Chap. 9] SEISMIC METHODS 459 



under test and if its deflection is d with the load P concentrated at 

 its end, 



1 Pt 

 d=-—. (9-22a) 



3EJ 



Since the moment of inertia J = a%/l2 for a rectangular section, and 

 J = rV/4 for a circular section, the deflections are: 



d = —3- for a rectangular section, (9-226) 



Ea b 



where h = breadth, a = thickness, and 



4 fP 



d = 5- for a circular section. (9-22c) 



3 ErV 



If the specimen is supported on either end by knife edges, the deflection 



1 P/' 

 d = — — . (9-22d) 



48 EJ 



Hence Young's modulus 



1 fP 

 E = 7 -TT-, for a rectangular section and 

 4 arbd 



1 fP 

 E = v^ -; — 1 for a circular section. 

 12 rVrf 



Deflections may be measured with two mirrors fastened to the ends of 

 the specimen. If the light is reflected from one to the other, the angle is 

 given by eq. (9-20), and Young's modulus 



E = - -— (9-23) 



4 a'6 tan a ' 



Eq. (9-22d) holds for beams supported on knife edges; for fixed ends the 

 factor is yiu instead of ^. 



By the second group of flexure tests, both Young's modulus and Poisson's 

 ratio are obtained. A slab is cut from the rock under investigation, sup- 

 ported on either end by knife edges, and a load is applied on the extreme 

 ends, outward from the supporting knife edges (see Fig. 9-10). Both 

 longitudinal and transverse strains are measured with an interferometer. 

 The top of the rock slab is polished, and a plane-parallel glass plate is laid 

 on top of it. Interference fringes resulting from the bending of the beam 

 are observed or photographed. A diagram of the apparatus has been 



