102’ +4™5 REPORT—1858. 
Let BA=a, the depth of origin ; 
BC=r, the radius where the horizontal force is a maximum 
AC=the normal due to this radius. 
The angle Cde= BAC=0. 
Then the force at C in the direction AC is 
- -; and that in the direc- 
+7" 
a 
tion of the horizon is sin @ x ———; and as 
a+r 
ind r 
ht 
Ver 
VETP 
2 2 —— 
Cen fe aaa 
we have + 1 iE ie 
1 r rT f 
XS Sg a MM 
and +r Ve+r (a?+7°)? 
3 “ 
Differentiating, (a?+7r°)? xdr—3(a*+7°)? x 2r°=0. 
e+r=3r? 
V2. 2 
The angle CAC’! is therefore very nearly 70° 31! 43", which is the angle 
of the cone whiose base in the horizontal plane limits the zone of maximum 
disturbance; and as the angles at B are right, the angle of emergence 
BCA=54° 44! 9", and the sides of the triangle, BC : BA: AC, are to each 
other in the ratios of at x 
1:/72: V3. 
Hence we arrive at the very simple practical rule. 
Having found the coseismal zone of maximum disturbance by observation, 
or three points in it, and the centre of the circle passing through them, the 
depth below the surface, of the origin or centre of impulse, will be the dia- 
gonal of the square whose side is equal to the radius of the given circle. 
Within certain approximate limits, then, the application of this rule is 
capable of giving some information upon that great object of research, to 
which, above all others, seismological investigation points, namely, the depth 
beneath our surface from which such impulses reach us, and, by consequence, 
that at which active volcanic forces are in operation within our planet. 
This method can scarcely be applied in very mountainous regions, unless — 
both mountain-formations and seismic energy be developed upon a grand 
scale, as in Mexico and SouthAmerica ; and in every case the observer will 
find himself encumbered and perplexed by the interference of many minor 
circumstances of disturbance to mask and render difficult his observations. 
These, however, should not prevent our bearing the method in mind when-— 
ever favourable conditions present themselves for its use. 
In the present state of the theory of wave-movements in elastic solids, it 
cannot be said to be experimentally certain, that the energy of the wave, in 
the normal, does diminish with the square of the distance. Another view of 
the primary conditions of its motion would make it diminish directly as the 
distance, in which case it may be proved that the angle CAC’ of the 
coseismal cone of maximum disturbance will be 90° and constant, and hence 
