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ON WAVES. 425 
Bee ae sil 
2 n+2 
1lTn+l1 1 
andv =a 5 tie) 
Ify=me 
sea eae 
ae 
iy = me 
Aaa 
a/ © 2, &e. 
Hence in the rectangular channel the velocity being that of 
gravity due to half the depth. 
In the sloping or triangular channel the velocity is that due 
to one-third of the greatest depth. In a parabolic channel the 
velocity is that due to three-eighths or three-tenths of the 
greatest depth according as the channel is convex or concave. 
From the identity of this formula with that for the centre of 
gravity, it appears that the velocity of the great primary wave 
of translation of a fluid is that due to gravity acting through a 
height equal to the depth of the centre of gravity of the trans- 
verse section of the channel below the surface of the fluid. 
7. The height of a wave may be indefinitely increased by pro- 
pagation into a channel which becomes narrower in the form of 
a wedge, the increased height being nearly in the inverse ratio 
of the square root of the breadth. 
8. If waves be propagated in a channel whose depth diminishes 
uniformly, the waves will break when their height above the sur- 
face of the level fluid becomes equal to the depth at the bottom 
below the surface. | 
9. The great waves of translation are reflected from surfaces 
at right angles to the direction of their motion without suffering 
any change but that of direction. 
10. The great primary waves of translation cross each other 
without change of any kind in the same manner as the small 
oscillations produced on the surface of a pool by a falling stone. 
11. The WAVEs OF THE SEA are not of the first order—they 
belong to the second or oscillatory order of waves—they are 
partial displacements at the surface which do not extend to con- 
siderable depths, and are therefore totally different in character 
from the great waves of translation, in which the motion of dis- 
placement of the particles is uniform to the greatest depth. The 
displacement of the particles of the fluid in the waves of the 
‘seais greatest at the surface and diminishes rapidly. There 
