To Splice a Wire Rope.-The tools required will be a small marline spike, nipping cutters, and either clamps or a small hemp-rope sling with which to wrap around and untwist the rope. If a bench-vise is accessible it will be found convenient. In splicing rope, a certain length is used up in making the splice. An allowance of not less than 16 feet for 1⁄2 inch rope, and proportionately longer for larger sizes, must be added to the length of an endless rope in ordering. Having measured, carefully, the length the rope should be after splicing, and marked the points M and M', Fig. 83, unlay the strands from each end E and E' to M and M' and cut off the centre at M and M', and then: (1). Interlock the six unlaid strands of each end alternately and draw them together so that the points M and M' meet, as in Fig. 84. (2). Unlay a strand from one end, and following the unlay closely, lay into the seam or groove it opens, the strand opposite it belonging to the other end of the rope, until within a length equal to three or four times the length of one lay of the rope, and cut the other strand to about the same length from the point of meeting as at A, Fig. 85. (3). Unlay the adjacent strand in the opposite direction, and following the unlay closely, lay in its place the corresponding opposite strand, cutting the ends as described before at B, Fig. 85. There are now four strands laid in place terminating at A and B, with the eight remaining at M M', as in Fig. 85. It will be well after laying each pair of strands to tie them temporarily at the points A and B. Pursue the same course with the remaining four pairs of opposite strands, stopping each pair about eight or ten turns of the rope short of the preced. ing pair, and cutting the ends as before. We now have all the strands laid in their proper places with their respective ends passing each other, as in Fig. 86. All methods of rope-splicing are identical to this point: their variety consists in the method of tucking the ends. The one given below is the one most generally practiced. Clamp the rope either in a vise at a point to the left of A, Fig. 86, and by a hand-clamp applied near A, open up the rope by untwisting sufficiently to cut the core at 4, and seizing it with the nippers. let an assistant draw it out slowly, you following it closely, crowding the strand in its place until it is all laid in. Cut the core where the strand ends, and push the end back into its place. Remove the clamps and let the rope close together around it. Draw out the core in the opposite direction and lay the other strand in the centre of the rope, in the same manner. Repeat the operation at the five remaining points, and hammer the rope lightly at the points where the ends pass each other at A, A, B, B, etc., with small wooden mallets, and the splice is complete, as shown in Fig. 87. If a clamp and vise are not obtainable, two rope slings and short wooden levers may be used to untwist and open up the rope. A rope spliced as above will be nearly as strong as the original rope and smooth everywhere. After running a few days, the splice, if well made, cannot be found except by close examination. The above instructions have been adopted by the leading rope manufac turers of America. SPRINGS. Definitions. A spiral spring is one which is wound around a fixed point or centre, and continually receding from it like a watch spring. A helical spring is one which is wound around an arbor, and at the same time advancing like the thread of a screw. An elliptical or laminated spring is made of flat bars, plates, or "leaves," of regularly varying lengths, superposed one upon the other. Laminated Steel Springs.-Clark (Rules, Tables and Data) gives the following from his work on Railway Machinery, 1855: A = 1.66L3 8 = bt2n 11.3L n = 1.66 L A = elasticity, or deflection, in sixteenths of an inch per ton of load, b = breadth of plates, in inches, taken as uniform, NOTE.-The span and the elasticity are those due to the spring when weighted. 