TORSION is that force with which a thread or wire returns to a state of rest when it has been twirsted'isy being turned round on its axis: the thread or wire, which is suspended vertically, is attached at the upper extremity to some object, and at the lower extremity is a weight with a horizontal Index, or a stirrup, which is to carry a needle or bar in a horizontal position.
Let z r be the wire, w the weight or stirrup, and A s an index or needle, and let Ira e be part of a graduated ring on the same level as the needle; then, on turning the object w round till a mark on the extremity A of the index is brought to any point, b, on the ring, the wire becomes twisted; and when the power by which w is turned is removed, the elasticity of the wire causes the point at A to oscillate within the ring through an arc, as b a c, which continually diminishes till the index rests in its original position.
Under ELASTICITY is given an investigation from which it is proved that, while the force of torsion is moderate, its intensity is directly proportional to the angle or aro through which the extremity A of the index is moved in twisting the wire. It is also proved that r, the time of a complete oscillation, is constant, or that the vibrations arc isochro nous, like those of a pendulum which is acted upon by gravity ; and further, that when a body, as w, is suspended, the squares of the times of vibration vary directly as the momentum of the body's inertia, and inversely as the force of torsion : consequently when the forms and weights of suspended bodies are the same, the force of torsion varies inversely with the square of the time. With respect to the effects which a variation in the length of the wire will cause in the force of torsion, it may be observed that in proportion as the lengths of the wires are increased, points at the lower extremities must be turned, about the axis, through greater arcs, in order to produce equal degrees of torsion at equal distances from the points of suspension ; and hence, if the number of revolutions be equal, the force of torsion will be in versely proportional to the length of the wire : it follows therefore that the time of a vibration varies directly with the square-root of the length of the wire.
These deductions from theory are confirmed by their agreement with the results of the numerous experiments made by M. Coulomb with an apparatus similar to that which is represented above; the times in which a certain number of isochronous vibrations were made with wires of different lengths, and carrying at their lower extremities cylinders of different weights, being observed. By comparisons also of experi ments on wires of the same length and of different diameters conse quently of different weights, Coulomb found that the times of vibration were inversely proportional to the weights, or to the squares of the diameters of the wires; aud since the force of torsion varies inversely with the squares of the times, it follows that when the wires are of the like material and of equal lengths, the force of torsion varies directly with the fourth power of the diameter. M. Poisson, in a memoir on the equilibrium and movement of elastic bodies (` Mdmoires de l'Acaddmie des Sciences,' torn. viii.), has deduced the same law from purely theo retical considerations.
It may bo convenient to compare the force of torsion with that of gravity, and for this purpose it will be necessary to observe merely that the time in which a pendulum, whose length is 1, makes a complete oscillation in a very small tire is expressed by a-