12 ART. 10.— S. KUSAKABE. 



should be proportionally many-valued. In the case of sandstone 

 No. 84, e.g. we have, 



I = 13-48 15-33 16-36 17-20 19-25 21-68 24-67 28-72 34-82 42-89 

 whence V 00 12-9 11-3 10-6 lO'l 9-0 8-0 7.0 6-0 5-0 4-0 



In Professor F. Omori's papers relating to seismometory we fre- 

 quently find what correspond to the above, calculated as the 

 velocities of seismic waves in their successive phases. 



Repeated experiments, however, showed that this confusion 

 was an effect of the tapping by the hammer, so that varying the 

 period of the impressed force we might obtain another series of 

 maximum values. Although the vibration is really of a free 

 nature, it is rendered intermittent by the periodic interposition 

 of an obstacle, so that a very dillerent result is arrived at. In 

 this case, a vibration of a frequency n varies in its amplitude 

 with a frequency m, which last is the frequency of the hammer. 

 The amplitude increases very suddenly and it is always positive 

 so that the motion may be assumed, though by a very rough 

 approximation, to be represented by the expression, 



•j=a 



Y=Ao cos 27r 7it+ 1' Av [cos 2;: {n+2o m) + cos 2;r (n~2u m)]. 



It is obvious that, in such a case as the above, the amplitude 

 takes its maximum value when the length of the strings corresponds 

 to any oiie of the numerous component vibrations. The relative 

 magnitudes of the several maximum amplitudes differ very much 

 from one another and in such a way that the greatest maximum 

 corresponds to the vibration in the natural period of the specimen, 

 and the smaller the amplitude the more it is affected by the 

 impressed force. 



When m is not too small to be compared with n, each 

 maximum may be distinctly observed ; but their consécutives 

 more and more approach each other as the ratio m/n becomes 



