Sensitiveness of the Ear to Pitch. 599 



condensations at corresponding points in the surrounding air 

 will be the same, provided the amplitudes of vibrations at 

 the prongs be themselves in the proportion of the linear 

 dimensions. Corresponding points are, of course, such as 

 are similarly situated with respect to the vibrating forks, the 

 distances from corresponding points of the forks being in 

 proportion to the linear dimensions of the latter. Since 

 times and distances are altered in the same proportion, 

 velocities are unchanged. In conformity with this, the 

 velocity-potentials in the two systems are as the linear 

 dimensions. 



It appears then that by means of the principle of similarity 

 we can obtain aerial condensations which may be recognized 

 to be equal in spite of a change of pitch. As has been said, 

 equality occurs when the amplitudes of the solid vibrators 

 are as the linear dimensions. In virtue of the principle of 

 superposition as applicable to the small vibrations of either 

 system, we are not limited to the case of equal condensations. 

 The ratio of condensations can be inferred from the ratio of 

 amplitudes by introduction of the factor expressing the linear 

 magnification. 



My first intention had been to use forks for the actual 

 experiments. But apart from the difficulty of obtaining 

 them of the necessary geometrical similarity over a sufficient 

 range, it appeared that the communication of vibration to 

 the air was inadequate. At a suitable distance there was 

 danger that the sounds might prove inaudible. In con- 

 nexion with this the difficulty of supporting the forks has 

 to be considered. It is essential that no sound capable of 

 influencing the results shall reach the ear by way of the 

 supports, to which the principle of similarity can hardly be 

 extended ; and the danger of disturbance from this source 

 increases if the direct communication of vibration to the air 

 is too much enfeebled. On the other hand the arrange- 

 ments must, if possible, be such as will render adequate the 

 optically observed amplitude up to the point at which the ear 

 is beginning to fail. We have in fact to steer as best we 

 may between difficulties on opposite sides. 



The requirements of the case seem to be best met by using 

 thin open metal cans vibrating after the manner of bells. 

 They were constructed by Mr. Enock from tin-plate or 

 ferrotype plate and were maintained in vibration electrically. 

 The wall is a simple cylinder and there is a flat bottom of 

 similar material. In the case of the largest/can, giving 85 

 complete vibrations per second, the height was 8 inches and 



