CONSTANTS OF ROCKS- 7 
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 deter- 
mined 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= T>wl A / ^bd *6, where / is the length of the bar 
between the supports, b is the breadth of the bar, d the depth, and 6 the 
angular change at the ends for a load, W ' . In order to determine the value 
of m, a specimen of rectangular section was twisted by a given torque, T, 
and the amount of the strain measured. It has been shown by St. Venant 
that for such a case the value of C is given by the formula 
tanh(2n+ i)~ 
(2U + l) 5 
where is the angular change, and from this formula values of C were calculated 
from the observations. 
This method appears to us 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 nevertheless only approximate, and 
it is well known that values of E obtained by flexure experiments in this 
manner often differ from the values of E obtained by direct compression 
experiments 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 load- 
ing, and this difficulty is noticed in the paper cited. 
As an example of the results obtained in this way, we may quote the 
results of certain experiments made by us with a pure white marble from 
Vermont. 
Lath-shaped pieces of the marble were carefully prepared and were sus- 
pended on two wedge-shaped supports and then loaded in the middle. The 
weights were placed in a light brass pan, hanging from a thick wire which 
passed over the middle of the lath and lay flat upon it. 
Each experiment occupied about half an hour, and the deflection was 
measured by attaching a scale to the marble and reading it with reference 
to a thin wire stretched in front of the specimen, a properly mounted tele- 
scope being employed for this purpose. The marble was in all cases placed 
so that its broader surface rested on the terminal supports. 
*Elastic Constants of Rocks and the Velocity of Seismic Waves. H. Nagaoka. Phil. 
Mag., Vol. L, 1900, p. 53. 
