THE PROPAGATION OF THE DISTURBANCE. 121 
Two sets of values of the second preliminary tremors are given for distances of 100° or 
more; they correspond to the two curves drawn in plate 2. The first set are more in 
accord with the observation at Batavia, the second with that at Mauritius; but both are 
very doubtful beyond about 110°, where they do not differ much. 
THE PATHS OF THE WAVES THRU THE EARTH. 
The velocities given show the average values between the focus and the distance 
indicated; but they do not show the actual velocity at any point of the path. The 
average velocity increases with the distance of the station; and this must be due to 
increasing velocity with greater depth ,. 
below the surface. With such increasing [\-~ 
velocities it is impossible for the rays to | SS a ne 
follow straight lines, but they must follow  bioo§\ OS 
paths which are concave upwards. Prof. | “ a he 
E. Wiechert* has given a method for | 
following out the paths of the waves, oe 
which is dependent upon the direction of 
the wave as it approaches a station. | 5600 
The angle at the station between this 
direction and the surface is the angle of N 
emergence, e, and its complement is the 00 
angle of incidence, 7 (see fig. 27). This | oS ae 
5000 
60° 

angle may be found immediately if we 
know the velocity of the wave near. the 
surface and the surface velocity. The hehe Ye 
former is about 7.2 km./sec.; the latter ; 
can be determined from the hodograph; “< Reais: Se i. 
it equals the angle made with the vertical Pras \ 
by the tangent line to the hodograph. 02 “oo? 
The value of the surface velocity depends, Os 
therefore, upon the actual direction of soy 
the hodograph line (plate 2), and can only ey: poet at 
be determined accurately provided the 
hodograph is accurate. This, however, is by no means true, so that our values for 
the surface velocity are only approximately correct. The paths of the waves depend 
upon the angles of emergence, and as they are only approximate the same is true of the 
paths. They, however, represent fairly well the course of the waves as they travel thru 
the earth to stations at various distances. Following Professor Wiechert’s method these 
paths have been drawn in fig. 27, the full lines representing the first preliminary tremors 
and the broken lines the second preliminary tremors. The paths have been drawn for 
the first preliminary tremors leading to distances up to 110° and for the second preliminary 
tremors to 100°; these are the limiting distances to which our hodographs yield fairly 
good values. 
It will be seen that the paths have a very marked curvature, especially those leading 
to stations which are not very distant. The paths leading to points less than 70° distant 
are less curved for the second preliminary tremors than for the first preliminary tremors ; 
but the opposite is true for paths leading to greater distances. The paths of both groups 
leading to this particular distance are practically coincident. As the waves penetrate 
deeper into the earth their paths become less curved; and the path leading to the antip- 
odes thru the earth’s center would be a straight line. 
aS 80° 
1 Ueber Erdbebenwellen. Nach. d. K. Gesells. d. Wissens. zu Gottingen, Math.-phys. K1., 1907. 
