AN INVESTIGATION INTO 
METHODS WHICH MAY BE USED IN THE DETERMINATION OF THE 
ELASTIC CONSTANTS OF MATERIALS. 
The determination of the cubic compressibility of solid substances is, as 
above mentioned, beset with serious difficulties. On the one hand, every 
direct method which has been suggested presents experimental difficulties 
which tend to impair its accuracy, while on the other hand the indirect 
methods are based on assumptions as to the isotropy of the materials, which 
are not warranted in the case of certain rocks. The indirect methods de- 
pending on the theory of elasticity are capable of considerable variation, and 
it is of interest to examine them in some detail in order to see whether certain 
of them at least may not be depended upon to give reliable and satisfactory 
results. 
The determination of the elastic constants of metals has engaged the 
attention of many physicists and at the present time a large amount of infor- 
mation exists as to the values of these constants for various metals. 
It is well known that in homogeneous elastic substances a simple compres- 
sion stress causes a lateral strain, which bears a fixed ratio to the compression 
strain for any particular substance within the limit of elasticity. If, then,* 
we call p x the stress ort a plane perpendicular to x in the direction x, and e x 
the corresponding strain, then for a direct compression stress p x there will 
be a strain in the direction of this stress of amount p x /E, where E is Young's 
modulus, and lateral strain of magnitude p x /mE, where m is the ratio of the 
longitudinal compression to the lateral extension per unit of length. 
If we suppose further that a body is subjected to cubical stress of in- 
tensity p x , we easily see that for small and therefore superposable strains the 
cubical strain e e is 
and since the modulus of cubical compressibility D is the ratio of the stress 
per unit of area to the cubical strain produced, we have 
e c 3 w- 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 
i m E 
2 m + i 
*See E wing's Strength of Materials, Chapters I & II. 
