ISOSEISMALS: DISTRIBUTION OF APPARENT INTENSITY. 329 
all the water that it would hold, so that it was very soft, almost semi-fluid. The amount 
of water was determined by weighing a portion of the wet sand and then weighing it 
again after it had been thoroly dried. In this case the material contained 20 per cent 
of water to 80 per cent of sand. 
The traces show at a glance that the amplitude of the motion of the sand was much 
greater than that of the box. By reference to the transverse lines aa/ and bb’, it is ob- 
vious that the motion of the sand lags behind the motion of the box —in this case 
about one-sixth of a complete period. Finally, the difference in the character of the 
two motions is shown by the sine curve in one case, and the zigzag line in the other 
case. The sine curve shows that the car has a simple harmonic or pendulum motion, 
as must necessarily be the case on account of the way in which it is shaken. On the 
contrary, the block embedded in the sand moves with an approximately uniform velocity 
until the end of the “stroke,” when its motion is very quickly reversed; after which it 
again moves with uniform velocity until its motion is again quickly reversed. The 
acceleration at the instant the motion is reversed is a proper measure of the quickness 
of reversal. This acceleration can not be measured, but the average acceleration during 
a short interval of time while the motion is being reversed can be determined. If cd and 
cd’ (see fig. 6) are drawn at corresponding parts of the curves, then the lengths of these 
lines are proportional to the times required for corresponding changes in the two motions. 
The square of the ratio of these two times, divided into the ratio of the two amplitudes, 
gives the ratio of the two accelerations during the motion cPd. The closer cd is taken 
to P the greater this ratio becomes. In the present case, in which cd is drawn at one- 
tenth of the amplitude from P, the ratio of the two accelerations is about 3. As moving 
forces are always proportional to accelerations, the bearing of this result on the destruc- 
tiveness of earthquakes is evident. 
The data obtained from fig. 61 may be presented as follows: Load shaken, sand 80, 
water 20. Depth of sand, 22 centimeters. Frequency of motion, 1.7 double vibrations 
per second. Amplitude of car, 4.5 centimeters. Amplitude of block in sand 8.5 centi- 
meters. Lag of block, one-sixth period. Ratio of accelerations at reversal, 3 or greater. 
A large number of experiments were made with a load of wet sand having the above 
composition. Results similar to the above were obtained whenever the frequency of 
the motion was rather small. However, when the frequency of the motion was con- 
siderably increased, or when the ratio of water to sand was changed, the results obtained 
were quite different. In general the less water the sand contains the more nearly does 
it move with the car. The accompanying tables contain results from a large number 
of experiments in which the composition of the load and the frequency of motion was 
varied. 
The data from these tables are plotted in figs. 62 and 63. In all cases the number of 
complete or double vibrations per second is plotted along the z-axis, while the amplitude 
of motion of the block embedded in the sand is plotted along the y-axis. The points 
representing observations do not fall upon smooth curves, but this is hardly to be ex- 
pected from the nature of the experiment. 
The data as illustrated by the plots show that when the load consists of sand and water 
in the ratio 4 to 1, for low frequencies, the sand oscillates through a much greater ampli- 
tude than the car, and that the amplitude rapidly decreases as the frequency increases 
and becomes quite small for frequencies of 3 or 4 per second. On the contrary, when 
the load contains only 15 per cent of water, it moves with the car, for low frequencies, 
and the amplitude increases with the frequency. The results actually obtained are 
subject to a large probable error, but there can be no doubt about the decreasing ampli- 
tude with increasing frequency in one case and the opposite result in the other case. 
When the sand contains about 15 per cent of water, it seems to be more adhesive and 
more capable of packing into a relatively compact mass. In this respect it is distinguished 
