Multiply the velocity of the driver by the number of teeth it contains, and divide by the velocity of the driven: the quotient will be the number of teeth it ought to contain. Or, multiply the velocity of the driver by its diameter, and divide by the velocity of the driven: the quotient will be the diameter of the driven. If the velocities of driver and driven are given with the distance of their centres, velocity of driver :: distance EXAMPLE 1. If a wheel that contains 75 teeth makes 16 revolutions per minute, required the number of teeth in another to work in it, and make 24 revolutions in the same time. . 50 teeth. = Ans. EXAMPLE 2. A wheel, 64 inches diameter, and making 42 revolutions per minute, is to give motion to a shaft at the rate of 77 revolutions in the same time; required the diameter of a wheel suitable for that purpose. EXAMPLE 3. Required the number of revolutions per minute made by a wheel or pulley 20 inches diameter, when driven by another of 4 feet diameter, and making 46 revolutions per minute. EXAMPLE 4. A shaft, at the rate of 22 revolutions per minute, is to give motion, by a pair of wheels, to another shaft at the rate of 15; the distance of the shafts from centre to centre is 45 inches; the diameters of the wheels at the pitch lines are required. Here 22+ 15·5: 22:: 45'5 in. : 22 × 45.5 26.69 in. the radius of the driven wheel; which, doubled, gives 53.38 inches, the diameter.=1st Ans. Therefore 45.5 inches-26 69 inches 18 81 inches, the radius of the driver; which, doubled, gives 37 62 inches, the diameter.=2d Ans. EXAMPLE 5. Suppose a drum to make 20 revolutions per minute, required the diameter of another to make 58 revolutions in the same time. Here 58 20 2:9, that is, their diameters must be as 2.9 to 1; thus, if the one making 20 revolutions be called 30 inches, the other will be 30 ÷ 2′9 — 10'345 inches diameter. EXAMPLE 6. Required the diameter of a pulley, to make 121 revolutions in the same time as one of 32 inches making 26. EXAMPLE 7. A shaft, at the rate of 16 revolutions per minute, is to give motion to a piece of machinery, at the rate of 81 revolutions in the same time; the motion is to be communicated by means of two gearing wheels and two pulleys, with an intermediate shaft; the driving wheel contains 54 teeth, and the driving pulley on the axis of the driven wheel is 25 inches diameter; required the number of teeth in the other wheel, and the diameter of the other pulley. Let the driven wheel have a velocity of 36, a mean proportional between the extreme velocities 16 and 81,; 24, the number of teeth in the driven wheel. 11.11 inches, diameter of the driven pulley.= EXAMPLE 8. Suppose in the last example the revolutions of one of the wheels to be given, the number of teeth in both, and likewise the diameter of each pulley, to find the revolutions of the last pulley. 36, velocity of the intermediate shaft. Ans. 81, the velocity of the machine. GOLD LUSTRE FOR STONE-WARE.-Gold, 6 parts; aqua regia, 36 parts. Dissolve: then add, tin, 1 part. Next add balsam of sulphur, 3 parts; oil of turpentine, 1 part. Mix gradually in a mortar, and rub it in until the mixture becomes hard; then add oil of turpentine, 4 parts. It is then ready to be applied to a ground prepared for the purpose. TO PETRIFY WOOD, &c.-Take equal quantities of gem-salt, rockalum, white vinegar, chalk, and pebbles powdered. Mix all these ingredients: there will happen an ebullition. If, after it is over, you throw into this liquor any porous matter, and leave it there soaking four or five days, they will positively turn into petrifactions. STEAM POWER AND THE STEAM-ENGINE. : STEAM is of great utility as a productive source of motive power; in this respect, its properties are elastic force, expansive force, and reduction by condensation. Elastic signifies the whole urgency or power the steam is capable of exerting with undiminished effect. By expansive force is generally understood the amount of diminishing effect of the steam on the piston of a steam-engine, reckoning from that point of the stroke where the steam of uniform elastic force is cut off but it is more properly the force which steam is capable of exerting, when expanded to a known number of times its original bulk. And condensation, here understood, is the abstraction or reduction of heat by another body, and consequently not properly a contained property of the steam, but an effect produced by combined agency, in which steam is the principal; because any colder body will extract the heat and produce condensation, but steam cannot be so beneficially replaced by any other fluid capable of maintaining equal results. The rules formed by experimenters, as corresponding with the results of their experiments on the elastic force of steam at given temperatures vary, but approximate so closely, that the following rule, because of being simple, may in practice be taken in preference to any other: RULE. To the temperature of the steam, in degrees of Fahrenheit, add 100; divide the sum by 177; and the 6th power of the quotient will equal the force in inches of mercury.. EXAMPLE. Required the force of steam corresponding to a temperature of 312°. 