ON THE THEORIES OF ELEVATION AND EARTHQUAKES. SJ 
sidcrabie, that small perumnent elevation may possibly be one of the effects 
of an earthquake. 
46. Vibrations from a Distttrbance of which the Sphere ts small, hut tm 
Intensity not small. Sea Wave of Eart}u]uak€s,^l( the intensity of the 
disturbance should be much greater than in the cases hitherto considered, 
while the space through which it extends is siuall, the inoveuicnts excited 
in the immediately aurroundiog rock*, but more especially in tb(^ situated 
vertically over the disturbance, will be greater than those to which the re¬ 
sults above given would be strictly applicable. Still the resulting waves 
would be propagated in nearly the same manner, and, at a sufficient distance, 
the vibrations would become small enough to render the results already 
enumerated as applicable to tbi* as to the former cases. In strictness wc 
should regm’d the original disturbance as extending to those limits within 
which the disturbance should be too great to be propagated accunling to 
the laws of propagation of stnall vibration*. The distinction however is 
perhaps scarcely worth much attention, in the applicalloo we arc now 
making of the theory of small vibratory motions to a case which can scarcely 
admit of any but somewhat rough approximations. • t r 
The (lificrcnce between this case and those considered in Section I. of 
Part II, consists in the horizontal extent of the disturbance. A superficial 
cleratiou will be here produced, hut it will be only nf small horizontal ex¬ 
teat compared with those produced in the other cases just referred to, and 
will not here call for further remark, unless it Ikj produced in the bod of the 
ocean. In this case, a sea wave will be generated of the nature of that 
already discussed (art..%}. This wave wUl diverge in all directions from 
the central points of the ilisturbcd portioD of the sea bottom. Let A, be the 
depth of the sea, h the lieigiit of the crest of the wave above the surface of 
the sea; then if hi be tnucli grea^' than A, the velocity with winch the 
wave will he propagated will = gh, nearly, and will therefore dojKind on 
the depth of the sea. If the depth be uniform, the velocity of projmption 
will be the same in all directions, and the front of the wave will form a 
circle whose centre will be the point from which the wave diveiges. After 
a certain time the point of the surface of the sea which was first clLsturbcd 
will come to i*est, while the wave will continue to diverge. It will then be 
hounded internallv by a circh* conepntrie with that which forms its outer 
boundar)', the space occupied by the wave being thus a circular annulus ox 
which both the outer ami inner radii arc constmitly increasing, wlnle their 
difference, or breadth of the wave, remains nearly tixe same. I ho height ot 
the crest of the wave will be nearly in proportion to the reciprocal of the 
square root of the space through which it has ilivorged. Ibis wave wi 
also aecompanied by a current, the velocity of which depends on e 
height of the crest (h) and depth of the sea (A,). It is generally much less 
than that with which the wave is propagated, especially in deep 
In the above description, the depth of the sea has ireeti considered uni¬ 
form. If the depth decrease the velocity of propagation will d<!CTOMe, or 
the converse; and consequently, if the wave diverge into parts of tie sea 
of different depths, its front will no longer preserve its circular ® 
rapidity with M-hich the wave will rise from its external boundary to tne 
awminit of its crest will deiwnd on the rapidity with wliieh the bottom ot 
the sea and the superincumbent water have been elevated from their un- 
dsturbed position. If the plcvati<m take place slowly, the distance 
the front of the wave and Hs crest may bo comparatively grea* ’ but i 
rievationhe rapid, the wave will assume the character of the tidal wave 
called a bore, and its crest will be near its extreme front boundarj*. In any 
