ON THE THEORIES OP ELEVATION' AND EARTHQUAKES. 85 
44. In the preceding calculations the mass through which the vibrations 
have been propagated has been considered homogeneous; but it will be 
easy to indicate the nature of the modification which will be introduced 
into the preceding results if wc suppose the wave to be propagated through 
masses of different degrees of elasticity, superimposed on each other. For 
I 
I 
the general explanation it will suffice to consider a single horizontal stratum 
resting on the mass in which the centre of disturbance is placed. Let H'H 
be the surface of the earth, and h'h, parallel to H'H the common surface of 
the upper and lower media. Let V denote the velocity of propagation in 
the lower medium, and V* that in the upper; and let //P be the direction in 
which the wave from O arrives at P alter refraction at The absolute 
direction of vibration will be changed by refVaction at p, as well as at P, 
but the direction of tlie horizontal projection of the normal vibnUions will 
not,be altered. Consequently the rule before given (art. 4S) for finding the 
point C will be equally applicable in the present case. 
If Pp produced meet CO produced in O', and CO'P= 6 '> e<iuation (a.) 
(art. 43 ^ becomes 
v='V’ sin 6'; 
and equation (j3.) will become 
CO'- 
«- 
where CPzsa. CO' being thus known, and Cc the thickness of 
sin 
stratum, cO' will be known, and since, by the law of refraction - 7 ^—y,, 
it will be easy to find 00', and thus to determine the position of 0. If A 
and 5' be not too large, a well-known formula in common optics gives as 
an approximation 
whence 
00'=Y--X.c0'. 
It would be easy to apply a similar calculation to any proposed more com¬ 
plicated case. 
If a wave proceed from a point 0 in a fluid mass, through the superin¬ 
cumbent solid crust, and then through the sea, the general course of the 
wave and successive positions of its front will be represented by the annexed 
Ji.', 
y 
