metal on metal may be taken at .15 to 20; for wood on metal, .25 to .30; and for wood on compressed paper, .20. The tangential driving force T may be as high as 80 lbs. per inch width of face of the driving surface, but this is accompanied by great pressure and friction on the journal-bearings. In frictional grooved gearing circumferential wedge-shaped grooves are cut in the faces of two wheels in contact. If P the force pressing the wheels together, and N the normal pressure on all the grooves, P = N (sin af cos a), in which 2a = the inclination of the sides of the grooves, and the maximum tangential available force TƒN. The inclination of the sides of the grooves to a plane at right angles to the axis is usually 30°. Frictional Grooved Gearing.-A set of friction-gears for transmitting 150 H.P. is on a steam-dredge described in Proc. Inst. M. E., July, 1888. Two grooved pinions of 54 in. diam., with 9 grooves of 134 in. pitch and angle of 40° cut on their face, are geared into two wheels of 127% in diam. similarly grooved. The wheels can be thrown in and out of gear by levers operating eccentric bushes on the large wheel-shaft. The circumferential speed of the wheels is about 500 ft. per min. Allowing for engine-friction, if half the power is transmitted through each set of gears the tangential force at the rims is about 3960 lbs., requiring, if the angle is 40° and the coefficient of friction 0.18, a pressure of 7524 lbs. between the wheels and pinion to prevent slipping. The wear of the wheels proving excessive, the gears were replaced by spurgear wheels and brake-wheels with steel brake-bands, which arrangement has proven more durable than the grooved wheels. Mr. Daniel Adamson states that if the frictional wheels had been run at a higher speed the results would have been better, and says they should run at least 30 ft. per second. HOISTING. Approximate Weight and Strength of Cordage. (Boston and Lockport Block Co.)-See also pages 339 to 345. Regular Mortise-blocks Single and strapped Blocks, will hoist about→ Working Strength of Blocks. (B. & L. Block Co.) Double, or Two Double Iron Wide Mortise and Extra Heavy about Where a double and triple block are used together, a certain extra propor tioned amount of weight can be safely hoisted, as larger hooks are used. Comparative Efficiency in Chain-blocks both in (Tests by Prof. R. H. Thurston, Hoisting, March, 1892.) No. 1 was Weston's triplex block; No. 3, Weston's differential; No. 4, Weston's imported. The others were from different makers, whose names are not given. All the blocks were of one-ton capacity. Proportions of Hooks.-The following formulæ are given by Henry R. Towne, in his Treatise on Cranes, as a result of an extensive experimental and mathematical investi gation. They apply to hooks of capacities from 250 lbs. to 20,000 lbs. Each size of hook is made from some commercial size of round iron. The basis in each case is, therefore, the size of iron of which the hook is to be made, indicated by A in the diagram. The dimension D is arbitrarily assumed. The other dimensions, as given by the formulæ, are those which, while preserving a proper bearing-face on the interior of the hook for the ropes or chains which may be passed through it, give the greatest resistance to spreading and to ultimate rupture, which the amount of material in the original bar admits of. The symbol A is used to indicate the nominal capacity of the hook in tons of 2000 lbs. The formulæ which determine the lines of the other parts of the hooks of the several sizes are as follows, the measurements being all expressed in inches: FIG. 164. The dimensions A are necessarily based upon the ordinary merchant sizes of round iron. The sizes which it has been found best to select are the following: Capacity of hook: 1 12 2 3 4 5 6 8 10 tons. Dimension A: 5% 11/16 34 11/16 114 1% 134 2 214 2% 2% 34 in. Experiment has shown that hooks made according to the above formulæ will give way first by opening of the jaw, which, however, will not occur except with a load much in excess of the nominal capacity of the hook. This yielding of the hook when overloaded becomes a source of safety, as it constitutes a signal of danger which cannot easily be overlooked, and which must proceed to a considerable length before rupture will occur and the load be dropped. POWER OF HOISTING-ENGINES. Horse-power required to Gross weight in lbs 33,000 Speed.-H.P. = raise a Load at a Given X speed in ft. per min. To this add 25% to 50% for friction, contingencies, etc. The gross weight includes the weight of cage, rope, etc. In a shaft with two cages balancing each other use the net load weight of one rope, instead of the gross weight. To find the load which a given pair of engines will start.