46 REPORT OF THE CALIFORNIA EARTHQUAKE COMMISSION. 
produced. For the normal pressures must be such as to produce no moment around any 
straight line in the plane of the points of contact and immediately under the center of 
gravity; otherwise, the object, when undisturbed, could not remain stationary. If now 
we take the straight lme parallel with the direction of vibration, the 
moments of each frictional force about the vertical, thru the center of 
gravity, will be proportional to the moment of the corresponding normal 
force about the straight line, and therefore their sum will be zero. Houses, 
however, are not rigid bodies resting on rigid foundations, like a statue on 
uf its base; and the ground itself, on account of slight variations in texture 
or firmness, would not behave like a rigid body during the earthquake, 
but would have somewhat different movements at different places under 
the house; in this way it is quite possible for a house to be slightly 
AG rotated by the frictional forces between it and its foundation. Examples 
of such rotations are given in vol. 1, pp. 170, 176. 
Second: Professor Thomas Gray * has shown that if the vibrations are at right angles to 
the edge of the rectangular base of a column, or along the line joining opposite corners, 
no rotating moment is developed; but if the shock les between these directions, as, for 
example, in the direction, of, in fig. 24, then the column tends A 
to rock on the corner, and to rotate around it; for the force is 
applied at the corner and acts in a direction parallel with the 
vibration and does not pass through the center of gravity. nage 
This is in entire accord with the laws of mechanics, and un- VEZ, 
doubtedly some small rotations are caused in this way; but it i) 
is to be noticed that the tendency is only to rotate until the aa 
edge is at right angles to the direction of vibration; if this 
direction is nearly at right angles to the edge, the rotation will be small; if the direction 
is nearly along the diagonal, the moment produced will be small; if the direction of 
vibration gradually changes, keeping pace with the turning of the column, a larger rota- 
tion might accumulate. In the case of columns with circular bases, the method would 
not apply at all; and it may be well doubted if any large rotations are produced in 
this way. 
Third: The combination of vibrations at right angles offers a simpler explanation for 
any amount of rotation and for any form of base. If an object, as a result of the vibration, 
is rocking on its edge and is then subjected to a second vibration at right angles to the 
first, a strong moment will be set up and the object will rotate; if these vibrations are so 
timed as to produce parallel rotation of the support, the body will continue to rotate 
as long as the vibrations are sufficiently strong. One can easily realize this experimentally 
by means of a chair. Raise the front legs slightly from the floor by pressing against the 
back; then press against the side of the chair, and it will swing around about 90° on one 
leg; or, place a box or bottle on a book, and then rotate the book, keeping it parallel with 
itself; if the movement be strong enough and the friction sufficient to prevent slipping, 
the object will rock and rotate. The principle of crost vibrations seems to be the 
true explanation of the rotation in most cases and in all cases where the rotation is large. 
Crost vibrations will not be produced by a single shock from a single center; but a 
protracted shock, or successive shocks from the same center, or shocks from different 
centers, will produce them; that is, they will practically occur at the time of all large and 
important earthquakes, for then the vibrations usually originate at many points and at 
slightly different times. 
Fig. 24. 


1 Milne, The Earthquake in Japan of Feb. 22,1880. Trans. Seism. Soc. Japan, vol. 1, part II, pp. 33- 
35; and Seismology, p. 170. 
