76 REPORT— 1900. 



rate than along a course near the surface. Thus, from the Alaskan group 

 ■we should infer an average diametrial speed of about 2-2 km. per sec. ; 

 from the Mexican group about 1*8 ; and from the Ceram group about 

 2*5. This suggests that the speed of propagation along a diameter de- 

 pends upon the particular diameter considered-^a very curious result 

 surely, unless, of course, the depth of the focus below the surface be very 

 different in the different cases. 



As regards the general question of the diminution of speed at greater 

 depths, all we can say is that it is not impossible. True, the result is un- 

 expected, seeing that there can be little doubt that the preliminary tremors 

 travel quicker at the greater depths. But then it is also certain that the 

 elastic constants involved in the transmission of the two types of waves must 

 be essentially different, and there is no necessity for them to obey similar 

 laws of variation with depth. In my ' Scottish Geographical Magazine ' 

 article I pointed out that the bulk modulus might increase at a much 

 quicker rate than the density, whereas the rigidity might increase at much 

 the same rate. To meet the new need we have merely to assume that the 

 rigidity does not increase so quickly as the density. We know that the 

 density increases with the depth, and we know nothing whatever about 

 the elastic constants except what we learn from seismic phenomena. It 

 was, in fact, with feelings of surprise that we first recognised the high 

 speeds of earthquake disturbances through the body of the earth. That 

 another type of wave should travel more slowly at the greater depths 

 should not therefore be matter of any surprise, although certainly re- 

 markable. 



The hypothesis that the large waves really pass along brachistochronic 

 paths seems to require that the speed diminishes with distance from the 

 centre. This means that the paths are convex outwards, concave towards 

 the centre. Hence the paths to points within 90° of the origin will tend 

 to follow more or less closely the arc of the outer crust. When the arcual 

 distance exceeds the quadrant, then the paths begin to pass through deeper 

 parts of the earth, and the fall off in the value of the average speed be- 

 comes more apparent. This is precisely what is indicated in the values 

 deduced from the Alaskan group, since it is not till the arc exceeds 105° 

 that the value of the calculated average speed shows marked diminution. 

 The Mexican group shows the same feature, but not so the Ceram earth- 

 quake. Still it is only one against five, and we shall be safer in following 

 the five. 



Comparing the two hypotheses, the surface wave and the brachisto- 

 chronic path, we see that up to distances of a quadrant or so they give 

 much the same result, because the brachistochronic path is largely con- 

 fined to the surface layers. As regards greater distances the evidence in 

 hand is not very clear. Increased ' arcual speed ' is hinted at, and this, 

 if it exist, is a serious stumbling-block in the way of accepting the surface 

 wave theory. But at best the increase is small, and, except in the case of 

 the Ceram quake, really too small to build any conclusions upon. I should 

 rather be inclined to say that the evidence so far is in favour of a practi- 

 cally constant ' arcual speed ' over all distances. But I still entertain 

 strong suspicion of the possibility of surface waves of the magnitude re- 

 quired being transmitted over the earth's surface. If we take the values of 

 the arcual speeds in the Ceram earthquake as being accurate, we meet 

 what seems to me to be an insurmountable difficulty in the surface wave 

 theory. On the other hand, we have no insurmountable diflBculties if we 



