INFLUENCE OF TEMPERATURE ON TORSION. 59 



Other things being equal, a wire will be more sensitive the greater 

 the charge it can bear for a given couple that is to say, the smaller 

 the ratio of the coefficients </> and T ; this is the case with silver. 

 This metal has also other qualities which have often led to its use in 

 torsion apparatus. 



712. INFLUENCE OF TEMPERATURE. The coefficient of torsion 

 varies greatly with the temperature. According to Kohlrausch's 

 experiments* on iron, copper, and brass, the elasticity of torsion p 

 at any given temperature, may be represented as a function of its 

 value ft at zero by an expression of the form 



For these metals the values of the coefficients a and /3 are 



ft 



Iron 4-47. io~ 4 5-2. io~ 7 



Copper 5*20. io~ 4 2*8. io~ 7 

 Brass 4*28. io~ 4 i3'4.io~ 7 



As the rise of temperature produces an expansion also, the co- 

 efficient of torsion for the temperature / of a wire of which / and d 

 are the length and diameter at zero, and 8 the coefficient of linear 

 expansion, will be given as a function of the coefficient of torsion C 

 for the temperature of zero, by the formula 



or more simply 



C = C [l-(a- 3 8)/]. 



For copper we have 38 = o*5i.io~ 4 ; the variation arising from 

 the change of elasticity is accordingly ten times as great as that due 

 to expansion. 



713. SILK THREADS. These threads as they proceed from the 

 cocoon are cylindrical ; they present great regularity and are very 

 strong. According to Coulomb's f numbers, a silk thread can 

 support 10 grammes without breaking. Weber J found that at the 



* KOHLRAUSCH. Pogg. Ann. [3], Vol. CXLI., p. 181. 1870. 

 COULOMB. Mem. de V Academie pour 1777. 

 WEBER. Comm. Gottin., vm. Pogg. Ann., Vol. xxxv. and LV. 1834-44. 



