124 REPORT OF THE CALIFORNIA EARTHQUAKE COMMISSION, 
without change of type, and the reflected waves will reach S; similarly the distance may 
be divided up into any number of equal lengths, and waves can be reflected successively 
at all these points without change of type, and reach S._ It would be very complicated to 
follow the course of waves of changing type, but the times of arrival at S of waves of 
unchanging type can easily be found. The interval for a singly reflected wave would be 
twice the interval required to go half the distance, and this interval can immediately 
be taken from the hodograph. ‘The interval for a wave which has suffered two reflections 
will be three times the interval required to go one-third the distance, and soon. These 
reflected waves are probably the most important cause of the variations of intensity 
during the early phases. The first preliminary tremors are always weak, but the addi- 
tion of the waves after one reflection to the direct waves may make the latter evident, 
when without them they would not be. This seems the case at Cairo, Batavia, and the 
Cape of Good Hope. The times of beginning at these observatories, as given by their 
directors, are within a half minute of the times at which longitudinal waves would reach 
them after one reflection. 
At the following stations the effects of the longitudinal waves after one reflection can 
be detected at an interval after the beginning which is given in minutes, these being the 
proper intervals as determined from the hodograph: Tacubaya, 0.5 minute; stations in 
Great Britain, 2.5 to 3 minutes; Upsala, slight, 2.5 minutes; Jena, 3 minutes; Munich, 
slight, 3 minutes; Géttingen, due in 2.5 minutes; slight effect in 3 minutes. The small- 
ness of the effects in all these cases, and the fact that the waves are weakened on reflection 
by having a portion of their energy transformed into waves of the other type, make it 
improbable that the effect of longitudinal waves after two or more reflections is at all 
noticeable at very distant stations. 
Horizontal transverse vibrations would suffer no transformation, and as they would 
practically lose no energy by refraction into the air, their amplitudes would diminish 
much more slowly than those of the longitudinal waves; they should tend, therefore, to 
cause marked variations in the intensity of the seismogram, the vibrations being trans- 
verse to the direction of propagation. Vertical transverse vibrations would suffer 
transformation like longitudinal waves, provided the angle of incidence were sufficiently 
small; if, however, the sine of the angle of incidence becomes greater than two-thirds 
the ratio of the velocities of the transverse to the longitudinal waves, that is, if the 
angle becomes greater than about 42°, there will be no transformation, and the trans- 
verse waves will be totally reflected as transverse waves. It is quite clear, therefore, 
that they will preserve their intensity far better than the longitudinal waves, and 
indeed will get energy from the latter. 
When we look for the reflected second preliminary tremors on the seismogram, we are 
disappointed that they are not more marked, but nevertheless evidences of them can be 
found on many seismograms. For instance, at Tacubaya the waves reflected once and 
twice coalesce and appear about one minute after the beginning of the second preliminary 
tremors; the waves reflected once arrive at stations in Great Britain and in Japan from 
4 to 5 minutes after the second preliminary tremors, and those reflected twice in about 6 
or 7 minutes; the latter are not evident on the Japanese seismograms. At Bombay 
the two waves reflected once and twice appear after 9 and 13 minutes; at Batavia they 
are due after 8.5 and 13 minutes; indications of them are found after 8.5 and between 
11.5 and 14 minutes; and many other stations could be cited. It is not entirely beyond 
question that the strengthenings of the seismograms are due to the reflected waves, both 
in the case of the first preliminary tremors and the second preliminary tremors; but 
they occur at the times indicated by the hodograph, and it seems most probable that we 
have interpreted them correctly. 
