Doppler effect

“ The operation of the Doppler effect, arising from the relative motion between the aircraft and the observer, prevents the possibility of the identification of the machine by means of the observed frequency, this being liable to change by as much as 20%, according to the speed and direction of flight. An interesting observation which has been constantly made is that the notes of low pitch continue to be heard at ranges where those of high pitch have ceased to be audible. ”

“ Thus to explain the maxima in the Doppler curve with displacements in this proportion it is not necessary to assume that the molecules give out the same spectrum as the atom. The occurrence of singly charged atoms of hydrogen with velocities in this proportion of to 1 might be accounted for in some such way as the following: the atoms with the larger velocity have been charged atoms during the whole of their career ”

“ In the positive rays in hydrogen the molecules frequently outnumber the atoms, but no radiation that can be attributed to the molecules has yet been detected.The spectrum of hydrogen is there, but as it does not show the Döppler effect it cannot be due to the molecules. ”

“ An example of this is shown in Fig. 17, Plate I. The intensity curve corresponding to the Doppler effect ought to have the same type of variations in intensity as these parabolas, and a beaded parabola ought to give rise to a Doppler curve with as many maxima as there are beads on the parabola. Sometimes these beads on the parabolas are quite numerous.
It is remarkable that the parabola corresponding to the atom of hydrogen is often beaded in such a way that the velocity of the particles producing one bead is to that producing the other as . ”

“ The kinetic energy in the field of flow round a body in motion is imparted to the fluid when the body is started from rest, and is given up when the motion is arrested. The effect of the fluid motion is thus to add to the apparent inertia of the body, so that a given force requires to act through a greater distance to impart a given velocity than for the same body in vacuo. Not only has a force to act for a greater distance, but also for a longer time, which means that the body possesses in effect a greater store of momentum for a given velocity. ”

“ In the new mechanics, on the contrary, we assume it to be impossible to communicate to a body starting from rest a velocity beyond that of light. What happens? Consider the same body at rest; give it a first impulse, the same as before, it will take the same velocity; repeat this impulse a second time, the velocity again augments, but it no longer will be doubled; a third impulse will produce an analogous effect, the velocity increases but less and less, the body opposing a resistance which becomes greater and greater. This resistance is inertia, it is what is commonly called mass ”

“ When a projectile force is necessary, a further condition is essential, viz., that they liberate by their chemical action gaseous matter, whereby a sudden increase in volume is produced, the expansion of which, augmented by the high temperature, produces the required effect of propulsion. ”

“ As the resistance of the air increases more rapidly than the velocity, it follows that there is a point where the retarding and accelerating forces will be equal, and that beyond this the body will move with a uniform velocity, equal to that which it had acquired down to this point. The buoyant effort of the air is equal to the weight of the volume displaced, or PdD; in which P is the weight and D the density of the projectile, and d the density of the air. ”

“ I contend that it was placed there at the birth of the molecule by the law of sympathetic etheric focalization towards the negative centres of neutrality with a velocity as inconceivable in its character as would be the subdivision of matter to an ultimate end. Again, what is the energy that is held in the molecular embrace of that small portion of dynamite which by slight concussion, another order of vibration, evolves volumes of terrific force, riving the solid rock and hurling massive projectiles for miles? If it is not latent power that is excited into action, what is it? ”

“ The velocity being so great, the air is pushed aside by the falling body, and fails to surround that portion of the body not directly in the line of descent, with air at the normal pressure. The air supply being thus diminished, the blood leaps through the veins, rushes to the brain, and the mind knows no more. A human body of 175 pounds weight falling from this height—10,000 feet—would reach the earth at the end of the twenty-fifth second, and would have, at that moment, a velocity of 802 feet per second. ”

“ But, on the other hand, the energy is not simply proportional to the velocity, for, if it were, the energy of the rifle stock and of the rifle ball would be the same, inasmuch as the rifle stock would gain as much by its superior mass as it would lose by its inferior velocity. Therefore, the energy of a moving body increases with the velocity more quickly than a simple proportion, so that if the velocity be doubled, the energy is more than doubled. ”

“ Therefore in the same fluid a projected body that moves swiftly meets with a resistance that is in the duplicate ratio of its velocity, nearly. For if the forces, with which distant particles act mutually upon one another, should be augmented in the duplicate ratio of the velocity, the projected body would be resisted in the same duplicate ratio accurately; and therefore in a medium, whose parts when at a distance do not act mutually with any force on one another, the resistance is in the duplicate ratio of the velocity accurately. ”

