(1) Friction does not increase with the extent of the rubbing surfaces, and so long as there is no violent heating or abrasion, the friction is simply in the proportion of the pressure keeping the substances together, or nearly so. It is, therefore, an obvious advantage to have the bearing surfaces of steam engines as large as possible, as there is no increase of friction by extending the surface, while there is a great increase in their durability. (2) "Friction does not increase with the velocity of the rubbing body, if the friction over a given amount of surface be considered, but it increases as the velocity, if the comparison be made with the time during which the friction acts. Thus the friction of each stroke of a piston is the same, whether it makes 20 strokes in the minute or 40; in the latter case, however, there are twice the number of strokes made, so that, though the friction per stroke is the same, the friction per minute is doubled. The force expended in overcoming friction varies with the nature of the rubbing bodies." 330. The Co-efficient of Friction is a certain fraction which, when multiplied by the normal pressure, gives the friction. EXAMPLES. Ex. 1. If the co-efficient of friction be '07 of the pressure, what horse-power is expended on the friction of a thrust bearing with 5 collars, the mean diameter of the collars being 15 inches, the shaft making 49 revolutions per minute, and the average pressure being 10 tons ? Here, although there are 5 collars, we take the friction as being concentrated on I collar only. Ex. 2. If the drag of friction be 25 of the pressure, what horse-power is expended in the friction of a thrust bearing with 5 collars, the mean diameter of the collars being 10 inches, the shaft making 60 revolutions, and the average pressure being 7} tons ? 7'5 tons = 7.5 X 2240 16800 lbs. Ex. 1. If the drag of friction be '07 of the whole pressure, and if the pressure of the connecting-rod on the crank-pin be uniform, what per centage of that is lost by friction on the crank-pin, the stroke being 36 inches, and the diameter of the crank-pin 10 inches? Distance travelled by piston in one revolution = 72 inches. Work done by the pressure on the piston during one revolution may be expressed by the formula. Work done =P X twice the stroke = P × 72 inches. And work done by the friction in one revolution P X 07 X (3'1416 × 10) = 2'19912. Ex. 2. If the drag of friction be '08 of the pressure, and if the pressure of the connectingrod on the crank-pin be uniform: what per centage of that is lost by friction on the crankpin, the stroke being 38 inches, and the diameter of the crank-pin 12 inches? (1). Distance travelled by the piston in one revolution (38 × 2) = 76 inches. (2). Circumference of pin = 3.1416 × 12 = 37′6992. (3). Ratio of distances = 17.690 ='4960. 76 (4). Ratio of work lost 4960 X 08 = '03968. (5). Per centage 03968 X 100 = 3′968. Or thus: work done by the pressure on the piston during one revolution =PX twice the stroke = P X (38 X 2) = P X 76. Work done by the friction in one revolution =PX 08 X (3°1416 × 12) = 3'015936. ON THE MECHANICAL POWERS. 331. The mechanical powers are the elements by the combinations of which are formed all the varieties of machines for enabling a smaller force to keep at rest, or put in motion, a larger weight, or to overcome a greater resistance. 332. Def.-The force which is applied to any machine to sustain or raise any weight, or to produce any other desired effect, is called the power. 333. The mechanical powers are, in fact, but three in number-the lever, the inclined plane, and cords; but it has always been customary to add to these the wheel and axle, the wedge, and the screw. Cords, as a mechanical power, are usually denominated pulleys, from their being passed round pulleys to change their direction. 334. Def.-Forces are said to balance, or to be balanced about a point or axis, when they keep a rigid body at rest about the point or axis. 335. Def.-A lever is a rigid rod, movable in one plane about a fixed point, and acted upon by forces which tend to turn it round the point. 336. Def.-The fixed point about which the lever is movable is called the fulcrum, or centre of motion. 337. Def.-The portions of the lever between the fulcrum and the points upon which the forces are impressed are called the arms of the lever. The lever will be supposed to be without weight, and the forces impressed upon it to act in the plane in which it is movable, unless the contrary be expressed. 338. Def.-The product of the numerical representatives of the magnitude of a force and the perpendicular let fall upon its direction from any fixed point, or centre of motion, is called the moment of the force about the centre. THE LEVER. Let P W be a rod or lever turning upon the fulcrum or centre F. P and W are weights which balance each other, or maintain the lever in equilibrium; then, when this is the case, PX PFW x WF; that is, the units of weight in P multiplied by the units in its distance from F, will be equal to the units of weight in W multiplied by the units in its distance from F. Here P is called F Λ tage is gained, inasmuch as a small weight or pressure is used to balance a greater one. The product of any weight, by its distance from the centre of motion, or fulcrum, is called the moment of that weight (Def. No. 338), and, therefore, when the sum of the moments tending to turn the lever in one direction, is equal to the sum of the moments tending to turn the lever in the opposite direction, then the lever will be in equilibrium. Or, the power and weight are reciprocally as the distance at which they act, and therefore For instance, if WF is one quarter of PF, then P must be one quarter of F. The moment of a force is so named because it measured the value of the force in balancing, or assisting to balance, other forces about the centre of motion. 339. Levers are sometimes divided into three classes, according to the position of the points of application of the power and the weight with respect to the fulcrum. In the first class the power and the weight act on opposite sides of the fulcrum. In the second class the power and the weight act on the same side of the fulcrum, the weight being the nearer to the fulcrum. In the third class the power and the weight act on the same side of the fulcrum, the power being the nearer to the fulcrum. Hence we may say briefly that the three classes of levers have respectively the fulcrum, the weight, and the power in the middle position. A crow bar, a claw hammer, the handle of a common pump, a pair of scissors, a fire poker, &c., belong to the first kind of lever. 341. The Second Kind.—It is best to resolve the second and third kinds of levers into the first kind, for whether, in the following figures, a force draws downwards with a force of 25 lbs. at C, or with a force of 25 lbs. at a distance equal to BC beyond the fulcrum of the lever produced, as at b (in |