Caption: Board of Trustees Minutes - 1886
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242 The ultimate tensile resistance, expressed in pounds per square inch of cross section, may be obtained from the observed averages of fineness or diameters and strains, by formula deduced in the following manner: Assuming, of course, cylindrical form of the fibres, Let S = the average ultimate tensile resistance (strain) in grammes for the specimens or classes tested. Let D = the average diameter of fibre for the specimen or class, in centimillimetres. When the area of cross section of the fibre in square centimillimetres will become Tl p 2 4 In a square millimetre there are 100x100=10,000 square centimillimetres. Hence 1 gramme per square centimillemetre = 10,000 grammes = 10 kilogrammes per square millimetre, and since 1 kilogramme per square millimeter = 1422.30786 pounds per square inch, 1 gramme per square centimillimetre = 14222.0786 pounds per square inch of section of fibre. Applying these values in the above formula, we obtain the expression for the ultimate tensile resistance in pounds per square inch. 4 S + 14223 E = TTD 2 Or s R = 18109 The practical application of this formula is as follows: Take the average results for fineness of strain for the Cots wold breed, 4.196 centimillimetres and 30.44 grammes respectively. Then 18109 + 30.44 = 31272 lbs. (4.196)* The same formula may be applied to any fibre, sample or class of samples for which we have the average diameter and the average ultimate resistance or strain required for rupture. The results of such calculations furnish data upon which to base absolute comparisons of the strength of the fibre in the different classes. The modulus of elasticity, or the ratio of the stretch to the strain required to produce it, is determined in the same way as before. That is, we divide the corresponding average tensile resistance (=18109-^) in pounds per square inch by the percentage of stretch suffered previous to rupture. Then if the resistance be represented by E and the percentage of stretch by P, and the modulus of elasticity by B, the formula becomes E=— p R Applying this formula to the figures for Cots wold wool above obtained we have E= 31272 .3545 =88214.
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