460 SEISMIC METHODS [Chap. 9 



given by Richards/ Poisson's ratio follows from the angle of spread of 

 the asymptotes of the fringe hyperbolas (see Fig. 9-11), o- = tan^ a. The 

 curvatures in the longitudinal and transverse directions may be determined 

 from the fringe patterns, according to the relation 



C = 4Xn/d^ , (9-24a) 



where C is the curvature, X the wave length of the interferometer light, 

 n a given number of the fringe used to calculate C, and dn is the distance 

 apart of the vertices of the nth pair of fringes. The ratio of the curvatures 

 is Poisson's ratio, 



and Young's modulus 



' = §'; (9-246) 



= = 2^. hr^^' (9-2*") 



where h = width, D = couple, and 2h = thickness. 



Torsion tests: For static torsion tests, the specimen is clamped in a hori- 

 zontal position, and a twist is applied to one end in a torsional testing 

 machine. The torsion of two sections with respect to each other is ob- 

 tained by a detrusion meter provided with mirror multiplication. Since 

 the torsion tests furnish the modulus of rigidity, and since Young's modu- 

 lus may be obtained from extension tests, Poisson's ratio and all other 

 desired constants may be calculated. The angle of twist between two sec- 

 tions of a bar separated by the length I is 



^=^, (9-25a) 



JpV 



where D is the rotational couple and Jp the polar moment of inertia. 

 Hence, the modulus of rigidity for a round bar with the radius r is 



1, = 5Z:?.?4pP (9-256) 



(p IT r* 



(with p = radius of gyration, P = force), when the angle <p is expressed 

 in degrees. 



(6) Dynamic laboratory tests. Elastic constants of rocks may be deter- 

 mined from the natural frequencies of their transverse, torsional, and 

 longitudinal vibrations. All these determinations are comparatively 

 simple, since only one parameter, time (or its reciprocal, frequency), is 



^ Loc. cit. 



