Volltext Seite (XML)
suspended by a rope wound round an axle, and moving very slowly, a certain number of revolutions in a minute will be given to it by the power, in passing through a given space, and the four dishes will raise, by their centrifugal force, a weight in the tube below, proportionate to the velocity and their distance from the centre. If the moving power be then doubled, with a slight addition to overcome the additional friction and atmospheric resistance, it will be found, that in moving through an equal space in the same lime, it will give twice the former velocity, and the dishes, at the same distance from the centre, will raise in the tube below, in an equal time, quadruple the weight first raised. Then by loading the dishes and increasing or diminishing the velocity, and varying the distances of the dishes from the centre, a variety of experiments may be made, and weights may be raised, with corresponding distances and velocities proportionate to those given above. By observing the manner of performing the experiments with the magnetized bar, it will be seen that a centrifugal force is excited, INDEPENDENTLY OF THE PROJECTILE FORCE, equal to the supposed power of the magnet, and we have shown that the same effects would follow without the use of the magnet. And that the impelling or moving power performs no other part in producing the complex effects attendant upon rotation, than simply to move the particles of a mass of matter in circles about a fixed axis, may be clearly shown by the theory of curvilinear motion, which those experiments were designed to illustrate. But without attempting to prove this at present, by ab stract mathematical reasoning, the nature of deflection and the extent of its operation in exciting the central forces, may be explained by a reference to the action of electro-magnetism as shown in Fig. 1. The bar A, when attached by the magnet, being supposed to revolve in a circle of one foot in diameter, at the rate of eight revolutions in a second, or 25*14 feet, to determine the amount of deflection in any unit of time, say one fiftieth of a second, the whole space through which it moves in a second may be divided into fifty parts, which will give six inches for each unit of time. If this space be measured on the tangent from B to ,r, and on the circumference of the circle to r, the deflection for the one fiftieth of a second would be equal to the square of Br, divided by BD, or the diameter. For by dynamics, “ if a body revolve uniformly in a circle, the space through which it would move by the action of the centripetal force alone in any unit of time, such as a second, will be equal to the square of the arch described in the same unit divided by the diameter or twice the radius.”* And the deflection of the bar in the r , B “ 2 62 q oi a second = —— = -- = d 2Bc 2 r inches. That is, the deflection from the tangent Bg, during the time that the bar would have passed over six inches in that line, is tbree inches; and the deflection corresponding with the space Bg, which is equal to two feet, and thfough which the bar would have passed in 2 = the -jA of a second, would be — = 4 feet, and so of any other 2r space. Now to show that the amount of this deflection or centrifugal force depends upon the curve in which the bar is moved in a given time, and not upon the moving power, or projectile force, we will cause the same bar, moving with an equal uniform velocity, to be attracted in a similar manner by the magnet m, attached to an arm revolving in a circle of eight feet in diameter, and let EF be an arch of that circle, touching the straight line Ag at B. As the velocity of the bar and the circumference of the circle are equal, the bar, after being attracted by the magnet at B, would move on with the same uniform velocity and perform one entire revolution in a second, friction and the resist ance of the atmosphere being considered equal to nothing. And its deflection from the straight line, or its centripetal force for ^ of a second, would be equal to the square of the arch Br, which is six , 0* inches, divided by the diameter of the circle, that is == — := *375 = f of an inch, or only one eighth of the deflection caused by the smaller wheel; and in the same ratio for any other spaces through which the bar would have passed whilst moving through equal spaces in the circle. And hence it is that the central forces are inversely as the diameters of the circles in which a body is made to move with a given velocity. The increment of deflection for an entire second being = 25-14= , —j— = G32 feet per second in the smaller wheel, and in the larger 25-14= 8 59 feet per second only; and yet the bar has pre Brewster’s New Edinburgh Encyclopedia, Art. Dynamics. cisely the same velocity, and consequently the same force in the latter that it had in the former. Therefore, aside from friction, it would, if welded to m, require no more force to revolve it in the former than in the latter case. For the same reasons, with a given