1314 EUGENE McDERMOTT 
where J is the coefficient of incompressibility, K is the rigidity coefficient, 
and D has the same meaning as in the first equation. 
The foregoing expressions are for longitudinal waves. In longitu- 
dinal waves the vibration of the particles is in the direction of wave prop- 
agation. Transverse waves also are generated in which the particles of 
the medium vibrate at right angles to the direction of travel of the dis- 
turbance. In all that follows, longitudinal waves only are considered. 
The velocity of the transverse wave, however, is determined from the 
following relation: 
ay hs 
D 
where K is the coefficient of rigidity. 
As the speed of propagation depends only on these physical con- 
stants of a medium, the longitudinal wave travels in all directions at the 
same speed in a homogeneous medium. It is obvious that a homogeneous 
medium must be one which has the same physical constants at all points 
and in all directions in the medium. By a non-homogeneous medium is 
meant one in which the physical properties and the velocity of a dis- 
turbance vary in different parts of the medium. The earth is such a 
medium. It is the non-homogeneity of the earth which gives value to 
the science of seismography. Variations in density are slight compared 
with variations in elasticity. Hard limestones occur overlain by rela- 
tively soft shales. The difference in elasticity of these two materials 
makes possible definite refractions and reflections. Hard limestones 
exist in which the velocity is ten times the velocity at the surface. This 
means that the elasticity of such a limestone must be one hundred times 
the elasticity of the surface materials, as there is very little difference in 
density. Even in undifferentiated alluvial sediments the velocity in- 
creases with depth as a result of overburdening. Such a gradual change 
of velocity has no practical value. It is the abrupt changes that are 
valuable. 
Referring again to Figure 2, the simplest example is that of the ray 
directed vertically downward, AB. On reaching B, some of. the energy 
in the wave is reflected vertically upward while the remaining part 
generates a wave in the lower medium which travels vertically downward, 
BC, and, of course, at a greater speed. This is the only example in which 
the direction of the refracted wave is the same as that of the incident 
wave. 
Now consider a ray travelling obliquely downward, as AF. The 
refracted ray is bent as shown at FG so that the ratio of sine a to sine c 
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