DETERMINATION OF THE COEFFICIENT OF TORSION. 57 



Coulomb's experiments tend to show that the coefficient C is 

 independent of the tension ; but this law is only approximate, and 

 more accurate researches have shown that the elasticity of a wire 

 diminishes as the tension increases, apart from the variation arising 

 from the change of length and of diameter.* 



The oscillations should always be comprised within narrow limits, 

 for permanent deformations are not long in showing themselves. 

 According to Wiedemann,t these deformations would be produced 

 even with the smallest angles, and the vibratory motion of a wire 

 about its axis would really be far more complicated than the simple 

 pendulum motion, the position of equilibrium being displaced at 

 every instant by the oscillations. 



Experiment seems to show, in fact, that the coefficient of rigidity 

 deduced from very small oscillations is greater than that furnished by 

 greater oscillations. To the same cause may be attributed part at 

 least of the differences found between the values of the coefficient 

 found by the method of oscillations and by the statical method of 

 simple torsion ; the latter, which are the smallest, have always been 

 deduced from more considerable torsions. 



A permanent torsion diminishes the rigidity. In one experiment 

 cited by Sir W. Thomson, a permanent torsion of 10 turns in a 

 copper wire 3*5 metres in length and 0.154 cm. in diameter, caused it 

 to lose the one-twentieth of its rigidity; for 100 turns the diminution 

 exceeded a tenth, and it went on increasing until the wire broke. A 

 permanent elongation produces the same effect. 



710. Another curious observation due to Sir W. Thomson is that 

 the rigidity of a wire always diminishes after a long period of oscillations. 

 The fatigue of the wire tends to diminish its elasticity of torsion. 



This influence of fatigue appears still more markedly in another 

 property to which Sir W. Thomson has given the name of viscosity, 

 and which is analogous to molecular friction in liquids. A body 

 cannot change its shape, even if it were absolutely elastic, without 

 an expenditure or dissipation of energy, and to this cause is due the 

 greater part of the gradual damping of the oscillations. Experiment 

 shows that the viscosity increases with the velocity of the oscillations, 

 with the tension and fatigue of the wire ; the time necessary for the 

 oscillations to decrease from 2 to i is, in fact, less as the initial 

 amplitude is greater ; and, all other things being equal, the oscil- 

 lations are more rapidly extinguished with a wire kept for a long time 



* SIR W. THOMSON. Encyc. Brit. Article, Elasticity, Si. 

 t WIEDEMANN. Wiedemann 's Annalen, Vol. VI., p. 485. 1879. 



