thin as a knife and should rest on very hard and polished supports such as steel and agate. What is the wheel and axle? It is a kind of lever so contrived as to have a continued motion about its fulcrum or centre of motion: the power acts at the circumference of the wheel, the radius may be reckoned one arm of the lever. Is the wheel and axle applied to various purposes? To a great variety of purposes. Will you mention some of them? The common windlass used for raising water and coals. Why are handles placed in opposite directions? To equalize the effect of the agents upon the general movement of the machine. What other examples of the wheel and axle can you mention? The capstan on board of ships for raising and lowering the anchor; the crane found in harbours and dock-yards for loading and unloading vessels, and mill-wheels of every description. Do wheels with teeth acting upon one another fall under the wheel and axle? They do; they are sometimes employed for the accumulation of power and motion. What definition do you give of a pulley? It is a small wheel of wood or metal turning round an axis, and having a groove cut in its circumference in order to admit a cord. If the axis of the pulley be fixed, what is the consequence? It only serves to change the direction of the power's action. What do you mean by a fixed pulley? A pulley is said to be fixed when its axis is fixed, and to be moveable when its axis is moveable. To what purposes are pulleys applied? To a great variety of purposes; windows are hung by means of pulleys, stones and goods are raised by them. The pulley is of most essential service to the sailor. How does an inclined plane act as a mechanical power? By its supporting a portion of the weight laid upon it, the remainder being kept from sliding down the plane by the power which is applied in the contrary direction. What portion of the weight upon the plane must the force or power be in order to an equilibrium? The very same portion that the height of the plane is of its length. Thus, if the height A B were half the length A C, of the plane, then the power P would require to be equal to the half of W. If A B were of A C, P would be of W, and so of all proportions between the height and length of the plane. Is the inclined plane much used in general mechanics? Not much; one of its common applications is in rolling heavy casks into warehouses. On what does the velocity of a body moving on an inclined plane depend? On the angle of elevation which the plane makes with the horizontal plane. What law is there respecting the angle of elevation? The greater this angle is, the more will the velocity on the plane resemble that of a free falling body. What power is required to stop the motion of a body on an inclined plane? It is necessary that it should be urged in the opposite direction, with a force which is to the weight of the body. What is the wedge? It is a solid figure composed of two inclined planes. What is the form of the wedge? It is a triangle prism formed of wood or metal. How is the mechanical advantage of a wedge determined? The power applied to the back is to the resistance applied to the two faces as the height is to the length or as the whole back is to the sum of the faces. Is the wedge a machine of great efficacy? It is the most powerful of all the simple machines or mechanic powers. What is the screw? The screw is a modification of the inclined plane, rolled about a cylinder. Of how many parts does the screw consist? Of two parts, the screw and the nut. The screw S, is a cylinder, with a spiral protuberance coiled round it, called the thread; the nut or box A, B, contains the screw; the handle from the nut L, is a lever which works the screw. How do you calculate the advantage gained by a screw? The first thing to be considered is the distance between the threads of the screw, and the second is the length of the lever. Suppose four threads in an inch of the screw, and the end of the lever L, describe a circumference of fifty inches, using P and W to denote the power and resistance, P: W:: 4:50 or as 1 : 200. For what purpose are screws employed? They are employed either for compression or to raise heavy weights. They are used in cider and wine presses, in coining, bookbinding, and for the purposes of minute division. A screw can easily be made with one hundred turns of its thread in an inch. What subjects of inquiry fall under dynamics? All such as have reference to the motion of solids, or to the phænomena arising from their motion. When is a body said to be in uniform motion? When it passes over equal spaces in any equal portion of time. How is the space found when the body moves with a uniformly accelerated velocity? By multiplying the space over which it passes in onesecond by the square of the time. Times 1 2 3 4 5 6 &c. Spaces 1 4 9 16 25 36 Through what space does a body fall from rest in one second, if falling freely under the influence of the earth's attraction? It is 16 feet, or more accurately 16, that is 16 feet and 1 inch. If a body is acted on by two forces, as A B and A C urging it in different directions, how will it move? In the direction of neither force, but in a direction intermediate between the two. What do you understand by central forces? Those which in their action have reference to a fixed point or centre. How many kinds of central forces are there? Two kinds, centripetal and centrifugal force. That whose tendency is to urge a body to a fixed centre is called a centripetal F or centre-seeking force; and that whose tendency is to urge a body from a fixed centre is called a centrifugal, or centre-flying force. What definition do you give of a pendulum? It is in its simple form a particle of matter attached to the end of a string. What is the most remarkable property of the pendulum? It consists in the equal duration of its oscillations. What is the length of the seconds pendulum? For the latitude of London it is 39.139 inches; for the latitude of Edinburgh, 39.155, it is longer by inch. What does hydrostatics treat of? It treats of the pressure and equilibrium of water. Describe the fundamental law of hydrostatics. It is that a liquid in a vessel cannot rest, until its surface is perfectly horizontal and level. What is the pressure of water or any other liquid upon the bottom of a vessel equal to? The pressure of water or any other liquid upon the bottom of a vessel is equal to the weight of the perpendicular column of the same liquid which has for its basis the bottom of the vessel. Upon what does the pressure upon any point in the side of a vessel depend? It follows that the pressure upon any point in the side of a vessel depends upon the weight of the liquid above that point. How do you find the pressure of a liquid on a solid immersed in it? This pressure will depend upon the depth of immersion : when a solid is immersed in a fluid, it sustains upon the whole an upward pressure equal to the weight of the fluid which it displaces. What general law is derived from it? A body immersed in water or in any other fluid loses as much weight as an equal bulk of the fluid weighs, and the fluid gains the same weight. What do you mean by the specific gravity of a body? The relation of its weight to that of an equal volume of some other body selected as a standard. How do you proceed, then, in determining the specific gravities of bodies? In order to determine the specific gravity of any body, it is first weighed in the usual way, or in air, and then in water. Now it will weigh less in water than in air, just by its own volume of water. If we mark the difference between its weight in air and its weight in water, we get the weight of its own volume of water; and as we have its own weight, we have thus the weights of equal volumes of the solid and water, and hence the specific gravity of the solid. To what purpose is the hydrometer commonly applied? It is applied either to determine the specific gravity of a liquid or of a solid. One of its uses is to determine the strength of spirit. To whom are we indebted for this branch of science? To the celebrated Archimedes of Syracuse in Sicily. What does hydraulics treat of? It treats of the motion of water through tubes and other contrivances. What may be considered the fundamental problem in hydraulics? To determine the velocity with which water would issue from an aperture at a given depth below the horizontal surface. SECOND COURSE OF NATURAL MECHANICS. What is Mechanics? The science which treats of the equilibrium of force. tends to put matter in motion. Name a force. The air in motion or water falling over a precipice; the attraction of the earth; the strength of animals. What is a mechanical power? A contrivance to increase or diminish the velocity of a force or prime mover. Whether does a level of the first or second kind increase or diminish the velocity? It diminishes it. Does a |