48 REPORT OF THE CALIFORNIA EARTHQUAKE COMMISSION. 
expansion of about 1: 30,000; if we assume that the weight of the overlying rock would 
make the vertical expansion practically disappear at the depth of a mile; and if we assume 
further that the average expansion above this point is one-third of its value at the 
surface, we should find a vertical amplitude at the surface of 0.66 inch, or a range from 
crest of trough of the waves of 1.33 inches. : 
Referring again to the expression for the ratio of the vertical expansion to the horizontal 
compression we see that its value will become greater as n becomes smaller, with unity for 
its greatest possible value. When the waves pass from rock into alluvium or distinte- 
grated rock, the amplitude may become distinctly larger, and since the value of n would 
be much less than for granite, we should expect far larger surface waves. The movement 
at the surface will be upwards, forwards, downwards, and backwards in the vertical plane, 
just like the movement in ordinary water waves. Waves of this kind must necessarily 
occur wherever we have longitudinal vibrations, at a great distance from the focus 
as well as near it, but it is only where the amplitude of the vibration is very large that 
the. surface waves are visible to the eye; and it is, therefore, only near the focus, and 
generally only on alluvium that they are observed, and only in the case of very violent 
earthquakes. These waves must not be confused with the Rayleigh waves, in which the 
horizontal component of the vibration dies out at a depth of about one-eighth wave- 
length, and the vertical component continues to indefinite depths; whereas the waves we 
have just described have exactly the opposite characteristic; they are simply the surface 
modification of the ordinary longitudinal waves, which exist below the surface. 
It is also possible that surface waves could be formed by transverse vibrations, in 
which the direction of motion is vertical. 
Major Dutton * thinks that the surface waves have no relation to the elasticity of the 
rock. Hesays: “Their lengths are too small, their amplitudes too great, and their speeds 
of propagation too slow to be dependent upon elasticity”; but if we refer to the modulus 
of elasticity which holds near the surface, and upon the square root of which the velocity 
of transmission depends, we see that its value becomes very small as the value of n diminishes 
and therefore in some alluvium it is quite possible to have slow speeds and short wave- 
lengths, and, as we have seen, large amplitudes. It is not necessary to believe that the 
amplitudes of surface waves are nearly as large as they appear, for it must be remem- 
bered that an observer being shaken by the strong vibrations of a violent earthquake 
is in a difficult position to make good observations on the phenomena about him, and 
particularly to distinguish between the movements which are actually taking place and 
those which he apparently sees, but which are really due to his own oscillations. We 
have many descriptions of trees and telegraph poles being swayed so violently as nearly 
to strike the ground, which of course is impossible, as the distortion of the earth neces- 
sary to produce this result would have caused disruptions which were not observed; and 
moreover, a small vibratory movement is sufficient to cause very great commotion among 
trees, which would naturally be referred by an observer to tiltings due to surface waves. 

1 Karthquakes, p. 144. 
