ON THE THEORIES OF ELEVATION AND EARTHQUAKES. 81 
it will be necessary to bear in mind that the coefficient K of cubical expan¬ 
sion must be determined as well as k, the coefficient of linear expansion. 
Both K and k are essentially positive quantities, and therefore Vi is neces¬ 
sarily greater than Vj, as has been already stated with reference to the pro¬ 
pagation of normal and transverse vibrations along a solid bar. 
Poisson, in investigating the vibratory motions of elastic bodies, according 
to his ^eory of molecular action, obtained didbrential equations of motion, 
which involve only one constant, and with which the equations above given 
become identical, if we make B=A. This would likewise give Vj=i. 
r ... ^ 
in any practical application, however, of our theoretical conclusion, it is not 
dwirable, as I have already intimated, to relv upon this imrnprical relation 
between V, and Vj, deduced as it is from a theory wliich cannot yet be re¬ 
garded as fully sanctioned by experiment. 
Rejkxion and Beffaction of a Wave .—In the cases hitherto considered 
w spherical waves, the direction of a wave at any point may be delined by 
the radius of the outer or inner surface of the wave tlu-ough that point. In 
. ^ cases in which the wave is not spherical, Its direction at any point of 
|ts front may be defineil, in all cases in which we are here concerued, by a 
me through the proposed point and perpendicular to the front, i.e. by a 
normal to the front. Any such line will continue to be a normal to the 
tront of the wave in its consecu- p. ..« 
the positions, when the medium 
through which the wave is pro¬ 
pagated is one in which the den¬ 
sity is uniform, and the elasticity 
the same at every point and in 
every direction. Consequently 
the vibrations may be said to be 
popagated through such media 
m straight lines. When the 
wave arrives at the common 
of two gaseous or fluid 
®edia in which the velocities 
O' prop^tion are different, a 
Jingle wave will be reflected 
***01 into tlie first medium, and 
another will be transmitted into 
t^ ^ond one. Let APB (fig. 
t ) be the common surface of 
•e two media, and let OP be the direction, os above defined, of a wave 
jr^l'^'^ted through the lower medium with a velocity V. Let PQ' be 
• °'J®otion of the reflected wave, and PQ that of the wave transmitted 
loi* medium, where the velocity of propagation is V'. Also 
be perpendicular to AB. Then shall we have Q'PN=OPN, 
^ ‘^'rection of the refracted wave will turn 
from or towards PM, according as V' is greater or less than V. Tliese are 
^be laws of reflexion and refraction of common light. 
V point from which the wove diverges, if the point of incidence 
eto the right of P, the direction of the refracted wave will approximate 
at ^ surface of junction, and if the incidence take place 
I84V 'I'staiice to the right, as at P,. the perpendicular to the re- 
