VELOCITY IN GRANITE AND LIMESTONE II5 
Where V zz is the longitudinal bulk velocity 
Vie is the longitudinal rod velocity 
g _ is Poisson’s ratio. 
By using the value of Poisson’s ratio obtained in the field meas. 
urements, namely, 0.36, the bulk velocities for the two samples were 
calculated to be 17,380 feet per second and 17,900 feet per second, 
respectively, the average being 17,640 feet per second. 
SOURCES OF ERROR 
The most important error in determining the longitudinal velocity 
in the rods used was in the determination of the recorded beat fre- 
quency. The oscillator calibration was known to one part in 5,000 
so that calibration errors were negligible. The lengths of the rod 
samples were easily measured with sufficient accuracy so that any 
error thus introduced could also be neglected. 
The equation relating the natural frequency of the rod to its length 
and the velocity of sound in the material is strictly accurate only if 
the length of the sample be very large compared with its lateral ‘di- 
mensions. In the case of relatively short rods, a correction must be 
applied to the experimentally determined value of natural frequency. 
The expression for this correction has been derived by Lord Rayleigh.® 
This correction was calculated for the particular samples used and 
was found to be considerably less than the experimental errors and 
so was neglected altogether. 
The total error in the determination of the rod velocity of any 
particular sample was less than 1 per cent. 
The temperature coefficient of frequency of the rock samples was 
not determined. The measurements were made at a temperature of 
ae (Co 
COMPARISON OF FIELD AND LABORATORY DATA 
The average bulk velocity for the longitudinal wave calculated 
from the laboratory data, namely, 17,640 feet per second, corresponds 
with the value of 17,950 feet per second observed over the long profile 
used in the field work and corresponds reasonably well with the value 
of 17,150 feet per second obtained for the 300 to 400-foot interval of 
the shot profile. To this extent, at least, the laboratory and field de- 
terminations may be said to agree. The values of Young’s modulus 
obtained by the two methods do not, however, show any such agree- 
ment. Furthermore, the velocity of 14,880 feet per second charac- 
teristic of the 100-to-200-foot interval of the short field profile is de- 
6 Lord Rayleigh, Theory of Sound, Vol. 1, p. 251. 
637 
