Page:The American Cyclopædia (1879) Volume XI.djvu/338

 326 MECHANICS oscillation to rise just as much as the expan- sion of the rod causes it to descend, the length of the pendulum will remain unchanged. Now, as mercury expands about 14 times as much as steel, if the rod and frame are of steel, the column of mercury should be a little less than 6 in. for a seconds pendulum. Fig. 26 is the gridiron pendulum. It is made of brass and steel, whose rates of expansion are about 10 to 6. The bars are so arranged that the expansion of the brass shall exactly compen- sate that of the steel both in the gridiron and in the rod above it. The pendulum is used as a standard of measures of length. The length of a seconds pendulum at London was in 1824 declared by parliament to be 39-1393 in., and our government has adopted that standard. The French government in 1790 adopted as its standard the -nr.inrV.Tnrff part of the quad- rant of a great circle of the earth, which they called a metre, equal to 39-37079 English inches. V. MECHANICAL POWERS. Theory of Machines. A machine is an instrument or contrivance by which force may be trans- mitted from one point to another. The force employed in working a machine is called the power; the resistance which the body acted on offers to the force is called resistance, weight, or load, and is expressed in terms of weight whose unit is usually the pound avoir- dupois ; the point at which the power is ap- plied is called the point of application ; the line of direction of the force is the line in which the force is applied, and in which it tends to make the body move, although it usually moves in the direction of a resultant. That part of a machine which is immediately applied to the resistance is called its working point. The power, like the resistance, is expressed in units of pounds avoirdupois. It is usual, in explain- ing the theory of machines, to neglect many conditions for the purpose of perspicuity and convenience, which are afterward taken into account. Thus the parts of a machine are primarily supposed to have no weight, to move without friction, and to encounter no resis- tance from the air. After the theoretical effects have been calculated, these accidental effects receive attention. Machines are divided into simple and compound. The definition of a simple machine is not so obvious as is often thought. It is sometimes defined as consisting of one part ; but as the pulley and wheel and axle are called simple machines, this definition is not exact, because each of these consists of several parts. If we conclude, however, that the only simple machines are the lever, the inclined plane, and the cord, this definition may be accepted ; but simple machines, or, as they are often called, the simple mechanical powers, have generally been divided into six classes, viz.: 1, the lever; 2, the wheel and axle ; 8, the pulley ; 4, the inclined plane ; 5, the wedge; 6, the screw. 1. The Lever. This power may be defined as an inflexible bar rest- ing on a fixed point or edge, called the fulcrum or prop. Levers are of three kinds, called the first, second, and third. The first kind is shown in fig. 27, where the fulcrum is between the power and the weight, and separates the two arms of the lever. These two arms are usually of unequal length, the weight having FIG. 27. FIG. 28. the same ratio to the long arm as the power has to the short arm. The second kind of lever, fig. 28, has the weight between the ful- crum and the power. The third kind, fig. 29, has the power between the weight and the fulcrum. In the first kind of lever it is evi- dent that to produce equilibrium the pow- ^/ )x . er may be either less or greater than the " f^ weight, according as FIG. 29. it is placed further from or nearer to the fulcrum. The propor- tion of power to resistance, in any kind of lever, to produce equilibrium is reckoned in the inverse proportion of the distance of these forces from the fulcrum ; the weight multiplied into the distance from the fulcrum being equal to the power multiplied into its distance from the same point. It cannot therefore be said that the second and third kinds of lever have two distinct arms. In the second kind, the weight, being always near the fulcrum, must always be greater than the power ; in the third, the power, being always between the weight and the fulcrum, must always be greater than the weight. As the distances through which the power and weight move are in proportion to their respective dis- tances from the fulcrum, it follows also that equilibrium is maintained when the product of their weights into the distances they respec- tively travel, or in other words, into their ve- locities, are equal, and furthermore that when a weight is moved by means of a lever, what is gained in power is lost in velocity. The com- mon steelyard is an example of a lever of the first kind, nut crackers of the second, and fire tongs of the third. All these three kinds of lever are found in various parts of the mech- anism of the human body and in that of many of the lower animals. An example of the first kind is seen in the movement of the oc- cipital bone upon the atlas or upper bone of the spinal column. The raising of the body upon the toes by the action of the muscles of the calf of the leg, if the ankle joint is con- sidered as a fulcrum, is an example of a lever of the second kind. The action of the biceps muscle upon the forearm, where the elbow joint is a fulcrum and the weight is held in the hand, is an example of a lever of the third kind. The power or the weight may act upon