ON THE THEORIES OF ELEVATION AND EARTHQUAKES. 79 
for a reiy short time (as the blow of a liammer), both kituls of vibrations 
will, generally, be excited, and two corresponding waves of ilefinitc length 
will be propagated along the bar with velocities Vj and Vj respectively. 
The longitudinal vibrations will be propagated in the manner already men¬ 
tioned, and the transversal vibrations will be propagated exactly in a similar 
manner, except as regards the directions of the vibratory motions. Conse¬ 
quently, supposing the bar of indcfinlle length, tlm two waves at a certain 
distance from their common origin will become entirely separated from each 
other, and the vibrations excited in any proposed p.arlicle by the first wave 
will then be entirely completed before those excited by the second will be¬ 
gin. We sballfiiid a similar separation of the two waves iu tlie mure gene¬ 
ra] case to which we shall now proceed. 
89. PfojwgaHon of Vibrations through a solid Mass. —In fin* general 
to which we are now proceeding, we may conceive tiie disturbance ex¬ 
citing the vibrations to take place at any points in the interior or on the 
mrface of the mass; but for the greater dUtlnctness, 1 shall suppose it to 
take place in the interior, to act for a very short time (as an explosion in a 
tnine), and to be restricted as in the previous coses to a space small com¬ 
pared with that into which the vibrations afterwards <liverge. I shall also 
suppose the density and elasticity of the mass to be the same at every point. 
Ill case, as in the one immediately preceding, the original disturbance, 
udess it be of a vei'y particular kind, w ill produce two waves, each of which 
will diverge in a manner exactly similar to that iu which a spherical wave 
diver^ in a fluid as already described (art. 87). Their velocities of pro- 
potion (V, and V.) will be different, and therefoto they will become com¬ 
pletely separated from each other (ns in the preceding case of article 38) 
at a distance from their origin, depending ou V„ the difference between V, 
^ 5, and the breadth of tlie first wave. After this complete sujiaration 
has taken place, the direction in which a particle will vibrate In the first 
''iil coincide with a line passing tlirough that particle and the centre 
ui disturbance. These arc worww/vibrations; they will bo completed and 
the particle restored to rest before the second wave reaches it. The same 
particle will then commence its second vibration in a direction porpendicuiar 
tu the former,e. in some direction in a jdane perpendicular to tin: line 
through the proposed particle and the centre of disturbance*. Such vibra- 
hons are tangtnlml. \Ve shall hereafter see tlie importance of this differ- 
^ character in the two waves, provided instruments cau be obtained 
e sufficient sensibility and accuracy to detect the diatiiictiou between their 
ctoracieristic vibrations. 
the si-paratioii of the two waves lias been completely effected, one 
W overlap, or will ho partially superimposed upon the other. 
that sjiacc in which this superposition exists each particle will move 
nder the simultaneous influence of both the above kinds of vibratuin. The 
reauth of Uie waves will depend on the time during wliich the original dis- 
ante is coiifinuetl, so tiiat if this time be nut very sltort, tlu: breadths of 
too great to admit of their complete separation within the 
•unite of sensible vibration. 
Ine ratio of the intensitica of these two sets of vibrations may vary in 
^degree, since eiiher of them may altogether disn])pear with particular 
™ of the original disturbance. Generally they must coexist. 
P-H *'5. ®/ ^'•opaga/ioti of the two IVavts.^ln the practical appli- 
«non winch it is proposed to make of these theoretical deductions, it is 
I'ropauBtion du Mouvement dans les Milieux Elsstiqucs/ 
11 Institut, Tol. X, Also Annales de Chimie, vol. xliv. p. 423. 
