THE PROPAGATION OF THE DISTURBANCE. 117 
After plotting in the times of arrival of the three phases at the various stations a 
smooth curve is drawn thru the points marked, so that the errors of the observations 
may be as small as possible; the velocity of the first preliminary tremors, as noted on 
page 7, is assumed to be 7.2 km./sec. near the origin; the velocity of the second pre- 
liminary tremors in the same region becomes 4.8 km./sec. from the Mount Hamilton 
observations, as they begin there 9 seconds after the first preliminary tremors. A special 
method was followed in drawing the straight line for the long waves and it will be given 
further on. These curves are called “hodographs.” ‘The average velocity of trans- 
mission to any station is evidently given by the time interval divided by the distance; 
that is, it would equal the tangent of the angle which a straight line, drawn from the 
origin to a point on the hodograph immediately above the station, makes with the vertical ; 
and the velocity along the surface would be given by the difference between the times of 
arrival at two stations divided by the difference of their distances from the origin, provided 
these distances differed but little from each other. 
THE PRELIMINARY TREMORS. 
The first thing that strikes us on examining the plate is that the hodographs of the 
first two phases are curved, indicating that the average velocity of transmission increases 
with the distance; and that the hodograph of the regular waves is straight, showing a con- 
stant velocity independent of the distance. These distances have been measured along 
the surface, or, as it is exprest, along the arc. When we plot the hodographs of the first 
two phases in terms of the distance of the stations from the origin, measured by the 
shortest route, that is, by the chord, as shown in the upper part of the plate, we find them 
still curved, but much less so than in the former case. It is the general belief that the 
curvature of these lines indicates that the waves travel thru the body of the earth and 
that their velocity increases with the depth of the path below the surface; if this be true, 
and no satisfactory arguments have been advanced against it, the waves would not follow 
the shortest path to a station, that is the chord, but would follow a curved path, convex 
downward, which would bring them to the station in the shortest time. Unfortunately 
at distances greater than 100° for the first preliminary tremors and 125° for the second 
preliminary tremors, the observations of the phases become extremely doubtful; and it 
is precisely the paths leading to stations beyond these distances that dip very deep 
towards the center of the earth, and that might reveal the nature of that region. 
The cause of the inaccuracy of observations at great distances is not far to seek. The 
first preliminary tremors are always very weak and are recorded as very small vibrations 
even at comparatively small distances. If, moreover, as we have given reasons to believe, 
their vibrations are longitudinal, a large part of their energy would be taken up in vertical 
vibrations at the surface, particularly at great distances, and would therefore fail to pro- 
duce an appreciable disturbance of instruments recording horizontal movements only. 
The horizontal and vertical components of the first preliminary tremors at Gottingen 
(distant 81.86°) have about the same amplitude, which is very small; and this shows 
that the weakness of this phase is not merely due to its tendency to produce vertical 
vibrations at the earth’s surface. Moreover, the amplitude of vibrations would decrease 
more rapidly than the distance, because, as Prof. C. G. Knott * has shown, the curved 
paths of these waves would cause the energy to be concentrated upon the nearer stations, 
with a corresponding diminution at the more distant ones. It also happens that all the 
instruments at stations beyond 105° have a low magnifying power, with the exception 
of Batavia; and even there the magnifying power, 65.5, may be insufficient to indicate 
the real beginning of the first preliminary tremors. It is quite possible that the beginning 
of the record at Mauritius may represent the second preliminary tremors, and that the 
1The Physics of Earthquake Phenomena, p. 253. 