-Let A = area of cylinder in square inches, or total area of both cylinders, if there are two; P= mean effective pressure in cylinder in lbs. per sq. in.; S = stroke of cylinder in inches; C circumference of hoisting-drum in inches; L = load lifted by hoisting-rope in lbs.; F = friction, expressed as a diminution of AP2S the load. Then L = C F. An example in Coll'y Engr., July, 1891, is a pair of hoisting-engines 24" X 40", drum 12 ft. diam., average steam-pressure in cylinder = 59.5 lbs.; 4 = 904.8; P= 59.5; S = 40; C = 452.4. Theoretical load, not allowing for friction, AP2SC 9589 lbs. The actual load that could just be lifted on trial was 7988 lbs., making friction loss F = 1601 lbs., or 20+ per cent of the actual load lifted, or 16% of the theoretical load. The above rule takes no account of the resistance due to inertia of the load, but for all ordinary cases in which the acceleration of speed of the cage is moderate, it is covered by the allowance for friction, etc. The resistance due to inertia is equal to the force required to give the load the velocity acquired in a given time, or, as shown in Mechanics, equal to the product of the mass by the acceleration, or R = in which R = resist ance in lbs. due to inertia; W = weight of load in lbs.; V = maximum veloc ity in feet per second; T = time in seconds taken to acquire the velocity V; = 32.16. g WV 9T' Effect of Slack Rope upon Strain in Hoisting.-A series of tests with a dynamometer are published by the Trenton Iron Co., which show that a dangerous extra strain may be caused by a few inches of slack rope. In one case the cage and full tubs weighed 11,300 lbs.; the strain when the load was lifted gently was 11,525 lbs.; with 3 in. of slack chain it was 19.025 lbs., with 6 in. slack 25,750 lbs., and with 9 in. slack 27,950 lbs. Limit of Depth for Hoisting.-Taking the weight of a cast-steel hoisting-rope of 1% inches diameter at 2 lbs. per running foot, and its break. ing strength at 84,000 lbs., it should, theoretically, sustain itself until 42,000 feet long before breaking from its own weight. But taking the usual factor of safety of 7, then the safe working length of such a rope would be only 6000 feet. If a weight of 3 tons is now hung to the rope, which is equivalent to that of a cage of moderate capacity with its loaded cars, the maximum length at which such a rope could be used, with the factor of safety of 7, is 3000 feet, or This limit may be greatly increased by using special steel rope of higher strength, by using a smaller factor of safety, and by using taper ropes. (See paper by H. A. Wheeler, Trans. A. I. M. E., xix. 107.) Large Hoisting Records.-At a colliery in North Derbyshire during the first week in June, 1890, 6309 tons were raised from a depth of 509 yards, the time of winding being from 7 a.m. to 3.30 p.m. At two other Derbyshire pits, 170 and 140 yards in depth, the speed of winding and changing has been brought to such perfection that tubs are drawn and changed three times in one minute. (Proc. Inst. M. E., 1890.) At the Nottingham Colliery near Wilkesbarre, Pa., in Oct. 1891, 70,152 tons were shipped in 24.15 days, the average hoist per day being 1318 mine cars. The depth of hoist was 470 feet, and all coal came from one opening. The engines were fast motion, 22 x 48 inches, conical drums 4 feet 1 inch long. 7 feet diameter at small end and 9 feet at large end. (Eng'g News, Nov. 1891.) Pneumatic Hoisting. (H. A. Wheeler, Trans. A. Ï. M. E., xix. 107.)— A pneumatic hoist was installed in 1876 at Epinac, France, consisting of two continuous air-tight iron cylinders extending from the bottom to the top of the shaft. Within the cylinder moved a piston from which was hung the cage. It was operated by exhausting the air from above the piston, the lower side being open to the atmosphere. Its use vas discontinued on account of the failure of the mine. Mr. Wheeler gives a description of the system, but criticises it as not being equal on the whole to hoisting by steel ropes. Pneumatic hoisting-cylinders using compressed air have been used at blast-furnaces, the weighted piston counterbalancing the weight of the cage, and the two being connected by a wire rope passing over a pulley-sheave above the top of the cylinder. In the more modern furnaces steam-engine hoists are generally used. Counterbalancing of Winding-engines. (H. W. Hughes, Columbia Coll. Qly.)-Engines running unbalanced are subject to enormous variations in the load; for let W weight of cage and empty tubs, say 6270 lbs.; c weight of coal, say 4480 lbs.; r = weight of hoisting rope, say 6000 lbs.; weight of counterbalance rope hanging down pit, say 6000 lbs. The weight to be lifted will be: = If weight of rope is unbalanced. At beginning of lift: W+c+r-W or 10,480 lbs. At middle of lift: If weight of rope is balanced. W+c+r-(W+r'), or 4480 W+c+(w+)or 4480 lbs. W+c++ - (++). lbs. At end of lift: W+c-(W+r) or minus 1520 lbs. W+c+(W+r), That counterbalancing materially affects the size of winding-engines is shown by a formula given by Mr. Robert Wilson, which is based on the fact that the greatest work a winding-engine has to do is to get a given mass into a certain velocity uniformly accelerated from rest, and to raise a load the distance passed over during the time this velocity is being obtained. Let W = the weight to