2 When extra thick back and short plates are used, they must be replaced by an equivalent number of plates of the ruling thickness, prior to the employment of the first two formulæ. This is found by multiplying the number of extra thick plates by the cube of their thickness, and dividing by the cube of the ruling thickness. Conversely, the number of plates of the ruling thickness given by the third formula, required to be deducted and replaced by a given number of extra thick plates, are found by the same calculation. 3. It is assumed that the plates are similarly and regularly formed, and that they are of uniform breadth, and but slightly taper at the ends. Reuleaux's Constructor gives for semi-elliptic springs: P= Snbh2 S = max. direct fibre-strain in plate; n = number of plates in spring; = one half length of spring; P = load on one end of spring; 6Pl and f= Enbh3* The above formula for deflection can be relied upon where all the plates of the spring are regularly shortened; but in semi-elliptic springs, as used, there are generally several plates extending the full length of the spring, and the proportion of these long plates to the whole number is usually about In order to compare the formulæ of Reuleaux and Clark we may make the following substitutions in the latter: s in tons = P in lbs. ÷ 1120; ▲ S = 16f; L = 2; t = 16h; then 1.66 X 81 X P As = 16ƒ= 4096 x 1120 × nbh39 whence f= Pls 5,527,133' which corresponds with Reuleaux's formula for deflection if in the latter we take E which corresponds with Reuleaux's formula for working load when Sin the latter is taken at 76,120. The value of E is usually taken at 30,000,000 and Sat 80,000, in which case Reuleaux's formulæ become Helical Steel Springs.-Clark quotes the following from the report on Safety Valves (Trans. Inst. Engrs. and Shipbuilders in Scotland, 1874-5): E compression or extension of one coil in inches, d = diameter from centre to centre of steel bar constituting the spring, in inches, w= weight applied, in pounds, D= diameter, or side of the square, of the steel bar, in sixteenths of an inch, Ca constant, which may be taken as 22 for round steel and 30 for square steel. NOTE. The deflection E for one coil is to be multiplied by the number of free coils, to obtain the total deflection for a given spring. The relation between the safe load, size of steel, and diameter of coil, may be taken for practical purposes as follows: Rankine's Machinery and Millwork, p. 390, gives the following: In which d is the diameter of wire in inches; c a co-efficient of transverse elasticity of wire, say 10,500,000 to 12,000,000 for charcoal iron wire and steel; r radius to centre of wire in coil; n effective number of coils; ƒ greatest safe shearing stress, say 30,000; W any load not exceeding greatest safe load; v corresponding extension or compression; W, greatest safe load; and vi greatest safe steady extension or compression. If the wire is square, of the dimensions d x d, the load for a given deflection is greater than for a round wire of the diameter d in the ratio of 2.81 to 1.96 or of 1.43 to 1, or of 10 to 7, nearly. Wilson Hartnell (Proc. Inst. M. E., 1882, p. 426), says: The size of a spiral spring may be calculated from the formula on page 304 of "Rankine's Useful Rules and Tables"; but the experience with Salter's springs has shown that the safe limit of stress is more than twice as great as there given, namely 60,000 to 70,000 lbs. per square inch of section with 3% inch wire, and about 50,000 with 1 inch wire. Hence the work that can be done by springs of wire is four or five times as great as Rankine allows. For 3 inch wire and under, 12,000 × (diam. of wire)3. Weight in lbs. to deflect spring 1 in. = Number of coils X (rad.) The work in foot-pounds that can be stored up in a spiral spring would lift it above 50 ft. In a few rough experiments made with Salter's springs the coefficient of rigidity was noticed to be 12,600,000 to 13,700,000 with 1/4 inch wire; 11,000,000 for 11/32 inch; and 10,600,000 to 10,900,000 for 3 inch wire. Helical Springs.