Axial tilt

“ If, then, he is not tilted far enough forward, the jumper can, by swinging his arms in a forward-upward-backward-downward direction, make the rest of himself revolve slowly in the opposite direction on the axis of his shoulder-joints, and so tilt himself gradually forward; or, if his forward tilt is too great—which is not very likely—he can reduce it by swinging his arms round the other way. ”

“ Also, we will place instruments called tiltometers on the mountain slope. These are devices that really measure tilt. You see, if the lens of magma is increasing, El Viejo will swell up slightly. The tiltometers will show it, and we will then have further proof of what is coming."
"But what can we do about it?" Rick demanded.
Balgos shrugged. "Quién sabe? The Spanish phrase is a good one, because it does not only ask 'who knows,' it also carries the meaning of a kind of resignation. There does not seem to be anything we can do." ”

“ If, however, the globe is now put into a state of rapid rotation round the axis, and then allowed to float freely in the water, we perceive that it is no longer in a state of equilibrium. The mass m being more dense than its antagonist particle at n, and having equal velocity, its momentum is greater, and it now tends continually to pull the pole from its perpendicular, without affecting the position of the centre. The same effect is produced by m′, and consequently the axis describes the surface of a double cone, whose vertices are at the centre of the globe. ”

“ In order that any body may vibrate when displaced and then set free, two conditions must exist. In the first place, there must be a controlling force tending to make the substance return to its original position when displaced. In the second place, the thing moved must have mass or inertia, and when displaced and allowed to return it must in consequence overshoot the mark, and acquire a displacement in an opposite direction. In the case of the pendulum the elastic control or restoring force is the weight of the bob, which makes it always try to occupy the lowest position. ”

“ Let us suppose that the principal axis is that of greatest moment of inertia, and that we have made it coincide with the axle of the instrument. Let us also suppose that the moments of inertia about the other axes are equal, and very little less than that about the axle. Let the top be spun about the axle and then receive a disturbance which causes it to spin about some other axis. The instantaneous axis will not remain at rest either in space or in the body. In space it will describe a right cone, completing a revolution in somewhat less than the time of revolution of the top. ”

“ It will be seen that the shorter the impulse radius, or in other words, the closer the ruby pin is to the balance staff and the longer the fork, the easier will the unlocking of the pallets be performed, but this entails a great impulse angle, for the law applicable to the case is, that the angles are in the inverse ratio to the radii. In other words, the shorter the radius, the greater is the angle, and the smaller the angle the greater is the radius. We know, though, that we must have as small an impulse angle as possible in order that the balance should be highly detached. ”

“ If they were to fall they would describe a large arc, and come down with great force, but they do not fall. A very slight movement of the stilt is sufficient to keep it under their centre of gravity. If they were lower down, greater exertion and a swifter movement would be necessary to correct every unsteadiness. Men cannot stand still upon stilts, because there are no muscles at the foot of the stilt to play upon the ground and react upon the body. ”

“ The first illumination of a joust at the tilt pictures the moment when the tilters have shivered their lances, tipped with coronals of three prongs, on each other’s bodies. The tilt is composed of six planks, and appears to be between five and six feet in height. Sir John Astley’s crest is seen to be a crowned harpy, with torse and mantling; his armour, the sort termed “tonlet”; the legs and feet are unarmed, being sufficiently protected by the saddle-steels. The horse is trapped and has a chamfron. But little of the person of his adversary can be seen ”

“ You see, then, that although every body has three axes about which it will rotate in a balanced fashion without any tendency to wobble, this balance of the centrifugal forces is really an unstable balance in two out of the three cases, and there is only one axis about which a perfectly stable balanced kind of rotation will take place, and a spinning body generally comes to rotate about this axis in the long run if left to itself, and if there is friction to still the wobbling. ”

“ When the shaft or axis revolves, the weights which move toward the ends of the arms above the center accelerate the motion, and the momentum of the machine aids in overcoming the resistance caused by the weights, which are below the center. At the same time the revolution of the eccentric and crank-pin upon the axis depresses the connecting-rods, which in turn depress the springs, which, being released as soon as the eccentric and crank-pin have reached their lowest point, contribute a lifting power to overcome the resistance above mentioned. ”

“ But since the longitudinal motion of an axis can be prevented by a point almost invisible applied to its centre, it follows that the effect of this tendency can be annulled, without any sensible loss of the active power. It may be added, that in vertical axes, those circumstances lose all their importance, since whatever force tends to depress the one and increase its friction, tends equally to elevate the other, and relieve its step of its load ”

“ If it be so placed that it must either remain at rest or ascend, it is clear, from the laws of equilibrium, that no motion derived from gravitation can take place; if it may descend, it must either continue to descend forever with a finite velocity, which is impossible,334 or it must first descend and then ascend with a vibratory motion, and then the case will be reducible to that of a pendulum, where it is obvious that no new motion is generated, and that the friction and resistance of the air must soon destroy the original motion. ”

“ If there is the slightest displacement of the centre of gravity of the system from the axis of revolution a force acts on the shaft tending to deflect it, and varies as the deflexion and as the square of the speed. If the shaft is therefore to revolve stably, this force must be balanced at any instant by the elastic resistance of the shaft to deflexion. ”

