462 SEISMIC METHODS [Chap. 9 



moment of inertia (^irr* for a round bar). Hence, the modulus of rigidity 

 for a round bar 



V = 87r^^,. (9-27) 



For a round disk attached as a revolving mass, the moment of inertia is 

 K = ^p^m (p = disk radius). 



The torsional frequency of a specimen and thus the modulus of rigidity 

 may also be determined by a resonance method analogous to the one 

 described in the next paragraph. In a drill core, a saw cut is made on one 

 end and a strip of iron is fastened rigidly in it. This strip is placed 

 between the poles of two electromagnets. An identical arrangement is 

 pro\'ided at the other end of the specimen. The electromagnets on one 

 side are excited by a variable-frequency oscillator, while those on the other 

 side are connected to an amplifier and rectifier meter. 



The torque produced on one end is transmitted to the other. Its ampli- 

 tude is greatest when the natural torsional frequenc}'^ of the specimen 

 coincides with the driving frequency. A bar clamped at its center has a 

 node at that point so that its length I is one-half the wave length. Since 

 the torsional wave velocity is \/v/6 and is equal to the product of wave 

 length and frequency, 



/o = i /l/?, (9-28) 



where /o represents natural frequency, I length, and y the rigidity modulus 

 as before. 



Longitudinal vibrations: The specimen, preferably in the form of a rod 

 or drill core, is arranged horizontally, clamped at its center, and excited 

 to oscillate horizontally. This may be done by attaching a piece of iron 

 to one of the faces and by exciting this end with an iron-core solenoid 

 supplied with current of variable frequency. A better arrangement is to 

 attach a light coil to each side of the specimen, each coil being suspended 

 in the field of a d3Tiamic speaker (Fig. 9-14). One coil is supplied with 

 current of variable frequency and thus drives the specimen. In the other 

 coil, currents are induced which depend on the frequency and amplitude 

 of motion of the other end. Resonance is again determined by maximum 

 amplitude.* 



Another way of setting the specimen into oscillation is by electrostatic 

 coupling. Fig. 9-15 shows an arrangement proposed by Ide** for such ob- 



8 J. M. Ide, Geophysics, 1(3), 349 (Oct., 1936). 



9 B. B. Weatherby and L. Y. Faust, A.A.P.G. Bull., 19(1), 12 (Jan., 1935). 



»° J. M. Ide, Proc. Nat. Acad. Sci., 28, 81, 482 (1936) ; Rev. Sci. Instr., 6, 296-298 

 (Oct., 1936); Jour. Geol., 46, 689-716 (Oct., 1937). 



