A Unit of Work is equivalent to one pound avoirdupois raised vertically one foot. The units of work done in raising a given weight to a given height, are found by multiplying the height in feet by the weight in pounds. The units of work done in raising a weight up an inclined plane, are equal to the work that would be done in raising the weight vertically through the height of the plane.

The Modulus of a Machine is the fraction which expresses the relation of the work done to that of the work applied, or the percentage of the power absorbed which a machine will give out in useful work.

Power and Weight of Men and Animals.—In working a cranehandle, a man can apply a force of 60 lbs. in an emergency with difficulty, or a force of 30 lbs. for a short time with difficulty, or a force of 20 lbs. for a short time easily, or a force of 15 lbs. in continuous work at a velocity of 220 feet per minute; hence the power of a man is = 15 × 220=3,300 foot pounds per minute, or one-tenth of a horse-power. A soldier on march travels about 30 inches per step, and occupies a front of 21 inches in the rank; the average weight of men is 150 lbs. each; five men can stand in a space of one square yard; the weight of ordinary crowds of people is 80 lbs. per square foot; the absolute force of a man in pulling horizontally or pushing with his hands is 110 lbs. : his lifting power with both hands is 280 lbs., and the greatest load he can support on his shoulders is 336 lbs. A horse will exert a pulling force of 120 lbs. at the rate of 2 miles an hour during 10 hours. A pony or mule will exert a pulling force of 60 lbs. at the rate of 2 miles an hour during 10 hours. An ass will exert a pulling force of 30 lbs. at the rate of 2 miles an hour during 10 hours. Each of these animals will carry a load on its back equal to one-fourth its own weight, at the rate of 2 miles an hour during 10 hours. A horse will draw a load of one ton at the rate of 2 miles an hour during 10 hours. A pony or mule will draw a load of 12 cwt. at the rate of 24 miles an hour during 10 hours. An ass will draw a load of 7 cwt. at the rate of 2 miles an hour during 10 hours. These forces are for a straight pull; when animals work by pulling while walking in a circle, their pulling force is only about 60 per cent. of their force for a straight pull; the diameter of the circular path should not be less than 25 feet, and the velocity should not exceed 2 miles an hour. The average weight of a cart-horse is 13 cwt.; a cob, 7 cwt.; a mule, 6 cwt.

Resistance of Carts and Waggons to Traction on Level Roads and Rails.-The resistance to traction in proportion to the whole weight is on fields; on gravel and on broken-stone roads in bad condition;

on dry hard turf; on good macadamized roads; on underground tramways with 8-inch diameter wheels; on wood pavement; on good London pavement; on street tramways with grooved rails;

on

underground tramways with 12-inch wheels on round top rails; on asphalte pavement; on granite tramway; on railways.

The force required to drag a weight on a level firm wood floor without rollers is the whole weight, and with the weight placed on rollers 3 inches diameter, it is of the whole weight.

Horse-power.-A strong horse can travel 2 miles per hour and work 8 hours a day, doing the equivalent of pulling a load of 150 lbs. weight up out of a shaft by means of a rope. 2 miles an hour is 220 feet per minute, and at that speed the load of 150 lbs. is raised vertically the same distance, that is equal to 300 lbs. raised 110 feet high, or 3,000 lbs. raised 11 feet high, or 33,000 lbs. raised one foot high per minute. The unit of power is the mechanical force necessary to lift 33,000 lbs. one foot high in one minute; but, in dealing with steam engines, two terms are used, viz., nominal horse-power, and actual horse-power.

Nominal Horse-power is a commercial term used by makers of engines to denote only the size of an engine without regard to the actual power it will exert.

Nominal Horse-power of Non-Condensing Steam-Engines.—The rule of ordinary practice is to make the sectional area of the cylinder equal to from 9 to 10 square inches for each nominal horse-power. The nominal horse-power of non-condensing engines may be found by the following rule, which accords with the best modern practice. Rule: Multiply the square of the diameter of the cylinder in inches by 7, and divide the result by 80.

