ON PASSIVE STRENGTH AND FRICTION. 109 



only remaining in their natural state. We might consider a wire as com- 

 posed of a great number of minute threads, extending through its length, 

 and closely connected together ; if we twisted such a wire, the external 

 threads would 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 remained 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 determined by experiment, varies simply 

 as the angle of torsion ; it cannot, therefore, be explained by the action of 

 longitudinal fibres only ; but it appears rather to depend principally, if 

 not entirely, 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 diameter, 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, 

 almost 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 alter- 

 ation 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 silver, lead, annealed iron and 

 copper, wax when warm, glass when red hot, and clay when moist, possess 

 considerable 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 regard to its new form, as it possessed in its original state ; and when 

 the alteration of form has once commenced, those powers are neither in- 

 creased nor diminished by continuing the operation ; the degree of flexure 

 or torsion required for producing a further alteration, appears also to be 

 little varied : thus if the spider's web could at first be twisted only one half 

 round, so as to retain the power of returning to its original state, without 

 a,ny permanent alteration of form, it would never acquire the power of 

 returning more than half a revolution, however it might be twisted. From 



* Experiments on a New Suspension of the Magnetic Needle, Ph. Tr. 1792, 

 Ixxxii. 82. 



