MISCELLANEOUS RULES AND TABLES. To ascertain the Strength of Cables.-Square the circumference in inches and multiply by 120: the product is the weight in pounds which may be safely attached to the cable. To ascertain the Strength of Ropes.-Square the circumference in inches and multiply by 200: the product is the weight in pounds the rope will bear with safety. To ascertain the Weight of Manilla Ropes and Hawsers.-Square the circumference in inches and multiply by 03; the product gives the weight of one foot in pounds. The weight of one foot of common rope may be found by squaring the circumference in inches, and multiplying by 045, and for cables by '027. These approximate rules are sufficiently accurate for most ordinary purposes. WATER-WHEEL GUDGEONS.-Ascertain the weight in pounds to be borne by each gudgeon; extract the square root of the sum ; then divide the root by 25 for cast, and 26 for wrought iron: the dividend is the diameter and length of the gudgeon bearing, expressed in inches. Ex. The gudgeons of a water-wheel support a load of 110,000lbs.: required their diameter at the bearings, the gudgeons being cast iron : Gross weight 110,000 = 55,000 s. on each gudgeon. √55,000 = 234 52 ÷ 25 = 9 inches nearly. In practice it will be prudent to somewhat exceed the results afforded by this rule. WINDING ENGINES.-When a kibble is required to be drawn from the bottom of a shaft by a given number of strokes, it is necessary to find the diameter of the winding-cage at the first lift, to know the depth of the shaft, and thickness of rope employed. When the thickness of rope and number of strokes are known, the depth of rope on the cage can be readily determined. Multiply the depth of the shaft in inches by the thickness of the rope, also in inches, for a dividend; then multiply the thickness of the rope, in inches, by 3 1416, and by the number of strokes for a divisor. Divide the dividend by the divisor, and from the quotient subtract the product, found by multiplying the thickness of the rope by the number of strokes, and the remainder will give the diameter of the cage in inches. This rule is only applicable to flat ropes lying on each other. (1.) Ex-If an engine make twenty-five strokes in drawing a kibble to the top of a shaft 120 fathoms deep, and the thickness of the rope be one inch, what will be the diameter of the the first lift ?— 120 fathoms = 8,640 inches × 1 = And 3 1416 × 1 × 25 = 78 54 8,640 dividend. divisor. cage at 8,64078.54 = 110 - 25 = 85 inches, or 7 feet 1 inch. (2). Ex.-If an engine make 16 strokes in drawing a kibble to the surface from a shaft the depth of which is 80 fathoms, with round ropes not lying on each other, what must be the diameter of a flat rope cage, so constructed that the engine may go the same number of strokes as before, the thickness of the rope being of an inch? 80 fathoms = 5,760 inches. 5,760 × 75 = 4,320 dividend. 3.1416 x 75 x 16 37 699 divisor. = 4,320 37 699 = 114.5. The product of the thickness of the rope and number of strokes is 75 × 16=12, hence 114·5 — 12=102·5 inches, or 8 feet 61⁄2 inches. When flat ropes are employed the kibbles will not meet each other at mid-distance; that which descends will pass through a greater space in the same time than the kibble ascending, owing to the circumference of the coil being always greater until the engine has made half its number of strokes. When the depth of the shaft, the thickness of the rope, and the diameter of the cage are given, to determine where the kibbles will meet, multiply the radius of the cage by the depth of the shaft, and consider this the numerator of the first fraction; then multiply the depth of the shaft by the thickness of the rope, and divide the product by 3.1416, to this quotient add the square of the radius of the cage, and extract the square root of the sum, then add this square root to the radius of the cage, and consider the result the denominator of the first fraction. Multiply the thickness of the rope by the square of the depth of the shaft, and the result is the numerator of the second fraction; then square the denominator of the first fraction, and T |