116 WEATHERBY, BORN, AND HARDING 
cidedly at variance with the velocity determined by the laboratory 
methods. It might reasonably be expected that the velocity in a small 
sample which is under no external pressure should check the velocity 
found for granite near the surface rather than that of the granite at 
some depth. It must be concluded, therefore, that there is a serious 
discrepancy between the two sets of data, which can not be accounted 
for by the experimental errors inherent in either method. The ques- 
tion, therefore, arises whether there is some factor influencing the re- 
sults obtained by the laboratory method which does not affect the 
results obtained in field measurements. -This point has been rather 
carefully investigated, but will be discussed only briefly. 
One decided difference between the velocity measurements made 
in the field and those made in the laboratory is in the frequency used 
in making the measurements. The frequencies recorded in the field 
are approximately 100 cycles per second, while the natural frequencies 
of the rock samples tested in the laboratory are about 7,000 cycles 
per second. The question arises whether there is su‘ficient variation 
of velocity with frequency to account for a difference in the results 
obtained in the two cases. One possible effect which might cause a 
change of velocity with frequency is due to the fact that the attenua- 
tion constant of an elastic solid is a function of the frequency, and 
that the velocity at any frequency is dependent, to some extent, on 
the value of the attenuation constant. 
The effect of attenuation upon the velocity may be disposed of 
very briefly. It may be shown that, if the attenuation in the rock 
sample under test is sufficiently low to permit the sample to oscillate 
vigorously enough to make the laboratory method practicable, then 
the effect of the attenuation upon the velocity will be negligible. 
Another factor which might affect the results is the different ampli- 
tudes used in the two methods. Little information is available con- 
cerning the propagation of disturbances of finite amplitude in solids. 
It is believed, however, that the amplitudes used in both field and 
laboratory measurements are in general small enough so that the 
velocity is independent of the amplitude. The amplitudes in both 
cases are estimated to be of the order 10~* cm. although, in the case 
of field measurements, the amplitude may be considerably larger at 
points near the shot point. A qualitative idea of the magnitude of the 
effect for this order of amplitude can be obtained by making use of the 
formula applicable to the transmission of plane waves of finite ampli- 
tude through gases. These calculations indicate that for the case as- 
sumed, the effect is entirely negligible. Calculation further shows that 
the amplitude would need to be of the order of 1o~* cm. to produce a 
638 