“ Hence, in accordance with the well-known laws of motion, gas-molecules must always move in straight lines and with a constant velocity until they collide with each other or strike against the walls of the containing vessel, when, in consequence of their elasticity, they at once rebound and start on a new path with a new velocity. In these collisions, however, there is no loss of motion, for, as the molecules have the same weight, and are perfectly elastic, they simply change velocities, and whatever one may lose the other must gain. ”

“ Even if the resistance of a fluid were not increased, the effect of a horse's power, by the condition of his nature, would be materially reduced by every increase of speed; and, on the other hand, even were a horse capable of working with the same effect at an increased speed, the resistance of a fluid, increasing in a greater proportion than the square of the speed, would impair the total effect. ”

“ Much of our knowledge of proper motions has been obtained indirectly by means of the spectroscope, on the Doppler principle already treated of, by which we are enabled to ascertain whether a source from which light is coming is approaching or receding. ”

“ This performance of work is otherwise represented by a resistance to motion, being the difference between the excess pressure on the head and the diminished pressure on the shoulder, according to the principle explained in § 11. If now we restore the buttock, so that the mutilation is confined to the simple loss of the tail (Fig. 15) , the diminished pressure on the buttock acts as a drag upon the body, and more work must be expended in propulsion. This additional energy will appear in the fluid as a radial component in the motion of the stream which does not exist if the whole run is removed. ”

“ When we bear in mind the power displayed by particles of air hurled in violent wind against a fixed obstacle, we are led to ask how these particles exhibit their energy when the air is traversed by a projectile—spherical it may be—moving with great velocity? Since the air, in spite of its extreme mobility, opposes a degree of resistance to any sudden displacement, the vacuum created behind the projectile is not instantly filled ”

“ In proportion, however, as the air is exhausted, the molecules find more room and the amplitude of the molecular motion is increased, and when a very high degree of exhaustion is reached the air-particles no longer bound back and forth on the vanes without change of condition, but they either bound off entirely like a ball from a cannon, or else, having transferred a portion of their momentum, return with diminished velocity, and in either case the force of the reaction is felt. ”

“ An atmospheric film, rotating on a twelve inch sphere at the same ratio as the molecular one, would be impenetrable to a steel-pointed projectile at its greatest velocity; and would hermetically enclose a resisting pressure of many thousands of pounds per square inch. The latent [329] force evolved in the disintegration of water proves this fact; for under etheric evolution, in progressive orders of vibration, these pressures are evolved, and show their energy on a lever especially constructed for the purpose, strong enough for measuring a force over three times that of gunpowder. ”

“ Increasing the velocity will diminish the pressure due to the greater kinetic energy to increase the velocity. The converse is the result of passing air at constant pressure through a channel gradually increasing from a smaller to a larger area, the velocity being then reduced and the pressure increased. ”

“ These three rates of deflection are exhibited in Fig. 2. An examination of this figure will give you a clear understanding of them. Let us first suppose a body to be revolving about the point, O, as a center, in a circle of which A B C is an arc, and with a velocity which will carry it from A to B in one second of time. Then in this time the body is deflected from the tangential direction a distance equal to A D, the versed sine of the angle A O B. Now let us suppose the velocity of this body to be doubled in the same circle. ”

“ It has been shown that the effect of body resistance is to make the resistance at high speeds greater than that at lower speeds; but we know that at low velocities the sail area requires to be increased and that consequently the weight becomes greater and the resistance will be increased on this account, and when the velocity becomes less than a certain value the increase of resistance from this cause will more than compensate for the decrease due to the reduction in the direct body resistance. ”

“ If latent force is not accumulated and held in corpuscular aggregations how is it that progressive orders of disintegration of water induce progressive conditions of increased volume and of higher power? I hold that in the evolved gases of all explosive compounds, dynamite or any other, there exists deeper down in the corpuscular embrace of the gaseous element, induced by the first explosion, a still greater degree of latent energy that could be awakened by the proper condition of vibration ”

“ When it is exactly neutralized, the projectile weighs nothing, and the pressure of the air is enough to make it rise more rapidly than a balloon. When I have created a negative current, the projectile acquires a buoyancy equal to its previous weight. That is, it will now fall up as rapidly as it would previously have fallen down. It will not do to put on the full negative current at once, for we should acquire a velocity that would simply burn us up by friction with the atmosphere. ”

“ Whenever, then, a heavy body suspended by a flexible string is drawn to one side, and dropped from the hand, a vibrating pendulum is made, because weight and acquired impulse influence it alternately with a sort of see-saw action, the power of the one diminishing as the power of the other augments. Weight pulls down—confers velocity and impulse during the pulling—and then velocity carries up. As velocity carries up, weight diminishes its impulse, and at last arrests it, and then begins to pull down again. ”