A.— MATHEMATICAL AND PHYSICAL SCIENCES 29 



The basis of the seismic method is the same as that underlying the 

 investigations of the propagation of earthquake shocks in relation to the 

 determination of the structure of the earth's crust. The difference is 

 only one of degree. Artificial and controlled explosions replace the 

 sporadic natural shocks, and, although the detonation of perhaps a ton of 

 gelignite may be spectacular and dangerous enough, it is trivial compared 

 with the natural disturbances occurring, even in England. The distances 

 involved are also correspondingly small. But in so far as there is a theory 

 of natural earthquake propagation, it serves also for the seismic method 

 of geophysical prospecting. In trying to determine the depth of an under- 

 ground stratum the most direct method of attack would be to measure, 

 if possible , the time of travel of a particular disturbance from the surface 

 to the interface and back to the surface after reflection. A knowledge of 

 the velocity of propagation in the upper medium only would then give 

 the depth required. This method has been used with great success in 

 determining the depth of the ocean by means of the Admiralty echo- 

 sounding machine. But it fails in application to the solid earth, for the 

 reason that the attenuation of vibrations with distance is far greater in the 

 earth than in the sea ; consequently much larger initial disturbances 

 have to be used — in fact, violent explosions. Even if — as ought always 

 to be done for the sake of efficiency — the explosion is arranged so that the 

 surface of the ground is not broken, thus eliminating danger to observers, 

 the delicate seismographs cannot as yet be properly protected against the 

 direct effect. They would thus be so greatly disturbed as to mask com- 

 pletely the onset of the small reflected disturbance arriving shortly after. 

 This effect, indeed, persists to a less but still important degree even when 

 the seismograph is removed to quite large distances from the explosion. 

 It is true that some important results have been obtained by employing 

 this so-called reflection method, but the reading of the records is a matter 

 of considerable uncertainty, owing to the difficulty of identifying the time 

 of onset of the reflected disturbance in the midst of the effect of that 

 propagated directly. For, in the first place, we have no means of knowing 

 the precise form of the initial motion arising from the explosion, or the 

 manner in which the form changes during propagation. And, secondly, 

 none of the portable seismographs at present available record with com- 

 plete accuracy the disturbances which reach them : all, to a greater or 

 less degree, display resonance at certain frequencies, and thus treat 

 preferentially corresponding components of the motion to which they 

 are subjected. This uncertainty has led to the more general adoption of 

 a method, properly called the diffraction method, although the adjective 

 * refraction ' is sometimes incorrectly used. Its great advantage is that 

 it enables the inevitably feeble disturbances, which have penetrated to 

 and through the lower medium, to reach the seismograph, under certain 

 conditions, in advance of the much greater direct wave. Consequently 

 the times of arrival of these indirect, or diffracted, disturbances are re- 

 corded unmistakably upon the seismogram, however much the instrument 

 may be agitated later on. 



The theoretical basis of this method has been worked out in a partial 

 manner only. Let us take in illustration the simplest possible case, 



