Mathematics for Practical Men: Being a Common-Place book of Principles ...
Mathematics for Practical Men: Being a Common-Place book of Principles ...
Olinthus Gregory
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When the parameter of the catenary, or the line which measures the tension at the lowest point, is equal to the depres- sion D c ; if each of these be supposed equal to I, then a b » 2*6339, the length of chain a o b = 3*4641 ; the strain at the points of suspension a and b will each be 2, that at th^ lowest point being 1 ; and the chain at a and b will make an angle of 60® with the horizon. 18. If the strain at o be equal to the weight of the chain, and each denoted by 1: then a b = -96242, d ...c == -1180340, Digitized by VjOOQ IC 178 CtTBTES: CATENART. the tension at a or b a 1*118, the angle of suspension at those points nearly 26° 34' ; the width of the curve is 8*1536 times, nnd the length 8*4719 times, the depression d c. \9, If the strain or tension at the lowest poini be double the weight of the chain : then if the parameter be 1, a b will be *49493, c D B '03078, the strain at a or b 1*03078, the angle of suspension about 14° 2*, the width or span 16*0816 times, and the length of chain 16*2462 times the depression.
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