234 



Mr. A. Mallock. The Physical [June 6, 



frequencies were noted of the vibrations which the respective elas- 

 ticities produced when acting on a known mass and moment of 

 inertia. 



As might be expected, the values obtained in these two ways do 

 not agree, those given by the dynamical method being in all cases 

 greater than the statical values. 



The volume of elasticity can be deduced from the values of Young's 

 modulus and the simple rigidity by the equation 



__ qn 

 ~~ Sq — 9n 



where k is the volume elasticity, q Young's modulus, and n the simple 

 rigidity. 



But since k for india-rubber is very large, q is very nearly equal 

 to S?i, and the measures of q and n must be very accurate to make this 

 formula of any use. The volume elasticity, therefore, was determined 

 by direct measurement. 



The mean values deduced from all the experiments are given in the 

 table at the end of the paper. The values in this table refer to small 

 strains. 



When the extensions and distortions are large the values of the 

 constants alter enormously, and the results are exhibited better by 

 diagrams than numerically. 



One property possessed by india-rubber, and to which part of the 

 difference between the dynamic and static values of the elasticities is 

 due, is that when strained by a given force, the extension due to the 

 force increases gradually, rapidly at first, and then more and more 

 slowly for many days. The difference between the extension at the 

 first moment after the application of the force and the limit to which 

 the extension tends is proportional to the extension, and the rate 

 at which the extension takes place an exponential function of the 

 time elapsed since the application of the force. 



When the force is removed, the contraction takes place gradually 

 in the same way, but not at the same rate, the constant multiplying 

 the time in the exponent being different in the two cases. On the 

 other hand, if the extension, not the force, is given, the force 

 diminishes according to an exponential law as the time elapsed since 

 the extension increases; and if the extension be quickly reduced, 

 until the force is nothing, and then maintained constant, a contractile 

 force will appear, and increase with the time until it reaches the 

 amount due to difference between the length the moment after reduc- 

 tion and the natural length. 



The material appears, in fact, to take a subpermanent set, which 

 ultimately becomes a definite fraction of the extension to which it is 

 subjected. 



