76 
REPORT— 1847. 
analogous to the above. It must be observed that these properties belong 
to the wave in its uninterrupted progress along the tube, and before it has 
been modified by reaching the extremity. We are not immediately con¬ 
cerned with the modification which will there take place. 
In the propagation of these waves of vibratory motion, the particles of 
fluid are necessarily cither condensed or rarefied, or they may be subject W 
alternate condensation and rarefaction during the period in which the wave 
is passing through them. 'J’hey may therefore be termed travet of coitdensa- 
tioH or rarefactio'n. All substances, gaseous, fluid or solid, have some 
gree of compressibility, and arc Ihcrefort! capable of transmitting more or 
less perfectly waves of this nature. If the tube AU, fur instance, were filled 
Avith water, a Avave of this kind might be propagated along it, having pro* 
perties exactly similar to those above staled for an aerial wave; but since 
the compressibility of water is so much less tlian that of air, the amplitudw 
of vibration Avill usually be much smaller. The velocity of propagation '« | 
also about four times as great in AA'ater as in air. It depends on the ratioof 
the elastic force of Avater to its density. 
36. Propagation of t’VnvoA' along the surface of Tfater in a mi/orm Canal, j 
—In the transmission of vibratory motion through wat<-r as above descriM. 
the tube has been supposed to bo completely filled with tlie fluid, so that no 
displacement of a particle from its place of rest could take place without 
condensation or rarefaction. If the fluid however exist in an open canal 
instead of u closed tube, it may transmit a wave of an entirely different cha* 
raeter. For the greater simplicity, suppose the canal to be of uniform dqtth | 
and width. Conceive a portion of the fluid occupying a part pj of the 
canal (fig. 11) to be disturbed, for example, by the sudden small elevation 
of the bottom of that part of the canal. The surface of the superincumbent 
fluid will be elevated in nearly the same degree, and being then left to itself 
Fig. 11. 
-.-.-, 2 . 
Avill attempt to restore the horizontality of the fluid surface in obedience to 
the law of gravity, and Avill thus generate two waves p'f and p,g,, which will 
be transmitted in oppo.site directions along the surface of the fluid. A wave 
of this kind will have the following properties, assuming the perfect fluidity 
of the fluid and the absence of friction along the sides of the canal. The 
depth is also supposerl much less than the length of the wave. 
stanV^ *cDgth (/) of the wave (not necessarily equal to pg) will be con- 
1 propagation Avill depend on the square root of the 
depth of the canal nearly, that depth beiug much greater than the height 
of the crest of the wave*. ® 
(3.) Particles ol the fluid situated in the same vertical section perpendi¬ 
cular to the axis of the tube, will Jmve the same motion at the same instant 
^very such section of particles will be carried in the direction of propf; 
gatioii through a certain space, during the passage of the wave, and will 
then be left at rest. Consctpicntly a wave of this kind will be attended by 
actirrenij the velocity of Avhich will depend on the height of the crest of the 
wave and the depth of the canal. 
(4.) The elevation of the bottombeing sudden, as we have supposed, 
• See Mr. Scott Ruasell’s Experiments on Waves. 