be set in motion: one cage, coal, number of empty tubs on cage, one winding rope from pit head-gear to bottom, and one rope from banking level to bottom. v = greatest velocity attained, uniformly accelerated from rest; t = time in seconds during which v is obtained; L= unbalanced load on engine; R = ratio of diameter of drum and crank circles; N= number of cylinders; S space passed over by crank-pin during time t; C, constant to reduce angular space passed through by crank, to the distance passed through by the piston during the time t; A area of one cylinder, without margin for friction. To this an addition for friction, etc., of engine is to be made, varying from 10 to 30% of A. The formula is the same, with the addition of another term to allow for the variation in the lengths of the ascending and descending ropes. In this case h1reduced length of rope in t attached to ascending cage; Applying the above formula when designing new engines, Mr. Wilson found that 30 inches diameter of cylinders would produce equal results, when balanced, to those of the 36-inch cylinder in use, the latter being unbalanced. Counterbalancing may be employed in the following methods: (a) Tapering Rope.-At the initial stage the tapering rope enables us to wind from greater depths than is possible with ropes of uniform section. The thickness of such a rope at any point should only be such as to safely bear the load on it at that point. With tapering ropes we obtain a smaller difference between the initial and final load, but the difference is still considerable, and for perfect equalization of the load we must rely on some other resource. The theory of taper ropes is to obtain a rope of uniform strength, thinner at the cage end where the weight is least, and thicker at the drum end where it is greatest. (b) The Counterpoise System consists of a heavy chain working up and down a staple pit, the motion being obtained by means of a special small drum placed on the same axis as the winding drum. It is so arranged that the chain hangs in full length down the staple pit at the commencement of the winding; in the centre of the run the whole of the chain rests on the bottom of the pit, and, finally, at the end of the winding the counterpoise has been rewound upon the small drum, and is in the same condition as it was at the commencement. (c) Loaded-wagon System. A plan, formerly much employed, was to have a loaded wagon running on a short incline in place of this heavy chain; the rope actuating this wagon being connected in the same manner as the above to a subsidiary drum. The incline was constructed steep at the com. mencement, the inclination gradually decreasing to nothing. At the begin. ning of a wind the wagon was at the top of the incline, and during a portion of the run gradually passed down it till, at the meet of cages, no pull was exerted on the engine-the wagon by this time being at the bottom. In the latter part of the wind the resistance was all against the engine, owing to its having to pull the wagon up the incline, and this resistance increased from nothing at the meet of cages to its greatest quantity at the conclusion of the lift. (d) The Endless-rope System is preferable to all others, if there is sufficient sump room and the shaft is free from tubes, cross timbers, and other impediments. It consists in placing beneath the cages a tail rope, similar in diameter to the winding rope, and, after conveying this down the pit, it is attached beneath the other cage. (e) Flat Ropes Coiling on Reels -This means of winding allows of a certain equalization, for the radius of the coil of tascending rope continues to increase, while that of the descending one continues to diminish. Consequently, as the resistance decreases in the ascending load the leverage increases, and as the power increases in the other, the leverage diminishes. The variation in the feverage is a constant quantity, and is equal to the thickness of the rope where it is wound on the drum. By the above means a remarkable uniformity in the load may be obtained, the only objection being the use of flat ropes, which weigh heavier and only last about two thirds the time of round ones. (f) Conical Drums.-Results analogous to the preceding may be obtained by using round ropes coiling on conical drums, which may either be smooth, with the successive coils lying side by side, or they may be provided with a spiral groove. The objection to these forms is, that perfect equalization is not obtained with the conical drums unless the sides are very steep, and consequently there is great risk of the rope slipping; to obviate this, scroll drums were proposed. They are, however, very expensive, and the lateral displacement of the winding rope from the centre line of pulley becomes very great, owing to their necessary large width. (g) The Koepe System of Winding.-An iron pulley with a single circular groove takes the place of the ordinary drum. The winding rope passes from one cage, over its head-gear pulley, round the drum, and, after pass |