The Screw. The screw is an inclined plane, and may be supposed to be generated by wrapping a triangle, or an inclined plane, round a cylinder. The base of the triangle is the circumference of the cylinder; its height, the distance between two consecutive cords or threads; and' the hypothenuse forms the spiral cord or inclined plane. RULE. To the square of the circumference of the screw, add the square of the distance between two threads, and extract the square root of the sum: this will give the length of the inclined plane. Its height is the distance between two consecutive cords or threads. When a winch or lever is applied to turn the screw, the power of the screw is as the circle described by the handle of the winch, or lever, to the internal or distance between the spirals. Case 1. When the weight to be raised is given, to find the power. RULE. Multiply the weight by the distance between two threads of the screw, and divide the product by the circumference of the circle described by the lever. The quotient is the power. EXAMPLE. Required the power to be applied to the end of a lever three feet long, to raise a weight of five tons with a screw of 1 inch between the threads. 11200 lbs. × 1.25 36 inches x 2 x 3.1416 61.9 lbs., the power. Case 2. When the power is given, to find the weight it will raise. RULE Multiply the power by the circumference of the circle described by the lever, and divide the product by the distance between two threads of the screw: the quotient will be the weight. The example is the converse of that in the former case, TO HARDEN AND POLISH ALABASTER.-1. Take a strong solution of alum, strain it, and put it into a wooden trough sufficiently large to contain the figure, which must be suspended in it by means of a thread of silk, let it rest until a sufficient quantity of the salt is crystallized on the cast, then withdraw it, and polish it with a clean cloth and water. 2. Take white wax, melt it in a convenient vessel, and dip the cast or figure into it; withdraw, and repeat the operation of dipping until the liquid wax rests upon the surface of the cast; then let it cool and dry, when it must be polished with a clean brush. TOOTHED WHEELS. The pitch (or the distance between the centres of two contiguous teeth) of cog-wheels is measured on the pitch-line, or extreme circumference of the wheel; and the distance between that line and the centre of the circle is reckoned as the radius of the wheel. The following rules have been laid down for the diameters and number of teeth for wheels and pinions. RULE 1. As the number of teeth in the wheel + 2.25, Is to the diameter of the wheel, So is the number of teeth in the pinion + 1·5, 210, the EXAMPLE. Given the number of teeth in the wheel diameter of the wheel = 25 inches, and the number of teeth in the 30, to find the diameter of the pinion. pinion As 210 225: 25 :: 30 + 15:37102, the diameter of the pinion. RULE 2. As the number of teeth in the wheel + 2.25, Is to the diameter of the wheel, So is (No. of teeth in pinion + No. of teeth in wheel) → 2, EXAMPLE. Given the number of teeth in the wheel=210, the diameter of the wheel = 25 inches, and the number of teeth in the 30, to find the distance at which their centres should be pinion placed. = As 210+2·25: 25 :: of their centres. 30 × 210 : 14-1342 inches, the distance 2 On the Velocity of Wheels, Drums, Pulleys, &c. When wheels are applied to communicate motion from one part of a machine to another, their teeth act alternately on each other; consequently, if one wheel contains 60 teeth and another 20, the one containing 20 teeth will make three revolutions, while the other makes but one; and if drums or pulleys are taken in place of wheels, the result will be the same, because their circumferences, describing equal spaces, render their revolutions unequal; from this the rule is derived, namely, 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, Then the sum of the velocities : velocity of driver :: distance EXAMPLE 1. If a wheel that contains 75 teeth makes 16 revolu tions per minute, required the number of teeth in another to work in it, and make 24 revolutions in the same time. 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+ 155: 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 58202.9, 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 802.9 10.345 inches diameter. EXAMPLE 6. Required the diameter of a pulley, to make 12 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 + 100 177 =2·3277o 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 -it 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. 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 |