 | Thomas Leybourn - Mathematics - 1814 - 420 pages
...EF = m, BE = v, EG = x, archBG = z, AF = «. GF = v, arch AG = w, the length of the chain =. /, and the length of a portion of the chain whose weight is equal to the tension at G ~—, a. Then jf-¿ is=thesine,aud X'-^-z~the cosineof the angle BDH, Also Kf-aMja — ' he sine,... | |
 | Isaac Todhunter - Statics - 1853 - 362 pages
...two -smooth pegs at a distance 2a apart in the same horizontal plane. When there is equilibrium, s is the length of the chain between the pegs, which...the length of the end that hangs down vertically. If 8s and 8/t be the small increments of s and h corresponding to a small uniform expansion of the chain,... | |
 | Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...the plane of the curve, be taken for the axis of Y, and let P be any point of the curve. Let a denote the length of a portion of the chain whose weight is equal to the tension atC. Let t denote the length of a portion of the chain whose weight is equal to the tension at P. Let... | |
 | Joseph Wolstenholme - Mathematics - 1867 - 368 pages
...endless heavy chain, of length 21, is passed over a smooth circular cylinder, whose axis is horizontal; c is the length of a portion of the chain, whose weight is equal to the tension at the lowest point, and 2<£ the angle between the radii drawn to the points where the chain leaves the cylinder; prove that... | |
 | Edward Spon, Oliver Byrne, Ernest Spon, Francis N. Spon - Engineering - 1870 - 398 pages
...•81649658 = t' - = 2c V [n] To find a convenient value t being put for • — ; в representing the length of the chain, whose weight is equal to the tension at the lowest point O. We propose to find the value of в under the form j ui u, for u„ assume г = j и„ then [a]... | |
 | Braithwaite Arnett - 1874 - 130 pages
...3.1-0,?--; «-0,y = -. 4. Let 2Z = length of chain, 2a = distance between the fixed points, c = length of chain whose weight is equal to the tension at the lowest point. Then the tension at either point of support is a minimum when it equals the weight of a length —... | |
 | Joseph Wolstenholme - Mathematics - 1878 - 538 pages
...heavy chain of length 21 is passed over a smooth cylinder of revolution whose axis is horizontal ; c is the length of a portion of the chain whose weight is equal to the tension at the lowest point, and 2<j> the angle between the radii drawn to the points where the chain leaves the cylinder : prove that... | |
 | Clement Mackrow - 1879 - 552 pages
...extremity X o of the parameter. The tension at any point P in the curve is equal to the length of a piece of the chain whose weight is equal to the tension at the point, and is thus equal to the ordinate PH. Ijj tin tin its to the Catenary (see fig. 179). x = abscissa.... | |
 | Peter Guthrie Tait - Dynamics - 1895 - 377 pages
...on the right is evidently of [Lr 1 ] dimensions, so that we may write ^=i, or T 0 =wa. 1 0 a Hence a is the length of a portion of the chain whose weight is equal to the constant horizontal component of the tension. The equation now becomes _ dx*~adx~a V Integrating, we... | |
 | George Alexander Gibson - Calculus - 1904 - 252 pages
...y\ at Z> in example 6 are , _ab(ba)W *l~ 3(a+b)EI' 8. Show that a in § 68 is the length of a piece of the chain whose weight is equal to the tension at the lowest point or vertex of the catenary. 9. Show that the tension at any point of the common catenary is equal to... | |
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... c is the length of a portion of the chain whose weight is equal to the tension at the lowest point, and h the length of the end that hangs down vertically. 
