ON SEISMOLOGICAL INVESTIGATION. 231 
These figures are too few in number to be used as a foundation for any 
certain conclusions, but they may possibly indicate results to be sought for 
‘in future records. With regard tothe first set of intervals, we know that 
for distances up to 8° from an origin that the time by which tremors out- 
race the main movement may be reckoned by seconds. Adding this fact 
to our list, it seems that here we have a table which indicates that as 
earthquakes travel at first the tremors only outrace the large waves at a 
very slow rate, but as the distance from the origin increases this rate 
increases. This goes on until a point between 48° and 62° distant from 
‘the origin has been reached, after which the rate at which the large move- 
ments are left behind decreases. 
One explanation for this is 10 suppose that the first precursors came 
through the earth with an average velocity which observation shows to 
increase approximately with the square root of the,average depth of the 
chord joining the centrum and the observing station, whilst the large 
waves travelled round the surface. One objection to this view is that 
observations exist which show the large waves have apparently travelled 
over paths varying between 20° and 110° at rates which, rather than being 
constant, have increased from 2:1 to 3:3 kms. per second. 
The velocities giving this comparatively slight difference were however 
determined on the assumption that the times at which various earthquakes 
originated were known, and there is therefore a possibility that they may 
be apparent rather than real. 
Also it must be remarked, as pointed out by Dr. C. G. Knott, that if 
we regard the large waves as being distortional, inasmuch as the coeflicient 
of elasticity determining the velocity of propagation of such waves may 
not be greatly influenced by pressure, it is quite conceivable that they 
should follow the preliminary tremors through our earth. The question 
then arises, whether these larger movements would be left farther and 
farther behind their precursors in the manner indicated. 
When we come to our second set of intervals, which indicate the 
duration of the first preliminary tremors before they are eclipsed by groups 
of vibrations, which usually grow in size, and appear from their periods 
to be distortional, we see that up to a point about 62° from an origin 
these figures apparently increase, but beyond that point they grow less. 
What we have to explain, in addition to this fact, is that of the 
continuity and growth in magnitude of what very often forms a long and 
continuous series of preliminary motions. As I have already stated, 
their very appearance indicates that they have travelled on different 
paths. The first have followed a path entirely through our earth, whilst 
its successors have travelled shorter and shorter distances through the 
earth to meet a crust, through which they have completed their journey 
to the observing station. The first followed Knott’s brachistrochronic 
path, or that of least time, whilst the successors took paths the latter 
parts of which were along arcs of increasing length. The result of this 
would be that at an observing station vibrations would arrive in series, 
each group corresponding to an originating impulse. The last of the 
rabble would be the series representing that portion of the main shock 
which had travelled entirely round and through the crust. 
To complete this hypothesis, I here reproduce a sketch given to me 
by Dr. C. G. Knott, showing the probable form of wave fronts and paths 
of compressional vibrations passing through our earth. 
The assumption on which this is based is that the square of the speed 
