THE TIME AND ORIGIN OF THE SHOCK. 13 
estimate of the depth if we were not confronted by another difficulty, namely the varia- 
tions of the effects due to the character of the foundation. These variations, as shown 
on the general map, No. 23, and on the intensity map of the city of San Francisco, No. 19, 
are so great that it is quite impossible to obtain accurate values for the depth of the fault 
all along its course; but opposite Point Arena the isoseismals are sufficiently regular 
to throw some light on the subject. In attempting to solve this problem, we must make 
a number of assumptions, which are by no means exactly true, but are nearly enough so to 
make our result of some value; they are: that the amount of energy sent out by each 
element of the fault-plane per unit time was the same; that the amount of energy sent 
out in any direction from each element was proportional to the cosine of the angle between 
that direction and the normal to the fault-plane; that the strong disturbance continued 
for a sufficient time all along the fault-plane to permit us to assume that points not very 
distant were receiving simultaneously the strong vibrations from a length of the fault- 
plane 8 or 10 times as great as their distances from it; and that the effective force at any 
point is proportional to the square root of the energy of the disturbance at that point. 
With these assumptions we can determine the energy of the disturbance at any point 
not far from the fault by adding together the amounts of energy sent to that point by 
each element of the line. 
The vibrational disturbances at the various points of the fault-plane do not unite to 
form a single wave-front, for the movements must be in different phases at different 
points, and both distortional and longitudinal vibrations in various directions are present ; 
for this reason it might appear that the energy would be sent out uniformly in all directions 
and not according to the cosine law; but if we make this assumption, we find an infinite 
amount of energy near the fault, which is, of course, impossible, and we are therefore led 
to assume the cosine law, which is probably not very far wrong." 
For a simple harmonic vibration of a given period the energy of the motion is pro- 
portional to the square of the amplitude, and the maxi- 
mum acceleration to the amplitude itself, that is, to the 
square root of the energy. When we consider that, at 
every place where the disturbance was felt, the vibra- 
tions were in all directions and had various periods and 
amplitudes, we see that it is quite impossible to deter- 
mine the true acceleration, but the square root of the 
energy will be roughly proportional to it. Professor 
Omori has shown that the effective force is proportional 
to the acceleration and has estimated the values of the 
various degrees of the Rossi-Forel Scale in terms of 
actual accelerations.” 
In fig. 3 let P be the point on the earth’s surface at Preiss 
which the disturbance is to be determined and z its 
perpendicular distance from the fault-plane, O’Obb’. Let b be any element of the 
fault-plane, whose depth below the surface is z and whose distance from O’, measured 
parallel to 0’b’, is y. Then the energy of the disturbance at P is found by adding the 
amounts sent from all such elements of the fault-plane, remembering that the intensity 



1 It is also probable that the vibrations sent out from each point are regular only for a very short 
time. These considerations lead to the conclusion that no places on the earth’s surface experience a 
low intensity of disturbance on account of the interference of vibrations; for altho the interference 
might exist at a particular moment, the irregularity of the motion would only allow it for a very short 
time; and the intensity ascribed to a particular place is the maximum intensity which is felt there at 
any part of the shock. On the other hand, it is quite possible for strong vibrations from two parts 
of the fault-plane to combine and cause unusual intensity along a particular line or zone. No definite 
instances of this, however, can be cited in the case of the California earthquake. 
2 Publications of the Earthquake Investigation Commission in Foreign Languages, No. 4. 