“ The composition of finite rotations about parallel axes is a particular case of the preceding; the radius of the sphere is now infinite, and the triangles are plane.
In any continuous motion of a solid about a fixed point O, the limiting position of the axis of the rotation by which the body can be brought from any one of its positions to a consecutive one is called the instantaneous axis. This axis traces out a certain cone in the body, and a certain cone in space, and the continuous motion in question may be represented as consisting in a rolling of the former cone on the latter. ”

“ Should the angle be too great for the velocity, then the rarefied area over the top of the surface becomes of irregular shape with attendant turbulent eddies. Such eddies possess no lift value, and since it has taken power to produce them, they represent drift and adversely affect the lift-drift ratio. Also, too great an angle for the velocity will result in the underside of the surface tending to compress the air against which it is driven rather than accelerate it downwards, and that will tend to produce drift rather than the upwards reaction, or lift. ”

“ Therefore, the product of the weight and the perpendicular distance of ascent is exactly equal to the product of the weight and the perpendicular distance of descent. Hence, there is an exact balancing of energies, and no motion results. Any motion imparted by wind, water or steam will, if the moving force be withdrawn, soon be overcome by unavoidable friction, and a state of rest follows. There can be no doubt that any attempt to attain Self-Motive Power by means of wheels, weights, levers, and the force of gravity must result in failure. The thing itself is physically impossible. ”

“ Escapement friction plays an important role in the position and isochronal adjustments; the greater the friction encountered the slower the vibration of the balance. The friction should be constant. In unlocking, the equidistant comes nearer to fulfilling this condition, while during the lift it is more nearly so in the circular. The friction in unlocking, from a timing standpoint, overshadows that of the impulse, and the tooth can be a little wider in the equidistant than the circular escapement with the pallet properly planted. ”

“ Now, in the case of the vibrating pendulum, it is the downward pull of the earth's attraction that first causes the stationary body to move, and as this commencing motion is downwards, in the direction of the pull, it is also an accelerating one. As soon, however, as this motion is changed by the resistance of the string into an upward one, it becomes a retarded one from the same cause. ”

“ We will notice that by employing a large impulse angle, and consequently a short radius, the intersection m of the two circles ii and cc is very safe, whereas, with the conditions reversed in favor of the impulse action, the intersection at k is more delicate. We have now seen enough to appreciate the fact that we favor one action at the expense of another. ”

“ Again, the friction on the dead part of the pallets tends to produce the same effect on the time ; the arc of course it tends to diminish. For in the descent of the pendulum the friction acts against gravity, but in the ascent with gravity, and so shortens the time ; and there is rather less action on the dead part of the pallets in the ascent than in the descent. For these reasons the time of vibration of a pendulum driven by a dead escapement is a little greater than of the same pendulum vibrating the same arc freely ”

“ It will most generally happen that a regular solid (such as an obelisk, &c.) will fall prostrate whenever the maximum velocity of the wave is such as to produce in it oscillation sufficient to destroy statical equilibrium; and as the arc of oscillation due to a given velocity may be assigned, if we know the angle of emergence of the wave, so as to arrive at its horizontal component of velocity, we can always assign an inferior limit to the maximum velocity of the wave that overthrew the object whose dimensions, &c., we have observed. ”

“ To derive the play of internal force, this energy function must be varied with respect to all these independent quantities; the result is elastic tractional stress in the medium across every ideal interface, together with forcive tending to displace each strain-centre, which we can consider either as resisted by extraneous constraint preventing displacement of the strain-centre, or as compensated by the reaction of the inertia of the strain-form against acceleration. ”

“ A moving principle has been sought for, but without success, in the magnet, in the gravity of the atmosphere, and in the elasticity of bodies. If a magnet be disposed in such a manner as to facilitate the ascension of a weight, it will afterwards oppose its descent. Springs, after being unbent, require to be bent by a new force equal to that which they exercise; and the gravity of the atmosphere, after forcing one side of the machine to the lowest point, must be itself raised again, like any other weight, in order to continue its action. ”

“ Angular velocity always falls as angular displacement grows (and vice-versa) , so each full period will look like an ellipse, and the loss of energy to friction will mean that each period will be represented by a slightly smaller ellipse as the system spirals toward its equilibrium position of zero displacement and zero velocity: straight up and down, and not moving. See Figure 5.1 for a rough plot of what the graph of this situation would look like in a state-space for the pendulum. ”

“ It, has been suggested that the distortion of the revolving mirror, either by twisting or by the effect of centrifugal force, might cause an error in the deflection.
The only plane in which the deflection might be affected is the plane of rotation. Distortions in a vertical plane would have simply the effect of raising, lowering, or extending the slit. ”

“ For reverse stresses it is advisable to keep the shear stress in any rivet so low, say 3 tons per square inch, that the frictional resistance of the parts gripped by the rivets shall be sufficient to prevent any tendency to slip under the influence of the smaller of the two forces to which the part is liable, to insure that, if brought to a bearing in one direction by the greater force, it shall not go back with reversal of stress. ”

“ If the initial disturbances are small enough, that one is ultimately preponderant for which the measure of instability is greatest. The smaller the causes by which the original equilibrium is upset, the more will the cylindrical mass tend to divide itself regularly into portions whose length is equal to 4.5 times the diameter. But a disturbance of less favourable wave-length may gain the preponderance in case its magnitude be sufficient to produce disintegration in a less time than that required by the other disturbances present. ”