THE INFLUENCE OF THE FOUNDATION ON THE APPARENT INTENSITY. 53 
front of it against the side of the box; this together with the return movement of the box 
produces a strong force which quickly reverses the movement of the sand, giving it a 
velocity slightly greater than the maximum velocity of the box; but the force is not 
active again until the box approaches its maximum displacement on the other side. The 
movement therefore depends upon the action of the sides of the box and is not trans- 
mitted from the bottom. It is clear from Mr. Rogers’s experiments that the forces when 
the sand is dry are very different from those when the sand is very wet; and when dif- 
ferent parts of the sand contain different amounts of water, that the movements would 
be so different as to produce much confusion. 
APPLICATION OF THE THEORY TO SMALL BASINS. 
When we attempt to apply the results of the experiments to explain the case of the 
greater disturbance in alluvial soil than in rock, we recognize with Mr. Rogers that it is 
dangerous to carry analogy from such small quantities to such large masses, and we must 
be very carefully guided by theory if we wish to avoid great error. 
As already noted, alluvium occupies basins in the rock of more or less extent, and in 
considering its motions we must divide the basins into two classes; the first comprises 
those basins which are small enough, in the direction of propagation, for all parts to 
move practically in the same phase, like the box in Mr. Rogers’s experiments; that is, 
they must be not much larger than an eighth of the wave-length of the waves in the sur- 
rounding rock. With waves whose period is as short as a half second, the basins may 
be somewhat more than a quarter mile across; but with periods as long as 10 seconds, 
they may be over 5 miles across, and still be in this class. The second class comprizes 
all large basins, where the progressive character of the wave-motion must be considered. 
Where alluvial basins are not extremely small, they are always much broader than 
they are deep, usually many times as much; and they are also saturated with water. 
When the material is largely sand or gravel, the grains are held so closely together by the 
weight of the material lying above them that the vibrations can be transmitted from the 
bottom in the same way as with dry sand; but when the material is soft mud, transverse 
vibrations can not be so transmitted and the influence on the sides becomes predominant. 
The limiting case of fluidity is exemplified by streams, ponds, and even vessels containing 
water or milk, where the liquid may be so greatly agitated as to be splashed out on the 
sides. Mr. Rogers’s experiments seem to explain pretty satisfactorily the larger surface 
amplitude and the greater damage done in the class of small basins of alluvium; but it 
must be noted that the basins have not a flat bottom like a box, but have rather an open 
V shape, like stream valleys; and there is no abrupt distinction between the bottom and 
the sides. Where the material is sufficiently solid, the vibrations are transmitted both 
as transverse and longitudinal vibrations from the bottom, the surface amplitude being 
in general greater than at the base and varying with the depth, the coefficient of rigidity, 
and the period of the vibration ; the depth of a basin is more or less irregular, the character 
of the material, and therefore the coefficient of rigidity, varies from point to point; there- 
fore the amplitude will vary from point to point on the surface, and points not far apart 
may be even in opposite phases, so that more or less discordant movements take place. 
The commotion may be sufficiently great to produce cracks in the ground, especially at 
the boundaries of softer and firmer material. The damage to buildings is due more to 
the discordant character of the disturbance than to the mere increase in amplitude at the 
surface of the alluvium, for deep pilings with a strong concrete capping diminish the 
damage to a remarkable degree; the capping must move nearly as a rigid body and 
relieve the building above it from different movements in different parts of its founda- 
tion. The capping must also diminish the amplitude, for movements in opposite direc- 
