32 KENNELLY AND KUROKAWA. 



the quiescent pressure intensity in the medium. The last equation 

 corresponds to the well known equation of differential increase in 

 alternating current dl, over an element of conductor length dl; namely 



dl = - E(jcco) a/ = - E (j"j dl rms. amperes Z (39) 



where c is the linear capacitance of the conductor in farads per km., 

 and s is its reciprocal. In this case, the linear leak-ance g of the con- 

 ductor is ignored. 



Since the complete electric conductor equations for (31) and (39), 

 including r and g, are 



dE = - J(r+j\!c^)dl = -Jzdl rms. volts Z (40) 



and 



dl = — E (g -\- j j dJ = — VjI/ dl rms. amperes Z (41) 



we may reasonably assume that the corresponding equations for the 

 acoustic conductor, including frictional resistance along the tube and 

 losses due to imperfect elasticity are, from (30) and (38) 



^F = — .('(r -\- jmoj) d\ = — i z ^1 rms. dynes Z (42) 



and 



d.v = -F lg-\-j ]d\= - Fy dl rms. kines Z (43) 



In electric conductors, the linear dissipation constants r and g are 

 accepted as constant at any single impressed frequency, whatever 

 values may pertain to E and 1; !>ut they are known to change when 

 the impressed frequency is varied oAer a wide range. Similarly, in 

 acoustic tubes, the linear dissipation constants r and g are perhaps 

 constant at any single frequency, although they may xavy when the 

 frequency is Aaried. Numerous measurements will ha\'e to be col- 

 lected before the acoustic dissipation constants of a tube can be de- 

 termined with precision. 



The known ecjuations of electric propagation along uniform lines 

 are applicable, following the above theory, to acoustic propagation 

 along uniform tubes, when hydrostatic difference of pressure F is sub- 

 stituted for electric difference of pressure E, vibratory displacement 

 .T for alternating ciuantity q, vibratory velocity .v for alternating cur- 

 rent I, linear mass m for linear inductance V*, linear frictional resist- 

 ance r for linear electric resistance r, linear acoustic elasticity loss g 



