352 REPORT — 1844. 



In one respect alone does the origin of the wave affect its history. Its 

 volume depends on the quantity of power employed in its genesis, and on 

 the distance through which it has travelled. A great and a little wave at 

 equal distances from the source of disturbance, arise from great or little 

 causes, but it is impossible to distinguish between a small wave which has 

 travelled a short distance, and one which, originally high, has traversed a 

 long space. 



This however does not apply to compound waves of the first order, here- 

 after to be examined. 



Form of Channel. — Its Effect on the Wave of Translation. — The conditions 

 which affect the phsenomena of the wave of translation are therefore to be 

 looked for in its actual circumstances at the time of observation rather than 

 in its history. The form and magnitude of the channel are among the most 

 important of these circumstances. Thus a change in depth of channel imme- 

 diately becomes indicated to the eye of the observer by the retardation of the 

 wave, which begins to move with the same velocity as if the channel were 

 everywhere of the diminished depth, that is, with the velocity due to the depth. 

 Thus in a rectangular channel 4"| feet deep, the wave moves with a velocity 

 of 12 feet per second, and if the channel become shallower, so as to have only 

 2 feet depth, the change of depth is indicated by the velocity of the wave, 

 which is observed now to move only with the velocity of 8 feet per second ; 

 but if the channel again change and become 8 feet deep, the wave indicates 

 the change by suddenly changing to a velocity of 16 feet per second. 



Length of Wave an Index of Depth. — In like manner, a wave which in water 

 4 feet deep is about 8 yards long, shortens on coming to a depth of 2 feet to 

 a length of 4 yards, and extends itself to 16 yards long on getting into a depth 

 of 8 feet. This extension of length is attended with a diminution of height, 

 and the diminution of length with an increase of height of the wave, so that 

 the change of length and height attend and indicate changes of depth. 



In a rectangular channel whose depth gradually slopes until it becomes 

 nothing, like the beach of a sea, these phsenomena are very distinctly visible ; 

 the wave is first retarded by the diminution of depth, shortens and increases 

 in height, and finally breaks when its height approaches to equality with the 

 depth of the water. The limit of height of a wave of the first order is there- 

 fore a height above the bottom of the channel equal to double the depth of 

 the water in repose. If we reckon the velocity of transmission as that due to 

 half the total depth, and the velocity of translation as that due to the height 

 of the wave, it is manifest that when the height is equal to the depth these 

 two are equal, but that if the height were greater than this, the velocity of 

 individual particles at the crest of the wave would exceed the velocity of the 

 wave form ; here accordingly the wave ceases, the particles in the ridge of 

 the wave pass forward out of the wave, fall over, and the wave becomes a 

 surge or broken foam, a disintegrated heap of water particles, having lost 

 all continuity. 



In like manner does the gradual narrowing of the channel affect the form 

 and velocity of the wave, but its effects are by no means so striking as where 

 the depth is diminished. The narrowing of the channel increases the height 

 of the wave, and the effect of this is most apparent when the height is consi- 

 derable in proportion to the depth ; the velocity of the wave increases in pro- 

 portion as the increase of height of the wave increases the total depth ; but 

 with this increase of depth, the length of the wave also increases rapidly, and 

 it does not break so early as in the case of the shallowing of the water. Its 

 phsenomena are only visibly affected to the extent in which a change of 

 depth is produced in the channel, by the volume of water added to the channel 

 taking the velocity and form peculiar to that increased depth. 



