ON PASSIVE STRENGTH AND FRICTION, 141 



be extended, and, in order to preserve the equilibrium, the internal ones would 

 be contracted ; and it may be shown that the whole wire would be shortened 

 one fourth as much as the external fibres would be extended if the length re- 

 mained undiminished; and that the force would vary as the cube of the angle 

 through which the wire is twisted. But the force of torsion, as it is de- 

 termined by experiment, varies simply as the angle of torsion; it cannot, 

 therefore, be explained by the action of longitudinal fibres only; but it ap- 

 pears rather to depend principally, if not intirely, on the rigidity, or lateral 

 adhesion, which resists the detrusion of the particles. If a wire be twice as 

 thick as another of the same length, it will require sixteen times as much force 

 to twist it once round; the stiffness varying as the fourth power of the dia- 

 meter, that is, as the square of its square. But if the length vary, it is 

 obvious that the resistance to the force of torsion will be inversely as the 

 length. 



A permanent alteration of form is most perceptible in such substances as 

 are most destitute of rigidity, and approach most to the nature of fluids. It 

 limits the strength , of materials with regard to practical purposes, al- 

 most as much as fracture, since in general the force which is capable of 

 producing this effect, is sufficient, with a small addition, to increase it till 

 fracture takes place. A smaller force than that which has first produced an 

 alteration of form, is seldom capable either of increasing, or of removing it, 

 a circumstance which gives such materials, as are susceptible of an alteration 

 of this kind, a great advantage for many purposes of convenience and of art. 

 The more capable a body is of a permanent alteration of form, the more 

 ductile it is said to be; pure gold and silvei', lead, annealed iron and copper, 

 wax Avhen warm, glass when red hot, and clay when moist, possess consider- 

 able ductility. Wood admits of little permanent change of form, except in 

 a green state, although it sometimes settles a little, when it has been exposed 

 to pressure. Even stone will become permanently bent in the course 

 of years, as we may observe in old marble chimney pieces. But the most 

 ductile of all solid substances appears to be a spider's web. Mr. Bennet 

 twisted a thread of this kind many thousand times, and shortened it more 

 than a fourth of its length, yet it showed no disposition to untwist. 



A ductile substance acquires the same cohesive and repulsive powers with 



