KINETIC MEASUREMENT OF THE ELASTICITY OF ROCKS. 13 



smaller and smaller. In the case Avliere the ratio is one-fiftieth 

 or smaller than that, the series of maxima become approximately 

 continuous and practically constitute one maximum with a small 

 gradient, as in the case of soft iron. 



Again, varying the period of the impressed force from m to 

 m', all the lengths corresponding to maximum amplitudes, except 

 that which corresponds to the uatili-al period of the specimen, 

 are changed. When these two facts are taken into account, it is 

 not a difficult matter to determine the natural period of vibration 

 for any specimen at hand. 



Let U and /p be the lengths of string, vibrating with one 

 loop, corresponding to the number of vibrations {71 + '2am) and 

 {7i + 2ßm) respectively, then for a certain length /, which is a 

 common multiple of Ix and l[-i, the string vibrates in a peculiar 

 manner apparently with one loop, nodes of one mode of vibra- 

 tion being over-lapped by loops of another mode and vice 

 versa. 



For example, in the case of sandstone, the result of one 

 experiment with a brass hammer showed that the string might 

 vibrate with a maximum amj)litude corresponding to any one of 

 the number of vibrations 



• 410-0±25'7 u 

 where u is an integer, so that we have 



^1=410-0 



2m = 20-7. 

 Another experiment with a lead hammer, in which the moment 

 of inertia was increased, gave a different result, as follows : — 



7i= 409-3 



2m' =15-3. 