-J. Begtrup, in the American Machinist of Aug. 18, 1892, gives formulas for the deflection and carrying capacity of helical springs of round and square steel, as follow: W= carrying capacity in pounds, S= greatest tensile stress per square inch of material, d = diameter of steel, D= outside diameter of coil, F= deflection of one coil, E torsional modulus of elasticity, P= load in pounds. From these formulas the following table has been calculated by Mr. Begtrup. A spring being made of an elastic material, and of such shape as to allow a great amount of deflection, will not be affected by sudden shocks or blows to the same extent as a rigid body, and a factor of safety very much less than for rigid constructions may be used. HOW TO USE THE TABLE. When designing a spring for continuous work, as a car spring, use a greater factor of safety than in the table; for intermittent working, as in a steam-engine governor or safety valve, use figures given in table; for square steel multiply line W by 1.2 and line F by .59. Example 1.-How much will a spring of " round steel and 3" outside diameter carry with safety? In the line headed D we find 3, and right underneath 473, which is the weight it will carry with safety. How many coils must this spring have so as to deflect 8" with a load of 400 pounds? Assuming a modulus of elasticity of 12 millions we find in the centre line headed F the figure .0610; this is deflection of one coil for a load of 100 pounds; therefore .061 x 4 = .244" is deflection of one coil for 400 pounds load, and 3 + .244 = 12 is the number of coils wanted. This spring will therefore be 434" long when closed, counting working coils only, and stretch to 734". Example 2.-A spring 34" outside diameter of 7/16" steel is wound close; how much can it be extended without exceeding the limit of safety? We find maximum safe load for this spring to be 702 pounds, and deflection of one coil for 100 pounds load .0405 inches; therefore 7.02 x .0405.284" is the greatest admissible opening between coils. We may thus, without knowing the load, ascertain whether a spring is overloaded or not. Carrying Capacity and Deflection of Helical Springs of Round Steel. d = diameter of steel. D= outside diameter of coil. W = safe working load in pounds-tensile stress not exceeding 60,000 pounds per square inch. F= deflection by a load of 100 pounds of one coil, and a modulus of elasticity of 10, 12 and 14 millions respectively. The ultimate carrying capacity will be about twice the safe load. 1.75 2.00 3.8 3.3 20.85 31.57 17.87 27.06 .50 .75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 17 3.107 4.334 Carrying Capacity and Deflection of Helical Spring Round Steel.-(Continued). D 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.7 605 500 426 371 329 295 267 245 226 209 .0136 .0242 .0392 .0593 .0854 .1187 .1583 .2066.2640 .3313 .0117 .0207 .0336 .0508 .0732 .1012 .1357 .1771.2263.2839 .0097 .0173 .0280 .0424 .0610 .0853 .1131 .1476.1886.2366 D 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 5.00 W 2163 1916 1720 1560 1427 1315 1220 1137 1065 945 .0056 .0081 .0112 .0151 .0197 .0252 .0316 .0390.0474.0679 .0048 .0070 .0096 .0129 .0169 .0216 .0271.0334.0406.0582.0 .0040 .0058 .0080 .0108 .0141 .0180 .0225 .0278.0339.0485.0 Ꭰ 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 5.00 5 W 3068 2707 2422 2191 2001 1841 1701 1587 1484 1315 1 .0034 .0049 .0068 .0092 .0121 .0155 .0196 .0243.0297.0427.0 .0029 .0042 .0058 .0079 .0104 .0133 .0168 .0208.0254.0366.0 .0024 .0035 .0049 .0066 .0086 .0111 .0140 .0173.0212.0305.0 D 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 5.50 6 2988 2723 2500 2311 2151 2009 1885 1776 1591 14 .0043 .0058 .0077 .0100 .0127 .0157 .0193 .0233.0279.0388.05 .0037 .0050 .0066 .0086 .0108 .0135 .0165 .0200.0239.0333.04 .0030 .0042 .0055 .0071 .0090 .0112 .0138 .0167.0199.0277.03 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 5.50 6. W 4418 3976 3615 3313 3058 2840 2651 2485 2339 2093 18 .0028 .0038 .0051 .0066 .0084 .0105 .0129 .0157 .0189 .0264.03 .0024 0033 .0044 .0057 .0072 .0090 .0111 .0135 .0162.0226.03 .0020 .0027 .0036 .0047 .0060 .0075 .0093 .0113.0135 .0188.02 5.25 5.50 6.00 6.5 3607 3413 3080 280 .0097.0115.0156.020 .0083.0098.0134 .017 .0069.0082.0112.014 The formulæ for deflection or compression given by Clark, Hartneli, and Begtrup, although very different in form, show a substantial agreement when reduced to the same form. Let d = diameter of wire in inches, D1 = mean diameter of coil, n the number of coils, w the applied weight in pounds, and Ca coefficient, then |