The effective mean Pressure on the piston throughout the stroke is found by this Rule: To the hyperbolic logarithm of the total number of expansions add 1, then divide by the total number of expansions, and multiply the quotient by the initial absolute pressure of the steam (that is, the boiler pressure plus 15 lbs.) which will give the average pressure of the steam expanded the given number of times, from which deduct the back pressure, usually 3 lbs., and the result will be the mean effective pressure of the steam on the piston. To find the Area of the High-pressure Cylinder of a compound, or double-expansion, steam-engine.-Rule: Multiply the initial absolute pressure of the steam in the high-pressure cylinder by '042, with which result divide the area of the low-pressure cylinder, and the quotient will be the area of the high-pressure cylinder. In order to provide for the loss due to the fall in pressure of the steam in passing between the two cylinders, their areas found by the above rules should be increased to the extent of from 10 to 20 per cent. The steam should be cut off in the high-pressure cylinder when the piston has moved 45 of its length of stroke, and in the low-pressure cylinder at one-half the length of the stroke. The final pressure in the low-pressure cylinder should be from 8 to 9 lbs. per square inch in theory, but in practice it is from 2 to 3 lbs. more than that, and the lowest economical final pressure is from 10 to 12 lbs. per square inch. Illustrations of these Rules.-Required the area of the cylinders of a compound, or double-expansion, steam-engine to indicate 100 horse-power: speed of piston 420 feet per minute: boiler pressure 86 lbs. per square inch. Then, allowing 5 lbs. for loss of pressure between the boiler and the cylinder, the initial pressure in the high-pressure cylinder will be 81 lbs., and the initial absolute pressure 81 + 15 = 96 lbs. per square inch; and presuming the steam to be worked down to a final pressure of 12 lbs. per square inch it will give = 96 initial absolute pressure in high-pressure cylinder 8, ratio of ex12 final pressure in low-pressure cylinder pansion. The hyperbolic logarithm of 8 is, from Table 2, = 2'0794 + 1 = *3849 × 96 lbs. per square inch = 36·95, the average pressure in lbs. per square inch of steam of 96 lbs. pressure expanded eight times, and if 3 lbs. be deducted for back pressure, it leaves 33'95 lbs. effective mean pressure per square inch; then 100 indicated horse-power required × 33,000 = 7857'14 gross pressure on 420 speed of piston in feet per minute the piston at that speed; and 785714 =23134, 33'95 effective mean pressure the area in square inches of the large cylinder, and 96 × 042 = 4'03, = 57'4 the area in square inches of the small cylinder. Then, end 231*34 4'03 PHL C = if 20 per cent. be added to provide against loss by the pressure falling during the passage of the steam between the cylinders, the area of the low-pressure cylinder will be = 23134 + 46.26 2776 square inches, and the area of the high-pressure cylinder will be = 57'4 + 11:48 = 68-88 square inches, or 18 inches diameter for the large, and 9 inches diameter for the small cylinder, being a cylinder ratio of 4 to 1, which agrees with the best modern practice for that pressure of steam. If the initial absolute pressure of the steam had been 75 lbs. per square inch, the Fig. 71.-Section of the Cylinders of a VerticalTandem Double-Expansion Steam-Engine. ratio of the areas of the cylinders would have been=75 × 042 = 3'15 ; and for a pressure of 60lbs. per square inch, it would have been =60 x '042 =252; and for an absolute pressure of 125 lbs. per square inch, it would have been = 125 X 042 =5'25. The cylinders of a vertical tandem, compound, or double-expansion, condensing steam-engine, are shown partly in section in Fig. 71. The cylinders are inverted and placed over a crank-shaft fixed on a boxshaped foundation-plate. The governor is fixed on the cover of the steam-chest, and is driven by a belt from a pulley on the crank-shaft. Triple-Expansion Engines expand steam in three stages, generally in three cylinders. A set of tripleexpansion engines is shown in Fig. 72. The cylinders are arranged in a line over the centre-line of the crank-shaft. The power of each cylinder is transmitted to a separate crank, the cranks being placed at angles of 120° apart. The high-pressure cylinder is 29 inches diameter; the intermediate cylinder is 47 inches diameter, and the low-pressure cylinder is 76 inches diameter; the length of stroke being 51 inches. The air-pump is single-acting, of brass fixed in a cast-iron casing, it is 25 inches diameter; the bilge-pumps and feed-pumps are each 4 inches diameter; and the circulating-pump for the surface-condenser is 15 inches diameter. The diameter of the crank-shaft is 14 inches diameter. The high-pressure cylinder is fitted with a piston-valve 14 inches diameter: the other cylinders have slide-valves. The Diameter of the Crank-shaft of Double, Triple, and Quadruple Expansion-Engines should not generally be less than that found by the following rule: in which P = the absolute pressure of the steam in lbs. per square inch; length of stroke in inches; D= diameter of low-pressure cylinder in S Fig. 72.