than consistent with the special functions which belong to this great physical agent.
If, then, the above value for the normal velocity of the ether particles be realized as a reasonable and consistent fact, then the existence of the intense store of energy — of the value of which we have endeavoured to give some idea by a comparison with the greatest observed cases of energy which appeal to the senses — follows as a necessary consequence, as certain as the mathematical fact that energy rises as the square of the speed.
We may just add here that a consideration of the physical conditions involved in the case given of a comet, may serve as another illustration of the mechanical fitness of the high normal velocity possessed by the ether particle?, these particles having such a suitable speed that they are not only able to follow up the matter forming the comet (traveling at 300 miles per second) with facility, but are capable of transmitting motion to it, i.e. of propelling the comet along its course.
171. Since the visible motions of large masses upon the earth's surface constitute the only means by which a distinct figure or illustration of energy can be presented to the mind, although energy in this form can never attain a high intensity, we will take a few more illustrative cases, as serving to exemplify the far higher intensity of the energy of concealed motion.
It is well to keep practically in view that if it were attempted
beforehand to devise what physical conditions should be satisfied to render possible the existence of a store of energy of the highest possible intensity, capable of producing dynamic effects of the most forcible character, then the conditions satisfied in the physical constitution of the ether would be precisely those required. Hence, in dealing with the value of the energy enclosed by the ether, it is to be expected beforehand that the results arrived at will represent extremely high figures as expressed in mechanical units.
172. If we take the case of a railway train whose weight amounts to 200 tons, moving at the rate of 60 miles an hour, then the energy contained in the train is such, that if the motion of the train were supposed diverted vertically upwards at any instant, the train would project itself to a height of 121 feet; or the work- producing power of the train is therefore 121 x 200 = 24,000 foot-tons. This, however, would only represent the energy of the concealed motion of the ether contained in about 2£ cubic feet of space.
If we suppose a collision of the train to take place, then the energy transferred to matter at the collision, the shock of which would be precisely equivalent to that produced by a fall of the train through 121 feet, would only represent the energy which 2£ cubic feet of ether are competent to transfer to matter; or, in other words, the transference to matter of the concealed motion of the ether occupying a portion of space of these moderate limits would involve a dynamic effect greater than that developed at the collision of a train of 200 tons at the above speed, this point being illustrated by the destructive effects of the transferred motion of the ether in the case of "explosives," the dynamic effect of "lightning," &c.
173. To take a further illustration: if we imagine the ether occupying a cubic foot of space to be replaced by a cubic foot of lead, or the ether occupying any unit volume of space to be replaced by lead, then from the known density of the metal, lead, and from the known fact that energy is in the ratio of the density or mass, and as the square of the speed, it may be computed that for the energy contained in this unit volume of space to remain as before, it would be necessary for the mass of lead to have a translatory motion at the rate of 1470 feet per second (about the speed of a cannon ball); or, in other words, therefore, if space were filled with flying projectiles which graze each other in their close proximity, the energy thus existing would be scarcely competent to represent the energy of the concealed motion actually existing in the normal state of the ether.
The speed attainable by gross masses of matter, such as projectiles in the atmosphere, is necessarily extremely limited; yet because this is about the highest form of motion that appeals to the senses, the motion is naturally considered extremely rapid;
yet it may be shown that the motion of a projectile vanishes when compared with the speed of the concealed motion of the ether particle. Taking the ordinary speed of a projectile, such as a rifle bullet, for example, at 1200 feet per second, then the speed of the ether particle (that of a wave of light) is to the speed of the bullet as 836,000 is to 1; or it may be computed that the speed of the ether particle bears the same proportion to that of the bullet, as the speed of the bullet bears to the rate of movement of the extremity of the large hand of a clock 10 inches in length. Since the motion of such a clock-hand is scarcely perceptible at a few feet distance, its rate of motion may be justly said to vanish com- pared with the speed of a bullet; in the same way, therefore, the motion of a bullet may be justly said to vanish when compared with the speed of an ether particle.