44 REPORT OF THE CALIFORNIA EARTHQUAKE COMMISSION. 
supports. This has given rise to the belief that there is a rotary motion of the various 
parts of the ground like that of wheels about their axes. It should be pointed out that 
this kind of motion can not exist, for it could not be propagated as an elastic disturbance, 
but would break up into waves of compression and distortion, which would be propagated 
at different speeds and would soon be separated from each other. Moreover sucha motion 
would produce rents in the ground, which have not been found; nor has any such motion 
of the ground itself ever actually been observed. Waves of elastic distortion do, however, 
produce very small rotations, whose maximum amount, we shall see (page 146), is given by 
92 
the expression 224 where A is the amplitude and » the wave-length; with a wave as 
short as 10,000 feet (3 km.) and an amplitude as large as 0.2 of a foot (6 cm.), the maxi- 
mum rotation would only be about 0.25 of a minute of arc, a quantity far too small to be 
noticeable; even if the rotation were 100 times as great as this, it would probably not 
be noticed. 
But there is another kind of rotation, which undoubtedly does occur, and which would, 
if strong enough, give rise to the sensation of twisting and would cause objects to rotate 
on their supports. If a swinging pendulum, as it passes its lowest point, should receive 
a blow at right angles to the direction of its motion, it would simply change its direction 
and continue to swing back and forth in a different plane; but if the blow should be 
received at any other part of its motion, it would swing in an ellipse ; if the blow were of the 
right intensity and were received at the end of the swing, the pendulum would swing in a 
circle. 
Two vibrations making an angle with each other would produce just such an elliptical 
or circular motion, unless they were so adjusted that they would combine to make a 
simple linear vibration in a direction between the two; but thiswouldrarely occur. If the 
two groups of combining vibrations had different periods, the resulting movement would 
be very complex; and we might have rotations first in one direction and then in the other. 
The kind of rotatory motion thus set up is not like that of a wheel about its axis, but is 
like that of a book which is carried around in a circle keeping the edge always parallel to 
its original position. We must look upon the rotatory motion of the earth reported dur- 
ing earthquakes as such that every point describes an ellipse, each point with a different 
center, but all with parallel axes; and the lines connecting near-by points remain parallel 
to their original directions, and do not, as in the case of a wheel, also rotate. For the 
sake of clearness let us speak of this kind of motion as parallel rotation, to distinguish it 
from rotations where the various points rotate around the same center. 
We have conclusive evidence that the motion of the earth during the Californian earth- 
quake was not merely a to-and-fro motion in one direction, but that the direction of the 
motion changed markedly. This is shown by the sensations of observers and by the fact 
that objects in the same place were thrown in various directions; statements that the 
earthquake was a “twister”? were not uncommon, and some observers reported that the 
motion was first in one direction and then at right angles to it; and lastly the seismo- 
graphs themselves indicate a combination of simple vibratory motions; this is well shown 
in the seismogram made by the simple pendulum at Yountville, and in all made by Ewing 
duplex pendulums. (See Seismograms, sheet No. 3.) 
We can picture to ourselves many ways in which movements in different directions 
could be produced at the same time. Suppose, for instance; that there were two shocks 
originating at the same place with some seconds interval between them; each in general 
would give rise to compressional and distortional waves; the first kind travels faster and 
hence outraces the second. The compressional waves of the second shock would over- 
take the distortional waves of the first shock in a circular zone surrounding the origin, and 
as their motions are at right angles to each other, we should find parallel rotations in this 
