225 
1907-8.] Professor C. G. Knott on Seismic Radiations. 
which there is variation of speed of propagation. Viewed as a problem in 
elasticity, this means that the modulus on which the speed of the second 
phase depends varies with depth according to a law not quite the same as 
that which holds for the modulus determining the propagation of the first 
phase, — a highly probable truth. 
If the second phase be supposed to be due to the arrival of the first 
tremors of the distortional wave with displacements perpendicular to the 
direction of propagation, then the horizontal component of the displacement 
will be equal to the maximum displacement multiplied by the sine of the 
angle of emergence. Consequently, at great arcual distances the second 
phase, as recorded by a horizontal pendulum, should tend to become 
proportionately in greater evidence than the first phase. There are, 
indeed, cases in which the second phase has been mistaken for the 
first, the latter having had too small a horizontal component to produce 
a record. 
It seems to me that the theory here sketched is amply sufficient to co- 
ordinate all the known phenomena. The first phase of the preliminary 
tremors is thus identified with the compressional waves passing through 
the body of the earth. No doubt, especially in the more heterogeneous 
crust, surfaces of discontinuity will start waves of distortional type along 
with the incident waves of compressional type.* But across the practically 
homogeneous nucleus the compressional waves will run ahead of their 
associates of other type, so that what emerges at the surface, although 
modified in detail, must be referable to these compressional waves. 
Similarly, when somewhat later the distortional waves flow in in quantity, 
there will be mingled with them waves of the compressional type. 
Nevertheless, the second phase will be largely composed of disturbances 
which have passed through the homogeneous nucleus as distortional waves, 
but have emerged modified in detail by refraction across discontinuous 
surfaces. 
The distortional waves need not necessarily be more energetic than the 
compressional ; but their generally greater amplitude, as measured on instru- 
ments recording horizontal motion, is at once explained in terms of the angle 
of emergence. Looking back to pages 222, 223, we see that for arcual 
distances greater than 60° the sine of the angle of emergence is greater 
than the cosine in ratios exceeding the value 2, rapidly increasing for 
greater arcual distances. 
The longer periods which observation proves to be associated with the 
* See my paper on “ Reflexion and Refraction of Elastic Waves,” Phil. Mag., July 1899, 
and abstract of address on Earthquakes, R.S.E. Proceedivqs, vol. xxii., 1899. 
VOL. XXVIII. 
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