142 PROCEEDINGS OF THE AMERICAN ACADEMY. 



?^ = total reluctance of the magnetic circuit (oersteds), 



'Slo = reluctance of circuit exclusive of that of the gaps (oersteds), 



N = total number of turns in the receiver coils, 



I = instantaneous current in the coils assumed to vary sinusoidally, 



or according to the real part of /e^'"' (absamperes), 



/ = normal air-gap between poles and diaphragm (cm.), 



^ = mean flux density in the air gap (gausses), and 



>S = area of one gap (cm^). 



The Equations of Current and Motion. — We can now express 

 the pull on the diaphragm in terms of the flux. It is a well known 

 fact, which may be derived from energy relations, that the pull on the 

 diaphragm is 



/ = J— ^ for a bipolar receiver dynes (12) 



and 



f = 5—5- for a monopolar receiver dynes (13) 



OTTO 



If now fi is used to denote the part of the pull due to the current ?", 

 and if this is small in comparison with the pull due to the perma- 

 nent magnet, we may write 



fi = J. i dynes Z (14) 



which by substitution from equations (12) and (10) becomes 



I = 1 tor a bipolar dynes Z (15) 



and 



mS n 



fi = -~^°i for a monopolar. dynes Z (16) 



In equations (15) and (16) ?5(, has been substituted for 32., since the 

 increment in ^J,, due to i, when multiplied by i, is assumed to be a 

 second order effect. 



In order to avoid carrying through separate discussions for the 



