M. de St.-Venant on the Work or Potential of Torsion. 61 



Melloni strives also to refer the greater radiation of powdered 

 bodies, wherever it occurs, to a difference in density. He holds 

 that the separated surfaces of the small particles are less dense 

 than is the smooth continuous surface of the same metal. This 

 view is scarcely tenable. It will scarcely be asserted that filings 

 are less dense than the rough surface of the metal from which 

 they are obtained ; nor will it be conceded that platinum-black 

 is less dense than spongy platinum, but merely that it is in a 

 state of greater distribution. We shall consequently be com- 

 pelled to assume that in metals the degree of distribution as well 

 as the density exerts an influence on the radiating power. 

 Whatever may be the condition of the metal, however, which 

 gives the greatest radiation, whether it be one of less density or 

 greater distribution of the substance, we are always compelled to 

 admit that the vibrating particles of the body, and the aether 

 which immediately surrounds them, are less able to communicate 

 their motion to the external aether when the surface of the metal 

 is smooth than when this surface is rough, or less dense, or when 

 the substance on the surface is in a condition of greater distri- 

 bution. 



An hypothesis might certainly be found to account for the 

 fact that change of density and distribution alter so greatly the 

 communication of the above motion ; and from such an hypo- 

 thesis a simple connexion could be easily deduced between the 

 radiation, absorption, diathermancy, and thermal conductibility 

 of bodies. 



XL On the Work or Potential of Torsion. New Method of esta- 

 blishing the Equations which regulate the Torsion of Elastic 

 Prisms. By M. de Saint-Venant*. 



THE general expression for the potential of elasticity per unit 

 of volume-element, that is to say, for the molecular work 

 $ which a deformed element of an elastic body is capable of 

 yielding during its detorsion or return to its natural and primi- 

 tive state — in other words, the formula for the external work 

 performed in forcing this element from its natural state to the 

 actually supposed state of deformation or tension — is 



where p xx . . . » denote the six components, parallel to the rect- 

 angular coordinate axes, of the pressures per unit of surface, on 

 three small faces drawn through the centre of the element per- 



* From the Comptes Rendus, November 14, 1864. 



