THE PROPAGATION OF THE DISTURBANCE. 127 
time at which the waves are brought into existence would be one of the two points where 
the hodograph of the regular waves crosses the hodographs of the first two phases. If 
the regular waves are started by the first preliminary tremors, this point would be at a 
distance of 3.88° or 431 km. from the origin; and the waves would begin there 1 minute 
after the shock occurred. If they were started by the second preliminary tremors they 
would originate at a distance of 8.41° or 935 km. from the origin and 3.25 minutes after 
the occurrence of the shock. It seems probable that the surface waves are due in a 
greater degree to the transverse than to the longitudinal waves, on account of their 
greater amplitude. As pointed out by Lord Rayleigh, the surface waves expand along 
the surface in two dimensions, whereas the other waves expand thru the body of the 
earth in three dimensions; the former, therefore, decrease in amplitude much more 
slowly than the latter and at distant stations cause a greater movement than the prelimi- 
nary tremors which started them. 
This would account for the preponderance of transverse motion in the principal part 
of the recorded disturbance, which has been observed in some cases. We must not 
infer, however, that there are no surface waves nearer the origin than the points we have 
designated; on the contrary, it is extremely probable that surface waves will be started 
at all parts of the surface within these distances when the earlier phases arrive there; 
but as the latter travel more rapidly than the former, new surface waves will be originated 
in front of them and will always lead them in their passage around the world. It seems 
probable that the regular waves are the leaders of the surface waves; hence their 
importance. If there are others which precede them, they are very irregular and their 
beginning does not produce a sufficiently definite point on the seismogram to be generally 
recognizable. 
The straightness of the hodograph of the regular waves shows that the velocity of 
propagation is uniform along the arc, and therefore it is practically certain that the waves 
travel along the surface of the earth and we can apply our equation to determine the 
time of arrival at any point on the surface when we know its distance from the origin. 
We thus find 88 minutes as the time necessary to travel 180° to the antipodes. 
PROPAGATION ALONG THE MAJOR ARC, 
We could find, from the equation, the time necessary to reach any station by the major 
arc. This would apply only to the regular waves, but other surface waves, moving with 
smaller velocities, would take longer times to reach the station. Waves of so many 
velocities occur that we can not work out the hodographs of them all; and we do not 
know at what points they start, but it is probable, as in the case of the regular waves, 
that they start very near the origin and that their velocity will be given with a sufficient 
approximation by dividing the distance of the station by the time interval of their arrival 
after the occurrence of the shock. With this method it is very easy to find the time 
interval of the arrival of waves having the same velocity by the major arc. Let 7’ repre- 
sent this interval and ¢ the interval by the minor arc; let d be the distance in degrees by 
the minor arc; then we find, very simply, 
ane 360° — d (Eat) kee) 
d 2 d 
These expressions do not contain the velocity explicitly, and apply to surface waves 
360 — d 180 —d 
and 
i 


having any constant velocity. The quantities are constant for each 
station ; and we merely have tomultiply the first by ¢, the time interval of the surface waves 
by the minor arc, to obtain the interval after which the corresponding waves would arrive 