312 + 100 2.3277 159 inches of mercury. To Estimate the Amount of Advantage Gained by Using Steam Expansively in a Steam-Engine. When steam of a uniform elastic force is employed throughout the whole ascent or descent of the piston, the amount of effect produced is as the quantity of steam expended. But let the steam be shut off at any portion of the stroke-say, for instance, at one half t expands by degrees until the termination of the stroke, and then exerts half its original force; hence an accumulation of effect in proportion to the quantity of steam. -it RULE. Divide the length of the stroke by the distance or space into which the dense steam is admitted, and find the hyperbolic logarithm of the quotient, to which add 1; and the sum is the ratio of the gain. EXAMPLE. Suppose an engine with a stroke of 6 feet, and the steam cut off when the piston has moved through 2; required the ratio of gain by uniform and expansive force 6÷2 28; 3; hyperbolic logarithm of 3 = 1·0986 + 1 : 1·09861 2.0986, ratio of effect; that is, supposing the whole effect of the steam to be 3, the effect by the steam being cut off at † = 2·0986. Again, let the greatest elastic force of steam in the cylinder of an engine equal 48 lbs. per square inch, and let it be cut off from entering the cylinder when the piston has moved 4 inches, the whole stroke being 18; required an equivalent force of the steam throughout the whole stroke. 18454, and 48412 Logarithm of 4 + 1 = 238629. Then 2:38629 × 12 28 635 lbs. per square inch. In regard to the other case of expansion, when the temperature is constant, the bulk is inversely as the pressure; thus, suppose steam at 30 lbs. per square inch, required its bulk to that of original bulk, when expanded so as to retain a pressure equal to that of the atmosphere, or 15 lbs. It is because of the latent heat in steam, or water in an aëriform state, that it becomes of such essential service in heating, boiling, drying, &c. In the heating of buildings, its economy, efficiency, and simplicity of application are alike acknowledged; the steam being simply conducted through all the departments by pipes, by extent of circulation condenses-the latent heat being us given to the pipes, and diffused by radiation. In boiling, its efficiency is considerably increased, if advantage be taken of sufficiently inclosing the fluid, and reducing the pressure on its surface, by means of an air-pump. Thus, water in a vacuum boils at about a temperature of 98°; and in sugar refining, where such means are employed, the syrup is boiled at 150°. The latent heat of steam at the common pressure of the atmosphere, according to very accurate experiments, is found to be 1000°; and we know that the sensible, or thermometric heat 212°. Now 212° 32° 180°, and 1000° + 180° 1180°; therefore, steam at 212° is simply highly rarified water, and contains 1180° of heat; hence, to find the latent heat of steam at any other temperature, subtract the sensible heat from 1180°, and add 32° the latent heat. EXAMPLE. Required the latent heat of steam whose sensible heat is-224°. 1180° 224956', And 956° + 32° 988° latent heat. A cubic inch of water produces about 1700 cubic inches of steam at 2120, or the common pressure of the atmosphere; but the boiling point varies considerably with the pressure on the surface of the fluid; thus, in a vacuum, water boils at about 90°; under common pressure, at 212°; and when pressed with a column of mercury 4 inches in height, at 216°; each inch of mercury producing by its pressure a rise of about 1° in the thermometer. The pressure or force of steam in the boiler (less than the weight upon the safety-valve) is generally indicated by a column of mercury in a bent iron tube, which causes the range of the float to be only half the range of the mercury, 2 inches of mercury being nearly equal to 1 lb. pressure of steam in the boiler, thus: Each inch rise of the float indicates a pressure of nearly 1 lb. Level of the mercury when there is no force of steam above the pressure of the atmosphere. To Calculate the Effect of a Lever and Weight upon the The lever, under all circumstances, is balanced by a known weight or weights, on the short end, making its point of rest on the valve the centre of motion; so that the weight, added to that of the lever, is the effective weight upon the valve, independent of any other additional weight, thus: There are three different ways that it may be required to calculate the lever: 1. When a certain pressure is required upon the valve, the distance of the weight upon the lever, and the distance of the valve from the centre of motion given, to find what weight will be required upon the lever at that distance. From the pressure on the valve in lbs. subtract the weight of the valve in lbs. and the effective weight of the lever, multiply the remainder by the distance between the fulcrum and the valve, and divide the product by the distance between the fulcrum and the |