134 F. GOLDSTONE 
of disturbance. These are best represented by a time-distance graph 
such as Figure 1, which depicts the relation between the distance from 
the origin and the time of arrival of the various wave fronts resulting 
from two strata, the upper one, in which the disturbance is generated, 
having the lower velocity of propagation, V;. The disturbance, let us 
say due to a dynamite explosion, set up at shot point A gives rise to 
at least three trains of elastic waves, namely, a longitudinal wave, a 
transverse wave, and a surface, or Rayleigh, wave; the velocities of 
propagation are here arranged in descending magnitude. Further, 
the longitudinal wave on striking the interface between V; and V2 
will be in part reflected as a longitudinal wave and in partas a trans- 
verse wave, and will set up a new series of surface waves on the inter- 
face; likewise the transverse wave on striking this interface will suffer 
reflexion as both longitudinal and transverse waves. Waves striking 
the interface at their critical angles will be refracted along the sur- 
face of V2 with velocities characteristic of the particular wave in that 
stratum and will be radiated thence back to the surface. Only selected 
impetii have been chosen for plotting on the time-distance graph to 
avoid too great complication; however, the principal longitudinal 
wave front impetii are all shown. Refraction seismic prospecting con- 
cerns itself with the first longitudinal wave front impetus to reach any 
point by any path, whereas reflexion seismic prospecting as applied 
at the present time confines itself to the longitudinal wave front im- 
petii reaching the seismograph after reflexion from an underlying 
discontinuity and consequently arriving later than the same wave 
travelling directly along the surface of the ground. Consider the vari- 
ous wave fronts striking a seismograph placed at point B; this ordi- 
nate erected to the time-distance graph shows that the first wave 
front to arrive will be the longitudinal wave in V;, the second will be 
the transverse wave in Vj, the third will be the Rayleigh wave along 
the surface, the fourth will be the sound wave in air, and lastly the 
longitudinal wave reflected from the interface of V; and V2. The rela- 
tive intensities of these various waves can only be learned by experi- 
ence in any particular area, since they do not seem to be amenable to 
mathematical analysis. Professor C. G. Knott, in his magnificent paper 
on the quantitative aspect of the reflexion and refraction of elastic 
waves at a rock interface,’ states that the energy carried by the vari- 
ous waves can be computed when complete physical data are available. 
In the particular case of the reflected longitudinal wave at an interface 
between slate and granite, Knott computes the energy contained in 
the longitudinal wave reflected at perpendicular incidence to be some 
Phil. Mag., 1899, 48. 
794 