Nominal Horse-power of Condensing Steam-Engines.-Rule: Multiply the square of the diameter of the cylinder in inches by 7, and divide the product by 120.

Actual Horse-power of Steam-Engines.-To find the actual horsepower. Rule: Multiply the area of the cylinder in square inches by the average effective mean pressure of the steam in lbs. per square inch, minus 3 lbs. per square inch for friction; and by the speed of the piston in feet per minute. The product will be the number of foot-pounds per minute which the engine will raise. Divide this product by 33,000, and the quotient will be the actual horse-power of the engine.

Brake Horse-power is the power of an engine measured by a frictionbrake, or dynamometer. It represents the effective horse-power, or the indicated horse-power of an engine minus the power absorbed by its own friction.

Dynamometers.-The power of a motor or engine may be measured by absorbing by friction the whole power developed by it, by means of a dynamometer, or friction-brake.

Prony's Brake, shown in Fig. 1, acts by absorbing the power transmitted to it; the friction is balanced by a weight at the end of a lever. It consists of a horizontal lever, having at one end a strap of iron, lined with blocks of wood, which embraces a pulley keyed on the shaft of the motor,

and at the other end a suspended-carrier for weights. The lever is prevented from rising or falling excessively by stop-blocks. If the reputed power of the motor is known, a weight corresponding to that power is hung on the lever, and after the engine is started, the strap is gradually

tightened, and the wood is drawn tightly against the surface of the pulley,which is kept cool by a stream of soapy water. The weight on the lever is increased or diminished gradually until the lever is in equilibrium. When the engine is running at its proper, or normal, speed, with the correct pressure of steam, the lever will be raised slightly above its horizontal

Fig. 2.-Iron-Strap-Friction-Brake.

position; if the lever be raised considerably, the power will be in excess of the calculated power, and the weight in the scale must be increased so as to obtain the maximum power.

To find the Dynamometrical horse-power. Rule: Multiply

the circumference in feet described by the lever, by the number of revolutions per minute and by the weight suspended, in pounds, and divide the product by 33,000.

To find the weight to be used to test an Engine. Rule: Multiply the horse - power by 33,000, and divide by the product of the circumference in feet described by the lever, multiplied by the number of

revolutions. The weight of the lever must either be balanced, or provided for in the calculation.

In using this brake it is difficult to maintain the lever in a horizontal position, or in equilibrium. This form of brake can only be efficiently applied to a pulley of small diameter, and it is only suitable for the measurement of a motor of small power.

A Friction-Brake of a convenient and efficient form for testing the power of an engine is shown in Fig. 2. It consists of a strap of hoop-iron lined with blocks of wood, placed round a pulley or fly-wheel on the crankshaft of the engine. A weight is hung on one end of the strap, and the other end is connected to a spring-balance, or a small weight may be used instead of a spring-balance. The end of the strap carrying the ascending weight should. be confined by a loose cord to prevent it being carried over the pulley.

Belt - Friction - Brake.A friction-brake of simple, but reliable, description and easy of application is shown in Fig. 3. It consists simply of a leather belt hung over the driving-pulley or fly-wheel of the engine, having a weight attached to the ascending end, and a spring-balance at the other end. The weight is prevented from being carried over the pulley while the

Fig. 3.-Leather-Belt-Friction-Brake.

engine is working by a safety-stop, consisting of a number of narrow strips. of half-round iron riveted on the inside of the ascending end of the belt. These strips come in contact with the face of the pulley, diminish the friction, and stop the ascent of the weight, in case it ascends much higher than its normal position when the brake is fully loaded. The engine lifts the weight, and the effective weight lifted is equal to the weight on the ascending end of the belt, minus the weight indicated by the springbalance on the descending end. The effective weight multiplied by the circumferential velocity of the pulley in feet per minute, and divided by 33,000 gives the brake-horse-power of the engine.

Example.-Required the power of an engine which, when tested by a belt-friction-brake, lifted a weight of 168 lbs. suspended from a belt placed