Radial velocity

“ If any diameter of the spherical portion be taken as the axis, and any plane through that axis be considered, the velocity of a particle at right angles to that plane can be at once expressed as the rate at which the velocity-potential varies per unit distance along the circle, symmetrical about the axis, on which the particle lies. The integral of the velocity-potential round this circle vanishes, and so the angular momentum for any thin uniform ring of particles about the axis also vanishes, and as the sphere is made up of such rings, the whole angular momentum is zero. ”

“ Whence since the weight of a globe of water, in the time in which the globe with a velocity uniformly continued describes a length of 30,556 inches, will generate all that velocity in the falling globe; it is manifest that the force of resistance uniformly continued in the same time will take away a velocity, which will be less than the other in the ratio of 1 to 3761/50, that is, the 1/3761/50 part of the whole velocity. ”

“ According to equation (1a) for the absolute phase velocity of light relative to the reference system fixed at Earth, the component of the body's velocity perpendicular to the ray direction doesn't matter, but it is only about the velocity parallel to it. 2. If a line has the smallest distance from the rotation axis and if its direction forms with it the angle , then the component of the body's velocity with respect to this direction is equal to in any of the points, where is the angular velocity of the rotation. ”

“ But although these circumstances be inefficient, a variation in the mean temperature would certainly occasion a corresponding change in the velocity of rotation: for in the science of dynamics, it is a principle in a system of bodies, or of particles revolving about a fixed centre, that the momentum, or sum of the products of the mass of each into its angular velocity and distance from the centre is a constant quantity, if the system be not deranged by an external cause. ”

“ If a solid body fails to impart all its rotational velocity to the medium there, then it will certainly fail to impart its full rotational velocity to the enveloping medium 100 miles away, and fail still more at a distance of 1000, and still more at a distance of 100,000,000, and so on proportionate to the distance. ”

“ The speed with which the surface waves move outwards in all directions, varies not only with the force of the wave, but also with the kind of material through which they pass. This velocity may be in the neighborhood of twenty miles per second, while in others the velocity is as great as 140 miles per second. ”

“ In § 5 the work is calculated, which must be performed to change the velocity of a cavity filled with radiation. The work that must be performed to increase the velocity, is gained again when it is decreased by the same quantity, in case the velocity change is carried out infinitively slow. ”

“ Such a freely moving cavity radiation, separated form outer space by thin rigid reflective walls, provides a good example of a rigid body, whose laws of motion completely differ from those of ordinary mechanics. Although it differs, considered superficially, in no way from other rigid bodies and also possesses a certain inertial mass and obeys the law of inertia, its mass changes significantly with temperature and it also depends in a certain specifiable way from the magnitude of the velocity as well as from the direction of the moving force in respect to the velocity. ”

“ Then if V represent the force arising from the gravity, proportional to the arc CD to be described, by which the body is acted upon in D, and R be put for the resistance, V - R will be the whole force with which the body is urged in D. Therefore the increment of the velocity is as V - R and the particle of time in which it is generated conjunctly. But the velocity itself is as the contemporaneous increment of the space described directly and the same particle of time inversely. ”

“ But now let there be a different rotational velocity imparted to the jointed square round the axis of the two projecting hooked rods, such as to give a resultant moment of momentum round any given line through the center of inertia of the system; and let pairs of the hooked rods in the model thus altered, which is no longer a model of a mere spring balance, be applied as connections between millions of pairs of particles as before, with the lines of resultant moment of momentum all similarly directed. ”

“ The uncorrected velocities, however, are in all cases too large, and by greater and greater amounts the higher the velocity. At 60 miles per hour the observed velocities are about 12 miles per hour too high, and for an indicated velocity of 90 miles the experiments show that the actual velocity is but a fraction over 69 miles per hour. ”

“ In reality, however, such increase of momentum is only apparent; the momentum of the body and fluid system combined is actually less than that of the body at the same velocity in vacuo by the amount due to its fluid displacement. That is to say, if the body be of the same specific gravity as the fluid the total dynamic system possesses no momentum at all, whatever the velocity. ”

“ On the other hand, a body thrown upward has uniformly retarded motion, that is, its acceleration is downward. The velocity acquired by a falling body in unit time is called its acceleration, or the acceleration due to gravity, and is equal to 32.16 ft. (980 cm.) per second, downward, each second of time. In one second, therefore, a falling body gains a velocity of 32.16 ft. ”

“ Accordingly two bodies, the earth and the comet, moving with unequal velocities 166through the ether, might be expected to have different velocities relatively to rays of light. For example, consider two cars on a road, moving at ten and twenty miles an hour respectively, and being passed by another car at fifty miles an hour. The rapid car will pass one of the two cars at the relative velocity of forty miles per hour, and the other at the rate of thirty miles per hour. ”

“ When estimated straight across from surface to surface, that is, in the direction of the liveliest change of pressure, it is the maximum pressure gradient. Along this normal direction the air tends to flow with an acceleration proportional to the gradient. The velocity thus acquired by any portion of air in being pushed along the line of falling pressure, combined with its velocity due to other causes, gives its true velocity. ”

“ We know by experiment what the effect of increased velocity has upon any whirling body; it tends to enlarge the body at those parts where the velocity is the greatest, the consequence being that the bulging out of the atmosphere would be greatest at the equator. ”

“ Now we want to investigate whether this definition is not in sharp contrast to the ordinary illustration of velocities. The distances proportional to the relevant velocities are used in ordinary mechanics as representing the velocities of uniform motions. Formula (2) leads to the same result at the limits of our ordinary experience. Only at velocities nearly comparable to the velocity of light, a notable difference occurs that quickly leads to infinite distortion. ”

“ Why does the velocity of its "violent" motion decrease as it rises, while that of its "natural" fall increases as it descends. If we mark closely the relation between these two facts, the problem will solve itself. We shall see, as Galileo did, that the decrease of velocity in rising and the increase of velocity in falling are one and the same phenomenon, viz., an increase of velocity towards the earth. Accordingly, it is not a place that is assigned to the body, but an increase of velocity towards the earth. ”

“ At first starting from the temperate zone, on its voyage to the equator, the cold air of that slow-moving region is impressed with a rotatory velocity of only 800 miles per hour to the eastward, but it soon comes over parts of the earth moving more than 100 miles per hour faster to the eastward than itself. The difference of velocity in the earth's rotation between latitudes 30° and 20° is 74 miles an hour, while between 20° and 10° it is only 45 miles, and in the next ten degrees the difference in rate per hour is reduced to 15 miles. ”