RESISTANCE OF MATERIALS 61 



In the majority of substances, however, the elasticity is im- 

 perfect ; the return to the initial state is incomplete owing to 

 internal friction, which dissipates a part of the energy (Ela^ichc 

 Nacdwirkung, Weber). Furthermore, the elasticity, even of 

 metals such as platinum or steel, is subject to fatigue and 

 diminishes. Workmen know that the best springs end by being 

 worn out. 



Furthermore, the internal " viscosity " of materials causes a 

 certain retention or accumulation of the effects of repeated stresses 

 and thereby the elasticity of those materials is modified. 



44. Tension and Compression. The simplest of the deforma- 

 tions is that which is produced by a stress F acting in the direction 

 of the axis of a rod of the substance considered, shortening it 

 (compression) or elongating it (tension). It is evident that, for 

 a given stress F, the deformation / will be proportional to the 

 length L of the rod and to a co-efficient a which is a measure of 

 the " souplesse " of the material^ 1 ) that is to say, to the product 

 L X a x F, but it will be smaller in proportion as the section S 

 of the rod is larger : therefore 



LX aX F 



the sign + marks the elongation, the sign the contraction. 

 The lengths /, L are expressed in millimetres, the section S in 

 square millimetres ; the effort F in kilogrammes. Thus the 

 higher the co-efficient of flexibility a, the greater the deformation 

 will be. 



It is convenient, however, to characterise bodies by their 

 resistance to deformation, their rigidity, or their elastic force 



being exactly the reverse of the co-efficient a. Then = E, E 



a 



being the " modulus of elasticity " or "Youngs" modulus. 

 Therefore : 



"Souplesse" and elastic force are often confused, but it will 

 be remembered that indiarubber has a large co-efficient of 

 "souplesse" and inversely a small " modulus of elasticity." 



The relation (1) allows the value of the modulus E to be cal- 

 culated. 



(*) It is a co-efficient analogous to that of the dilatation of bodies by 

 heat. 



