Adams and Coker — Elastic Constants of Boohs. 97 



and since the modulus of compressibility D is the ratio of the 

 stress per unit of area to the cubical strain produced, we have 



e c 3 m—2 



Hence if we know E and m we can calculate the value of D. 

 Further, it is shown in treatises on elasticity that if C is the 

 modulus of shear, then 



2 i)i + l 



and since C and E are quantities which can be ascertained by 

 experiment, we can from them calculate m and D. 



In an important paper by Nagaoka* this latter method has 

 been used to determine the elastic constants of a series of rocks. 

 The value of E was determined by supporting a bar at the 

 ends and measuring the angular change at the support due to 

 a given load applied at the center ; the value of E is then 

 obtained by the formula E=3ivF/4:bd 3 0, where I is the length 

 of the bar between the supports, b is the breadth of the bar, d 

 the depth and 9 the angular change at the ends for a load W. 

 In order to determine the value of m, a specimen of rectangu- 

 lar section was twisted by a given torque, T, and the amount 

 of the strain measured. It has been shown by St. Tenant that 

 for such a case the value of O is given by the formula 



ri6 S2 2 b' ^ tan A (2n + l) ~ "1 



L~3 tt & -«--* ; ,, j 



o (2n+\Y -J 



T= C6b 5 h I — 



(2n+\y 



where 6 is the angular change, and from this formula values 

 of C were calculated from the observations. 



This method appears to be open to some minor objections in 

 that the formula for determining E is based upon a theory of 

 flexure, which although sufficient for many purposes is never- 

 theless only approximate, and it is well known that values of 

 .ZT obtained by flexure experiments in this manner often differ 

 from the values of E obtained by direct compression experi- 

 ments by not inconsiderable amounts. 



Further, in experiments upon the deflection of beams cut 

 from rocks, it is difficult to obtain consistent readings because 

 of the time effect of the loading, and this difficulty is noticed 

 in the paper cited. 



Experiments on the determination of the elastic constants of 

 rocks when subjected to twist were also found to be fre- 



- Elastic Constants of Eocks and the Velocity of Seismic Waves; H. Nag- 

 aoka.— Phil. Mag., vol. l, 1900, p. 53. 