velocity for the particles of the rims, the smaller a fly-wheel is, the greater will be the amount of cen trifugal force, other things being equal. This will appear obvious upon inspecting the figure -, for it will be seen that a particle of iron at v in the rim of a small wheel would be deflected from the straight line eight times as many inches in a given unit of time as a pai-ticle would be at the point z of the large wheel. The measure of the de flection from that line must therefore be the measure of the centri fugal force for any instant of time; and consequently the aggregate amount -will be proportionate to the curve in which the body moves. This deflection takes place when a body is moved in a curved line, and the tendency to resist it and move in a straight line is excited in such a mass of matter in obedience to the important law of inertia, with as much certainty as electricity would result from the action of sulphuric acid upon two contiguous plates of zinc and copper. Centri fugal force may therefore with propriety be considered a physical agent, which is called into action, by an inscrutable law of nature, whenever matter is made to move in a curve;—which ought to be no more a sub ject of surprise, than that magnetic force should be excited in a bar of iron by certain chemical operations, the precise nature of which is as little understood as that of inertia. The centrifugal principle has been employed as a projectile force from the earliest ages. It would be interesting to notice the extent to which it was used in ancient wars; and particularly to point out, as might be done even with the feeble lights afforded us, how much Archimedes was indebted to the central forces for the destructive effects of his engines, which I believe to have been no fabled nor ima ginary productions of genius. As I shall here come in conflict with some generally received opi nions, I will give a short extract from Professor Renwick’s Elements of Mechanics. Not that he differs from other writers on this subject, but I find that the extract will be useful in explaining what is to follow-. “The simplest case of central force is where a body connected with a fixed point by an inflexible straight line is impelled by a projectile force at right angles to that line. The latter force would have im pressed upon the body a motion with a uniform velocity. The body, then, in consequence of its connexion with a fixed point, describes a circle of which that point is the centre. If the connexion were to cease at any point in the curve, the deflecting force would cease to act, and the body would go in a straight line whose direction would be a tangent to the cuive. The force acting at any point in the curve must therefore be decomposed into two, one of which is in the direc tion of the curve, the other in that of the radius.”* If a ball at A, Fig. 4, weighing one pound, and attached to an in flexible rod AC, two feet long, be impelled by a projectile force or moving power at the rate of two entire revolutions in a second, or 25-p^ feet per second, it will have a centrifugal velocity equal to 157-7G feet per second.!; Those two velocities, then, equivalent to the forces 1*58 lb. and 9-87 lb. respectively, constitute the aggregate amount of force acting on the body at any point of the curve or circle; the former acting in the direction of the curve, and the latter in that of the radius—one caused by the motion of the particles of matter, the other excited by a cause producing pressure, resisted by cohesion. Now, according to the fundamental principles of mechanics, “ the same cause acting upon a body will either produce motion or pressure, according as the body is free or restrained.” And, “ if two forces act upon the same point of a body in different directions, a single force may be assigned which, acting on that point, will produce the same results as the united effects of the other two.” Here we have two forces acting on each particle of the revolving body, but they are re sisted by cohesion, therefore when cohesion ceases to act, the effect of the two forces must be, according to the theorem of the composition of forces, to impel it in the direction of their resultant, and with an amount of force equal to their mechanical equivalent; and experiment shows the correctness of the theory. If an ounce ball of lead, with a small hole drilled through it, be firmly secured by a catgut string close ‘to the perimeter of a fly-wheel, or any other wheel that can be rapidly revolved, it may be discharged from the vertical point of the circum ference, whilst the wheel is revolving, by interposing a sharp knife well fixed in a slide. When the velocity necessary to project the ball horizontally at a given short distance has been ascertained, then by increasing the velocity and taking care to-discharge the ball irom the same point of the circle, and at an equal distance from the centre of the wheel, its elevation will be found to increase with the increased Cavallo, p. CG. It 2 t Page C2,