-Sectional Elevation or a Set of Triple Expansion Engines, by Falmer & Co, Limited, Jarrow-on-Tyne. inches; C is a constant = 10,000 for double-expansion engines, 17,000 for triple-expansion engines, and 19,000 for quadruple-expansion engines. Other rules and data for double, triple, and quadruple-expansion engines are given in the author's work, "The Practical Engineer's Handbook." Friction of Crank-Shafts.-The friction of the crank-shaft of a steam-engine depends upon the load on the bearings, the finish and F alignment of the rolling and bearing surfaces, the nature of the unguent employed, and the efficiency of the lubrication. For crank-shafts making from 60 to 150 revolutions per minute, in true bearings efficiently lubricated with good oil, the resistance of friction due to a pressure of 1 lb. approximately averages as follows— Wrought-iron crank-shaft working in bearings of Steel - crankshaft working in bearings of hard Wrought-iron crank-shaft working in bearings of gun-metal, having strips of antifriction- Wrought-iron crank-shaft working in bearings of antifriction-metal of fine quality. Co-efficient of Friction *00178 *00172 '00124 '00120 *00115 The friction increases slightly with the speed above 150 revolutions per minute. When the alignment of the crank-shaft is defective, either horizontally or vertically, it causes excessive friction, and may result in thumping and hot bearings. LOCOMOTIVE - ENGINES. The power of a Locomotive-Engine is determined by the tractive force it can exert upon the rails. The tractive force is the power which the pistons of the engine are capable of exerting through the driving-wheels to move the engine and train. The power a locomotive is capable of exerting with useful effect depends upon the adhesion or frictional hold of the driving-wheels upon the rails. The Adhesive Power of a locomotive depends upon the weight on the driving-wheels, and is in ordinary weather about of the load on the driving-wheels; in goods engines the wheels are coupled, and the adhesive force is due to the weight resting on the coupled wheels. Hence, to prevent the wheels of a locomotive slipping on the rails, the weight resting on the driving-wheels must be about six times as great as the power exerted by the engine to slip the wheels. Train-Resistances.-The power developed by a locomotive-engine is expended in overcoming the resistances due to wheel-friction, gradients, curves, and wind-pressure. Mr. D. K. Clark's formule for the resistances on railways are as follows: R = total resistance of engine, tender and train in lbs per ton gross; R' = resistance of train alone in lbs. per ton; V = speed in miles per hour. These rules are for a straight line of rails; and one-half more is to be added for the resistance due to curves, imperfections of the road, wind-pressure. Table 6.-RESISTANCE OF TRAINS. Speed in Miles per Hour. Frictional Resistance in lbs. per Ton of Engine, Tender, and Train Frictional Resistance in lbs. per Ton of the Train alone and It requires a force of about 7 lbs. per ton, to keep waggons moving on a level line of rails, at a very slow speed after they are started. The Tractive Power of a locomotive-engine is found by this Rule: Multiply the square of the diameter in inches of one cylinder, by the length of stroke in inches, and divide the product by the diameter in inches of the driving-wheel. The quotient will be the tractive force in pounds, for each pound of effective pressure per square inch on the piston; and this quotient multiplied by the effective mean pressure in the cylinder, will give the full tractive force in pounds exerted by the engine. The Effective Mean-Pressure on the Pistons equivalent to a given tractive force at the rails may be found by this Rule: Multiply the diameter of the driving-wheel in inches by the total equivalent tractive force at the rails in pounds, and divide the product by the product of the square of the diameter of the cylinders in inches by the length of stroke in inches. The Maximum Boiler-Pressure of locomotives is about 180 pounds per square inch. The standard working-pressure of the steam is 160 lbs. per square inch on some railways, and 140 lbs. per square inch on others; but the effective mean pressure is much less, owing to working the steam expansively. The maximum mean-pressure on the pistons under any circumstances does not generally exceed three-fourths of the boiler-pressure. The Resistance in lbs. per ton of the train due to gravity, on an incline may be found by this Rule: Divide 2240 by the rate of the gradient. To find the resistance in lbs. per ton due to the velocity of the engine, tender, and train. Rule: Square the speed of the train in miles per hour, and divide the result by 171, and add 8 to the quotient. To the sum, add 50 per cent. for resistance due to curves, imperfections of the road, and wind-pressure. The Load the Engine can take, in tons, including the weight of the wagons, but not that of the engine and tender, may be found by this Rule: Add together the resistance due to gravity, and the resistance due to |