OF ARTS AND SCIENCES. 



235 



R meaning resistance, P pressure, and a and (3 constants. But 

 C meaning current, and y a constant ; therefore 



Suppose the sound waves due to the pipe to cause a varying pres- 

 sure on the contact, whose extreme values are ±8. The extreme 

 values of the resulting current will be, in each vibration, 



y(^ + *) and y(P-*) 



*(** +*) + ?' a{P — 6)+0' 



The difference between them will be proportional to the secondary 

 current /. The secondary current depends on the rate of change in 

 the primary. This relation may be expressed by the equation 



J=e 



p + s 



P — 8 



2/3S0 



(1) 



|_a(P + d)+0 a (P — 8)+p\ a\P* — S 2 ) + 2 a P + /** 



If P is less than 8, it is evident that the electrodes will break con- 

 tact, a minus pressure being impossible. In this case the current at 

 one extreme will be instead of 



y(P-S) 



a(P-8)+P> 



and the secondary current /will be 



e(P + 8) 



(2) 



a(P+d)+/3' 



"When P= 8, these two values for / are identical. The curve 

 obtained by following (2) up to the point P = 8, and (1) after that, 

 is similar to the accompanying sketch (Figure 4). 



Fig. 4. 



