8 B. B. WEATHERBY AND L. Y. FAUST 
be expected that such sediments would show a different rate of in- 
crease under compaction, since the increase of density tending to 
decrease the velocity might be greatest in uncemented materials. 
The increase of velocity with age appears to be linked with the 
general increase of the lithification of sediments with age. This ap- 
pears especially reasonable in view of the high velocities observed in 
sections of calcareous sand and shales. 
The formula for longitudinal velocity (v) in a solid is given by 
the equation 
v,= —— 
p 
where & is the bulk modulus, the rigidity, and p the density of the 
solid. It is, therefore, apparent that any increase of density of a sec- 
tion with depth would tend to decrease the velocity. Since an increase 
of velocity with depth is observed, it is apparent that the numerator 
of the equation must be increasing more rapidly than the denomina- 
tor. That is, either incompressibility or rigidity or both increase 
with depth more rapidly than the density. Likewise the effect of 
lithification must be to increase the elastic constants at a greater rate 
than the density. 
668 
