ON THE THEORIES OP ELEVATION AND EARTHQUAKES, 83 
with the horizoota! direction required*. Tins apparent ambiguity however 
will be removed in all cases in which the observed direction of vibration is 
that of the particles at the^r^^ instant of tlieir motion ; for it lias been shown 
(art 4'0) that the velocity (Vj) of propagation for the normal vibrations is 
greater than diat for the tangentim vibrations (Vj), and consequently tlie 
ooroial vibrations will always be those which arrive first at any point of the 
mass, and fay which therefore every particle of it will be affected at the first 
instant of its motion. In many cases also the approximate horizontal di¬ 
rection of the wave, as known from other circumstances, may serve to re¬ 
move the ambiguity above-mentioned. 
43. Portion of the Centre of Disturbance .—^Let O (fig. 13) be the centre 
o 
of disturbance; OC a vertical line meeting the surface II'II in C; P, P' two 
points on the earth’s surface, situated on different linos through C. The 
diredions of the horizontal projections of tho nortnal vihratiom will deter¬ 
mine the directions of PC and P'C, whose intersection will determine the 
^ raanifestly desirable tlmt, for this particular purpose, the 
should be nearly a right angle. 
Todeterraiue the aptiarent horizontal velocity of the wave at P, suppose 
so situated that CP' is not much greater than CP. J-.et tho time of the 
niM instant of the shock at each of the places P, P' be observed. Then the 
ifierence of the distances CP, CP' divided by the difference of tlic ob- 
^rvert times of the two shocks, will give the mean velocity with which the 
ave will pass from P through a distance equal to the dilFcronce between 
and CP. The velocity thus iktormiacd (as will apjibar by the next 
I'aragraph) will he somewhat loss than tho horizontal velocity at P, but will 
*PP'’®**™^tely equal to it. Practically, it is desirable that the angle PCP' 
® d not be large for the particular purpose here considered. 
Lei r be tlie horizontal velocity at P, COP=d, and V the velocity of pro- 
PH'Wiou <)f tl„, vriive witbiQ i|,e earth. Take p a point indefinitely near to 
in line CP produced. Draw IV perpendicular to OP; then wliile the 
f,«!f npropagated from s to p, it will be apparently propagated 
iQ P top, and we shall have 
V 
V 
V=t>.8in $ .(*•) 
Hence the apparent horizontal velocity of the wave is much greater than the 
of vibration will not be the same at i/ie surface as in the interior 
I out tlie direction of its horizontal projection will not be Stored. 
G 2 
