1884.J Stress and Strain on the Properties of Matter. 43 



given of the method of eliminating from the results the effect of the 

 resistance of the air, which with some metals plays a very unimportant 

 part in diminishing the amplitude as compared with the internal fric- 

 tion, but with others, especially under certain conditions, is to be 

 credited with almost the entire loss of energy. 



A mathematical investigation of the loss of energy which would be 

 experienced by a wire vibrating under the influence of torsional elas- 

 ticity, if the internal friction of solids were like that of fluids, proved 

 with reference to the proportionate diminution of amplitude (a) that 

 it should be independent of the amplitude ; (b) that it should vary 

 inversely with the vibration-period. From the experiments it followed 

 that though the condition (a) was satisfied, (&) was not, so that when 

 the moment of inertia of the vibrator was altered without any change 

 of mass, instead of the proportionate diminution of amplitude being 

 in the inverse ratio of the vibration-period, it seemed to be to a con- 

 siderable extent independent of the period. 



"The fatigue of elasticity" (a term first used by Sir William 

 Thomson), according to which a wire which had been kept vibrating 

 for several hours or days through a certain range, came to rest much 

 more quickly when left to itself than when set in vibration after it 

 had been at rest for several days, was next the subject of investiga- 

 tion, and it was found that this elastic fatigue never showed itself 

 when the wire, whatever might be the metal of which it was 

 composed, was vibrated through amplitudes sufficiently within the 

 limits of elasticity, but, on the contrary, repeated oscillation was in 

 this case always attended with diminution of loss of energy, the 

 diminution being subpermanent. No trace of elastic fatigue was 

 discernible in the case of most of the metals examined so long as the 

 vibrations did not exceed in amplitude the limits of the scale, but 

 with nickel it was necessary to confiue the amplitude to 100 scale- 

 divisions, in order to avoid "fatigue of elasticity." 



Moderate permanent extension was found to diminish the loss of 

 energy of a copper wire and to increase that of an iron wire, provided 

 a rest of one day was allowed ; recent permanent extension increased, 

 in both cases the loss of energy. The difference between copper and 

 iron in the above respect is no doubt due to the greater " coercive 

 force " of the latter. Moderate permanent torsion had a much 

 greater effect than permanent extension in increasing the loss of 

 energy of an iron wire. 



An examination of the effect of passing an electric current of from 

 '1 to '3 ampere through a vibrating iron, nickel, or tin wire ended in 

 proving that such a current, though capable of producing sensible 

 circular magnetisation of the first two metals, had no sensible effect 

 on the loss of energy of any of them. 



During the investigation it was thought advisable to make experi- 



