THE CARBON MICROPHONE 187 



becomes greater than and N less than its Hmiting value. The limiting 

 value of N" is greater than that which would be obtained through the 

 contact of hemispherical surfaces and represents a more rapid stiffening 

 of the contact with compression. 



We will first give our attention to the limiting value of N". 



A consideration of the nature of contact surfaces as revealed by the 

 microscope furnished the clue to the interpretation of our results. 

 A typical surface is shown in the photomicrograph (Fig. 23). Evi- 



Fig. 23 — Photomicrograph of the surface of a carbon granule (X 240U). 



dently it is very hilly, the hills being much the same size and height. 

 The magnification (X 2400) is such that the small white circle has a 

 diameter of 8 X 10~^ cm. and it is clear that the circle encloses several 

 hills. 



From the theory of elasticity we may deduce that if two hemi- 

 spherical hills of carbon having a radius of the order 1 X 10~^ cm. are 

 brought together with forces of the order of 1 dyne the maximum 

 stresses will probably not exceed the elastic limit of carbon and hence 

 that the hills will deform elastically. The motion involved in such a 

 deformation will be of the order of 1 X 10~® cm. and if other hills are 

 encountered, as is most probable with such a movement, the stresses 

 will be shared and hence the stress per hill reduced. According to 

 this view forces larger than one dyne can be applied without exceeding 

 the elastic limit merely by virtue of the distribution of the hills which 

 will come in to share the stresses. Furthermore, such a contact will 



