On hanging : considered from a mechanical and physiological point of view / by Samuel Haughton.

  • Haughton, Samuel.
Date:
[1866]
Catalogue details

Licence: Public Domain Mark

Credit: On hanging : considered from a mechanical and physiological point of view / by Samuel Haughton. Source: Wellcome Collection.

Provider: This material has been provided by The Royal College of Surgeons of England. The original may be consulted at The Royal College of Surgeons of England.

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    Tj sin Aj = T„ sin a 4- W • • \') Tg sin cc^ = To sin flo -4- W \°) To sin oto = o o T4 sin +W, . . (9) T4 sin a^= Tgsina, +W, . . . (10) TgLinag +W, . . . (11) Tgsin «6= - rVina,|^^ . • • (13) The twelve unknown quantities in these equations, which denote the inclinations and tensions of the first six portions of the rope, may be all expressed as follows, after a few reductions, in terms of X, the horizontal strain on the funicular polygon :— Ti=v/36W^ + X2, tan a, Tg=x/25W+Y^ tan T3=v/l6W2 + X2, tan«3 T4=v/9W2 + X2, tan «4 T5=\/4W2 + X2, tan T6=\/W2 + X2, tanag If flj, ffg, Cg, 04, «5, «g denote the lengths of the six portions of the rope, we obtain, from geometrical considerations, the follow- ing equation:— a, cos aj + ^2 *2 + % 3 + ^4 *4 + '^b 5 4-ff6COS<*6=^o°s^v in which equation the constant depends on the span of the poly- gon from the pillar of tlie hall to the top of the vaulted kitchen. If we were to substitute in equation (14) the values of the cosines of the angles found from (13), it would become an equa- tion ultimately of a high degree, the real root of which would give the solution of the problem sought; but it is not necessary to trouble ourselves with this equation, as we know that the value of X must be real and positive, and by (13) we have Ti= \/(6W)2 + X2. In this equation Tj denotes the pull on the rope that Telema- 6W -T' 5W -XT' 4W 3W W X ■ (13) } . (14)