PIERCE. — THEORY OF COUPLED CIRCUITS. 321 



because of the larger development of heat in the- rest of the Circuit IV. 

 Since the resonance is sharper with the low-resistance circuit, the re- 

 sistance of a thermal detector, provided its indications are proportional 

 merely to the heat developed in it, ought to be as low as is consistent 

 with the localization of a large part of the energy in the detector ; that 

 is, for example, in order to get 9/10 of the maximum effect, the re- 

 sistance of the detector, if its indications are proportional merely to the 

 heat developed in it, ought to be nine times the high-frequency resist- 

 ance of the rest of Circuit IV. 



Similar considerations apply to a detector of the electrodynamometer 

 type. If the deflections of the electrodynamometer are proportional to 

 n^ Y\ where n is the number of turns of wire in the coil, and if the size 

 of the channel of windings is fixed so that the resistance M of the de- 

 tector is ^, I and S being the length and cross section of the wire in 

 the coil, then we have 



I = 2'n-r-n, 



in which r is the mean radius of the windings ; and approximately 



n 

 A being the area of the channel. 



Therefore, B = - — ^ — > 



or B "^ n^. 



Whence if the deflection, 



D'^ RY\ 



In this, R is the resistance of the detector alone. Now according to 

 equation (23) the quantity of Ri Y^ is not changed by changing R^. 

 Hence if the resistance R is made nine times the resistance of the rest 

 of Circuit IV, the deflection of the high-frequency dynamometer will be 

 9/10 as large as would be obtained with a detector of very high resist- 

 ance, and the resonance with the low resistance detector will be much 

 sharper than with the detector of very high resistance. 



However, it must be borne in mind that this conclusion holds only 

 between different detectors of the same type, and presupposes that the 

 factor by which R Y^ is to be multiplied to get the deflection or other 



VOL. XLVI. — 21 



