ox WAVES. 325 



These examples serve to convey an accurate idea of the longevity of a 

 wave of the first order. And this longevity ap])ears to increase with the 

 depth and the breadth of the channel, and with the height of the wave crest. 

 Degradation of the Ware of the First Order. — In the progress of a wave 

 of the first order, it is observed that its height diminishes with the length of 

 its path ; the velocity also diminishes with the diminution of height, though 

 very slowly. This degradation of height is observed to go on more rapidly in 

 proportion as the channel is narrow, shallow or irregular, and rough on the 

 sides, and is diminished according as the channel is made smooth and regular 

 in its form, or deep and wide. It is to be attributed to the imperfect fluidity 

 of the water in some degree, but also to the adhesion of water to the sides. 

 The particles of fluid near the sides and bottom are retarded in their motions, 

 and the transmission takes place more slowly among them. The wave passes 

 on, leaving in these particles a small quantity of the motion it had communi- 

 cated, and of its force and volume, and in consequence of this there exists 

 along the whole channel, over which the wave has passed, a residual motion 

 or continuous residual wave, very small in amount, but still appreciable by ac- 

 curate means of observation. The volume of the wave is tlius diffused over 

 a large extent along its path, where finally it has deposited the whole of its 

 volume, and so disappears. This degradation is therefore the means by which 

 the motion of a wave in an indefinite channel is gradually and slowly termi- 

 nated. In the history of a solitary wave of the first order, the progress of this 

 degradation is to be observed from the examination of Table II. column B, 

 which gives the height of the wave as observed at every 40 feet along its path. 

 In the first 200 feet this diminution amounts to about i of the height at the 

 commencement. At the end of the second 200 feet, the height is diminished 

 by ^ of the height at the commencement of that space. During the third 

 space of 200 feet the degradation produced is nearly | of the height of the 

 wave; this appears to be the most rapid degradation, and in the next space 

 of 200 feet it is little more than i ; in the next, less than a third of the height 

 at the beginning of that space. These successive heights are given graphi- 

 cally in Plate XL VIII. fig. 7. & o r 



The Velocity of Transmission of the Wave of the First Order. — The history 

 of a single wave has suflSced to show us that the velocity with which its crest 

 is transmitted along the channel is nearly that which a heavy body will 

 acquire falling freely through a height equal to half the depth of the fluid. 

 This is a very simjile and important character in the pheenomena of this wave, 

 by which, when the depth of the channel is known, we may at once predict 

 approximately the velocity of the wave of translation. The following are 

 approximate numbers deduced from this conclusion, and which I find it con- 

 venient to recollect. 



In a channel whose depth is 2| inches, the velocity of the wave is 2|- feet 

 per second. 



In a channel whose depth is 15 feet, the velocity of the wave is 15 miles an 

 hour. 



In a channel whose depth is 90 fathoms, the velocity of the wave is 90 miles 

 an hour. 



These numbers are, however, only first approximations, for it is to be ob- 

 served in reference to wave. Table II., that the wave, when its height is con- 

 siderable, moves with greater velocity than when it is small. These numbers 

 become accurate, if in the depth, the height of the wave be included. 



The Height of the Wave oftJie First Order, an element in its velocity The 



height of the wave appears to enter as an element in its velocity, and to cause 

 It to deviate from the simple formula A. Thus the velocity of the wave only 



