Chap. 9] 



SEISMIC METHODS 



595 



If the detector is coupled directly to a galvanometer; if the total im- 

 pedance of detector, external circuit, and galvanometer is Z; and if U = 

 — HJ/Z is a galvanometer transmission constant; the peak value of the 

 current is 



/« = 



Vicl - o^'f + 46^ 



2 2 



CO 



(9-92c) 



Wmrt 



'^ 



N 



M 



An electromagnetic seismograph equipped with a coil transducer is known 

 as an inductive detector. If the coil is replaced by an iron armature 

 separated by an air gap from a magnet provided with coils (telephone 

 receiver), the seismograph becomes a reluctance detector or, more specifi- 

 cally, an unbalanced reluctance detector. A station seismometer of this 

 kind has been developed by Benioff." A more advantageous design is 

 afforded by a balanced reluctance detector which is so arranged that the 

 pull of a magnet on two armatures, or the pull of two magnets on one 

 armature, is balanced. The Baldwin telephone receiver, most phono- 

 graph pickups, and the seismic detectors shown 

 in Figs. 9-11 5a and 9-1156 are examples of bal- 

 anced receivers. 



Although fundamentally the theory of these 

 receivers is the same as that of the inductive 

 detector as far as voltage output in proportion 

 to the velocity of ground motion is concerned, 

 a modification is introduced because of the de- 

 pendence of the natural frequency on the mag- 

 netic field. The force of attraction of the 

 magnet on the armature F' opposes the elastic- 

 restoring force F = zd {z = spring constant, 

 d = deflection). The magnetic force is a func- 

 tion of the field in the air gaps; the field, in 

 turn, is equal to magnetomotive force over reluc- 

 tance. If, in the schematic reluctance detector 

 shown in Fig. 9-103, M is the m.m.f. of each 

 magnet, the upper field for two gaps in series 

 is Hi = M/2(a — d) and the lower H2 = 



M/2(a 4- d), where a is the normal gap and d the displacement from its 

 position. If S is the section of the magnet, the force 



_5. 



M 



.N. 



\mlMT 



T 



Fig. 9-103. Scheme of 

 balanced reluctance de- 

 tector. 



F' = 



H^'S 



= ^ (H? - H,^) = 



SM'.ad 



(9-93a) 



Stt 47r "'■' 47r(a2 - d^Y 



Neglecting in the denominator d against a , the force F' = SM d/Ava . 

 Since, in the position of equilibrium, cd — F' = 0, we have 



" Loc. cit. 



