56 MEASUREMENT OF COUPLES. 



angle equal to unity, a cylinder the section of which is equal to unity, 

 and one of the bases fixed. 



Supposing now that a circular cylinder of length /, and diameter d 

 is twisted through an angle ; each of the primitive generating lines 

 becomes a helix. The lower base being fixed, the displacement of a 



point of the upper base, at a distance r from the axis, is equal to r6, 



f\ 



and the corresponding inclinations of the helix to the axis is a = ; 

 the elastic reaction for unit surface is 



F = a< = 0yr, 

 and its moment, in reference to the axis, 



The moment in respect to the axis of the elastic reactions relative 

 to the surface of a circular corona comprised between the radii r and 

 r + dr has the value 



x r . 2irrdr = - r^dr. 



The torsion couple CO is equal to the integral of this expression 

 extended to the entire base of the cylinder ; we have then 



3 2' I 



Comparing this value with that of Coulomb given by equation (2), we 

 deduce 



7T 



P Y*' 



32 



709. DETERMINATION OF THE COEFFICIENT OF TORSION. The 

 application of the methods we have been discussing, to the determi- 

 nation of the torsional coefficient of a wire is not without serious 

 difficulties. ' 



If the wire used is to have a fixed moment of torsion, it must be 

 reheated with the greatest care, so as to deprive it of any trace of 

 previous torsion. If there were any residues of torsion, the zero 

 would become displaced in the course of time, and moreover the 

 elastic reaction would not be the same on either side of the position 

 of equilibrium. 



