183 
1918-19.] The Propagation of Earthquake Waves. 
regarded as proportional to the horizontal displacements in the plane 
of the ray. 
In the case of the Secondary waves the displacement is at right angles 
to the direction of the ray, and may indeed be in any direction perpen- 
dicular thereto. If the displacement be supposed to be along the principal 
normal to the ray, the associated horizontal displacement is obtained by 
multiplying by the cosine of (p. If, on the other hand, the displacement 
be regarded as codirectional with the binormal, that is, perpendicular to 
the plane of the ray, this displacement at the point of emergence will 
itself be horizontal. Instead of limiting our attention to either of these 
special directions, we might consider as more satisfactory the average 
arrangement in which the energy is equally distributed in the two 
perpendicular directions specified. The squares of the displacements 
perpendicular to and parallel to the plane of the ray are proportional 
respectively to £<SE/<SA and |<5E/<5A . cos 2 <p ; and the square root of the 
sum of these may be taken as representing the average resultant displace- 
ment in the horizontal plane, namely, 
V^SK/SA^+cos 2 0)}. 
The values are tabulated in the sixth column of the table relating to the 
Secondary waves. 
In these estimates of the displacements the minimum at 65° or 70° 
is still in evidence, but much less apparent than in the corresponding 
measures of the energy. It is not surprising, then, that a comparison of 
the complex records of natural seismic disturbances as given by different 
types of seismometer at different distances from the epicentre should 
fail to indicate the presence of this minimum. Moreover, there is a further 
masking of a possible minimum in virtue of the decay of motion due to 
viscosity. 
The comparison of the horizontal displacements associated with the two 
types of waves brings out very clearly the tendency for the Primary- wave 
records, as obtained with the horizontal pendulum, to be smaller at the 
greater distances than the Secondary-wave records, each being assumed 
to start with the same energy. 
We should expect, therefore, that the advent of the Secondary waves 
would be more distinctly marked at the greater distances than they seem 
to be. At moderate arcual distances from the epicentre the Secondary 
waves frequently show a comparatively large disturbance, and their 
advent is clearly recognised. Why, then, at arcual distances greater than 
110° are the records so uncertain that what one observer calls the 
