Hogben. — Path of Earthquake-waves through the Earth. 425 



for by the probable fact that they pass from the origin along 

 chords to the several places of observation, I have examined 

 the records of several earthquakes as given by Milne seis- 

 mographs at different stations situated all over the world, 

 with the object of determining the question whether the 

 waves in question are propagated along arcs or chords of the 

 earth. 



Taking the great Guatemala earthquake of the 19th April, 

 1902, as a fair specimen of the calculations, the evidence is, 

 in my opinion, almost wholly in favour of the theory that 

 the tine vibrations commonly called "preliminary tremors" 

 do not travel along chords, as some have maintained, but 

 along arcs at no great depth, the most probable speed 

 being, in the case of this earthquake, 15-6 kilometers per 

 second. 



The table shows the distances (arcual and chordal) of the 

 observing stations from the origin of disturbance, and the 

 times of arrival of the preliminary tremors. 



The diagram shows the same facts in a graphical form, the 

 dots showing the points on the velocity-curve for the same 

 places on the assumption of paths along arcs, the small 

 crosses corresponding points on the assumption that the paths 

 were chordal. The scale of the diagram is so chosen that the 

 same unit represents 1,000 kilometers along the axis of y, or 

 100 seconds along the axis of t. Hence the velocity at a 

 distance y from the origin = 10 dyjdt kilometers, which can 

 be read directly from the diagram. 



It does not seem possible to make any assumption of vary- 

 ing rigidity and elasticity of the internal rocks that would 

 account for the varying velocity on the latter assumption ; 

 whereas the fact that on the former hypothesis Imamura's 

 curve is almost a straight line shows that the velocity is 

 nearly constant {dyjdt = constant = 156 ; therefore v = 15-6 

 kilometers per second, as stated above). 



Theoretically, the velocity should be constant while the 

 waves are travelling through a homogeneous medium. Hence 

 we may fairly conclude that the waves travel parallel to the 

 surface at a uniform depth such that the elasticity and rigidity 

 of the rocks allow of a high velocity, probably between fifteen 

 and twenty miles below the surface. 



paper, and I think it due to myself, as well as a confirmation of his 

 investigation, to publish in brief the results at which I had arrived. 

 But his diagram represents the facts so much better than the diagram 

 accompanying my paper that 1 have substituted for the latter a modi- 

 fication of his diagram, introducing a simplification which I venture to 

 think gives a still clearer graphical representation of the facts. This 

 modified diagram I have called " Imamura's curve." 



