600 SEISMIC METHODS [Chap. 9 



it is connected to a load. This load may be the seismograph coil or the 

 transformer secondary in the output stage of an amplifier. The counter 

 e.m.f. Ec = HS^, where ^ is the velocity of motion. The current resulting 



H'S 



from it is, for pure D.C. resistances in the circuit, Ic — .5 — r—^,-<P, where 



R -\- R 



R is the resistance of the external circuit and R' the oscillograph resist- 

 ance. Since the torque of a current, I, passing through the loop, is HS/, 



the torque due to the counter e.m.f. is ^ — -^ <p, or de-<p, with de as the 



R -\- R 



electromagnetic damping factor. To this may be added a damping factor 



dm resulting from mechanical damping (oil or the like), and their sum 



de + dm may be combined into a resultant galvanometer damping 



factor dg . Then eq. (9-96a) is Kip + dg<p -\- t<p = H^S/. Dividing by 



K, and letting dg/K = 2ig (the damping constant of the galvanometer) 



and t/K = (jil (the square of the natural frequency of the galvanometer) , 



we get 



^ -{- 2€,.^ + co,V = ^ / . (9-966) 



This may be converted into record amplitudes h by letting h = 2^1), 

 with D as focal length of the lens in front of the oscillograph mirror: 



6 + 2tgh + <4.h = ^^?^ . /. (9-96c) 



For a coil galvanometer the right side of the last equation is multiplied 

 by Ng , the number of turns in the galvanometer coil, so that 



6 + 2e„.6 + c.;.6 = '^^^o'^-^o . /. (9_96d) 



In a string galvanometer a wire or "harp" of wires of the free length I 

 is suspended between pole pieces of the length L in a field of the strength 

 Hg . The natural frequency of a string (fundamental) is given by 



I V as' 



where a is its sectional area, P the tension, and 5 the density. The free 

 oscillation with combined air and electromagnetic damping and with m 

 as mass of the string is then 



h + 2eg-h +«> = 0, 



where h is the deflection corresponding to a current / as viewed under a 

 microscope of the magnification M, so that h = ULIM. Hence, the gal- 



