52 REPORT OF THE CALIFORNIA EARTHQUAKE COMMISSION. 
the base. As the frequency increases the wave-length, A, decreases, and the surface 
amplitude increases; we have to do with a longer part of the curve in fig. 26. When the 
frequency becomes too large, the surface amplitude begins to decrease, suggesting that 
the sand no longer acts as a solid, but that slipping takes place. The addition of a 
small amount of water to the sand diminishes the cohesion between the grains, which 
reduces the value of the coefficient of rigidity, n, and shortens the wave-length, for a 
given frequency; we therefore get larger surface amplitudes, but slipping occurs at 
lower frequencies than with drier sand. As the sand is probably only able to bear a 
definite shearing force without slipping, an increase in the amplitude of vibration would 
cause the slipping to begin at a lower frequency than with smaller amplitudes. The 
conclusions are in good accord with Mr. Rogers’s results as shown graphically in his 
figs. 62 and 63. 
When, with increasing frequency, the slipping first begins, it must take place only at 
the ends of the strokes where the acceleration, and therefore the force, is greatest; but 
as the frequency gets still higher, the slipping is spread over a greater and greater part of 
the stroke and the surface amplitude becomes less and less; the mathematical theory we 
have sketcht out does not apply after slipping begins. 
So far we have considered the motion as communicated to the sand from the bottom 
of the box and not by the pressure of the sides, which would undoubtedly modify it, but 
the results given by Mr. Rogers are for the sand near the middle of the box where the 
sides have the least influence; and in one experiment where the sand was piled up on 
the bottom of the car without touching the sides, the results were not altered; it appears 
therefore that in the case of sand which is not too wet, and for frequencies not high 
enough to cause slipping, the influence of the sides has not been great enough to alter the 
general character of the motion of the sand in the middle of the box; but near the sides 
their influence causes much confusion in the motion of the sand. 
When the sand is thoroly soaked with water, it becomes very plastic, the elastic forces 
become very small and viscous forces become the predominating forces between the 
successive layers. We therefore determine what is the character of the motion trans- 
mitted from the bottom by means of viscous forces. We find that transverse waves are 
set up which advance to the surface and are there reflected back again. These waves 
have a wave-length dependent upon the density of the material and the viscosity, and are 
very quickly damped out. Indeed, the amplitude of the advancing wave is reduced to 
less than 1/500 of its original value at a distance of one wave-length from the base, and 
the reflected wave starts with a small amplitude and dies out very rapidly. We find that 
the amplitude at the surface is always less than that at the base and that its value is 
twice as great as that of the direct wave at the surface if it were not reflected ; that is, if 
the depth of the sand were one wave-length the amplitude at the surface would be about 
1/250 of the amplitude at the base, instead of about 1/500, as in the case of no reflected 
wave. It is quite evident that waves of this character could not explain the movement 
of the wet sand in the experiment; and we therefore turn our attention to the influence 
the sides of the box would have on the motion of a fluid as viscous as the mixture must 
be. As Mr. Rogers says, the damping is so great that the mixture could not have a free 
period of its own. The experiment described in vol. 1, pp. 328 and 329, and illustrated 
by fig. 61, shows very well the character of the motion, namely, that the surface material 
moves very steadily during the greater part of its excursion with a fairly uniform velocity, 
somewhat greater than that of the base, and that its velocity is rapidly reversed at the 
end of the stroke. This being the case we conclude that there is little force acting upon 
the sand except near the ends of its excursion and that there a strong force acts for a 
short time. It seems probable, therefore, that as the box diminishes in velocity towards 
the end of the stroke the sand, by its inertia, is carried forward and raises the mixture in 
