ON THE THEORIES OF ELEVATION AND EARTHQUAKES. 77 
the front of the wave will be steep, the descent from the crest to the pos¬ 
terior boundary being a gradual slope. 
The total diference in the characters of these two waves M’ill be at once 
apparent. In the first case the waves depend entirely on the compressibility 
and clastic force of the fluid, the motions being independent of gnivitation ; 
while in the latter the motion depends on graviUitiou, and is independent 
of the compressibility and elasticity. In ordinaiy cases the velocity of pro¬ 
pagation is very much greater in the former than in the latter kind of waves. 
In the larger disturbance which is necessary to produce the superficial wave 
of sensible magnitude, the disturbing force does not necessarily act with 
sufficient intensity at any instant to produce much coiuprewiun, or therefore 
to cause a vibratory wave of the first kind of consideraljle intensity. When 
produced simultaneously, they will, in ordinary cases, separate very rapidly, 
on account of the great difiereuce between the velocities with wliich they 
arc propagated. 
37. tVares propagated Sn Fluids in all directions from a centre .—The 
wares here contemplated 5ro what I liave termed waves of compression or 
dilatation. Let us suppose the original disturbance to take place in the 
interior of a fluid mass, perfectly or imperfectly elastic, the disturbance being 
restricted within a space which is small compared with that into which the 
wave subsequently diverges. The disturbing force being assmned, as in the 
preceding cases, to act only instantaneously, or for a very small space of 
time, the vibratory motion will be rapidly communicated to the neighbour¬ 
ing particles, leaving those originally disturbed at perfect rest. The space 
wthin which the vibratory motion will exist at any instant (i. c. the wave 
itself), will be comprised between two concentric spliero.s whose common 
centre is the centre of disturbanco. At a sufficient distance from the origin 
the vibratory motion will be in a certain degree independent of the particular 
form of the original disturbance, and the wave will have the following pro¬ 
perties. 
(1.) The breadth (V) of the wave (which corresponds to what I have 
termed its length when propagated along a tube), measured by the differ- 
^ce of the radii of its exterior and interior surfaces, will depend on the 
time during which the cause exciting the vibrations continues to act It 
will remain constant during the progression of the wave. 
(2.) velocity (V) with which the wave will be propagated along any 
•^ius will be constant 
(3.) The time during which each particle will vibrate will =y* 
(4’-) The amplitude of the vibrations will decrease as the space through 
which the wave has expanded increases, being inversely as the distance of 
^^^^'hrating particle from the centre of disturbance, when that distance is 
sumcicmly great 
(5.) Ihe direction in which a particle vibrates approximates more nearly 
to a line joining the particle and centre of disturbanco, as the particle is fa¬ 
ther removed from the centre; and foraparticlewlio.se distance is sum- 
ciently great, the direction of vibration sensibly coincides with that line . 
It is by waves of this kind that sound is propagated through the atmo¬ 
sphere or through water, the velocity in the former case being nearly 1200, 
and m the latter about iSOO feet per aueond. 
• Poison’s memoir,‘Sur laTli^oriedu Son,’ Journal Polvtcchnique, Cahict 14. Also a 
“““‘Of* ‘ Sut le Mouvement de deux Fluidea superposccs, in the M6. 
moires del’Institut,’ vol.s. 
