CONCLUSIONS, 141 
Damped instruments. — Of the instruments which were damped the majority were 
not damped enough. There are two great advantages in strong damping. The pen- 
dulum has a more uniform magnifying power for waves of different periods, and it takes 
up the true movement more quickly. The curves in fig. 47 show the variations in mag- 
nifying powers for different periods and for different degrees of damping. Where the 
damping is insufficient there is a distortion of the record, as in the case of undamped in- 
struments, but to a less degree. It will be noticed that when the damping ratio is 8 : 1 
the magnifying power is nearly constant for all periods shorter than that of the pendulum 
itself. For longer vibration periods the magnifying power gradually diminishes, but not 
excessively. When the vibration period is twice as long as that of the pendulum the 
magnifying power is about 0.8 as great as it would be for an undamped pendulum; and 
for periods longer still the magnifying power becomes more nearly equal to that of an 
undamped instrument. 
With the damping ratio mentioned the free movement of the pendulum dies out very 
rapidly. If the pendulum is displaced 64 mm. and allowed to swing freely its amplitude 
will die down to 1 mm. after one whole vibration. Therefore the free movement of the 
pendulum will always disappear rapidly, and it will record pretty closely the true move- 
ment of the ground. Prince Galitzin advocates “dead-beat”’ instruments, where the 
damping is in the proportion 8: 1. Under this heavy damping he has shown by experi- 
ment that the free movement disappears immediately and the pendulum follows very 
closely the movement of the ground; but the curve in fig. 47 shows that the magnifying 
power is not constant, but varies continuously for different periods, and therefore a cal- 
culation must always be made before we can compare the relative amplitudes in different 
parts of the record. It seems to me therefore that the most advisable damping ratio 
ir hte ee 
Period of the pendulum. — If the vibrations have a much longer period than the pen- 
dulum, the magnifying power of the instrument is greatly reduced. The advantage of 
long periods in undamped pendulums is that they hold up the magnifying power for long- 
period waves. For waves of very short period there is no advantage in giving a long 
period to the pendulum. For instance, other things being equal, a pendulum with a 
period of 10 seconds and one with a period of 60 seconds would have practically the same 
magnifying power for waves whose period was 1 second. 
We have seen that when the instrument is damped in the ratio of 8 ; 1 the magnifying 
power varies little for periods up to that of the pendulum; and, therefore, the longer the 
latter the greater the range over which the magnifying power will be practically constant. 
A pendulum whose period is 30 seconds and which is damped in this ratio will give a very 
correct record of the relative amplitudes in all parts of the seismogram ; for waves having 
a longer period than this are not very frequent. 
Magnifying power for short periods. — Among the instruments which recorded the 
California earthquake magnifying powers for very short periods of 2 or 3, 6 or 7, 10, 15, 
25, 100, and more, are found. The majority of those with low magnifying powers gave 
unsatisfactory determinations of the beginning of the shock, even at stations less than 
90° distant; and for greater distances than this the beginning in general was not recorded 
at all. We have been unable to determine the time of the arrival of the beginning of the 
shock at the very distant stations, as they are all provided with low magnifying instru- 
ments. This is most unfortunate, for it is true not only in the case of the California earth- 
quake but of all other shocks whose times and origins are accurately known; and there- 
fore our knowledge of the velocity of propagation to very great distances is still quite 
vague. To get satisfactory records of earthquakes at distances more than 100° it is 
necessary to have instruments with magnifying powers of at least 100. 
