48 MEASUREMENT OF COUPLES. 



CHAPTER III. 

 MEASUREMENT OF COUPLES. 



699. The torsion couple, which tends to bring an apparatus 

 movable about its axis towards its position of equilibrium, might be 

 rigorously determined by the action of an antagonistic couple, such 

 as is obtained by a weight attached to the end of the arm of a lever 

 of known length ; this direct method was used by Wertheim* in 

 studying the elasticity of torsion of metal bars ; but in most cases it 

 would not be applicable, and the value of a torsion couple would 

 most frequently be deduced from the study of oscillation. 



The time T of infinitely small oscillations, when the damping can 

 be neglected, enables us to determine the ratio of the coefficient C 

 (675) to the moment of inertia K of the system, by the formula 



V 700. MOMENTS OF INERTIA. The determination of the moment 

 of inertia K may be made either directly, when the body is homo- 

 geneous, and of geometric shape, from its weight and dimensions, or 

 indirectly by comparison with a body the moment of inertia of which 

 can be directly calculated. 



We shall collate here the principal formula relative to moments of 

 inertia of which we shall have to make use. 



In the C.G.S. System (612), the mass of a body is given directly 

 by the numerical value of its weight / in grammes. When the 

 gramme is taken as unit of force the mass is equal to - , g being the 



> 



acceleration of gravity expressed in centimetres. 

 * WERTHEIM. Ann. de Chim. et de Pkys. [3], Vol. L., p. 195, pt. 385. 1857. 



